LEO-II---2.3.1.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SWV239-1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n007.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 10:56:28 AM UTC 2026

% Result   : Unsatisfiable 181.38s 36.50s
% Output   : CNFRefutation 181.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      : 1401
% Syntax   : Number of formulae    : 8888 (5116 unt;   0 typ;   0 def)
%            Number of atoms       : 38044 (12127 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives : 65709 (7283   ~;8740   |;   0   &;49686   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  221 ( 218 usr;  24 con; 0-6 aty)
%            Number of variables   : 15643 (   0   ^;15643   !;   0   ?;15643   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_0,type,
    c_0: $i ).

thf(tp_c_1,type,
    c_1: $i ).

thf(tp_c_Datatype_Oo2s,type,
    c_Datatype_Oo2s: $i > $i > $i ).

thf(tp_c_Datatype_Ooption_ONone,type,
    c_Datatype_Ooption_ONone: $i ).

thf(tp_c_Datatype_Ooption_OSome,type,
    c_Datatype_Ooption_OSome: $i > $i > $i ).

thf(tp_c_Datatype__Universe_OAtom,type,
    c_Datatype__Universe_OAtom: $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_OIn0,type,
    c_Datatype__Universe_OIn0: $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_OIn1,type,
    c_Datatype__Universe_OIn1: $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_OLeaf,type,
    c_Datatype__Universe_OLeaf: $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_ONumb,type,
    c_Datatype__Universe_ONumb: $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_OScons,type,
    c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_Odprod,type,
    c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_Odsum,type,
    c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_Ouprod,type,
    c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).

thf(tp_c_Datatype__Universe_Ousum,type,
    c_Datatype__Universe_Ousum: $i > $i > $i > $i > $i ).

thf(tp_c_Divides_Oop_Advd,type,
    c_Divides_Oop_Advd: $i > $i > $i > $o ).

thf(tp_c_Divides_Oop_Amod,type,
    c_Divides_Oop_Amod: $i > $i > $i > $i ).

thf(tp_c_Equiv__Relations_Oquotient,type,
    c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).

thf(tp_c_Extraction_Osumbool_OLeft,type,
    c_Extraction_Osumbool_OLeft: $i ).

thf(tp_c_Extraction_Osumbool_ORight,type,
    c_Extraction_Osumbool_ORight: $i ).

thf(tp_c_Finite__Set_OFinites,type,
    c_Finite__Set_OFinites: $i ).

thf(tp_c_GCD_Ogcd,type,
    c_GCD_Ogcd: $i > $i ).

thf(tp_c_Infinite__Set_Oatmost__one,type,
    c_Infinite__Set_Oatmost__one: $i > $i > $o ).

thf(tp_c_IntDef_Oint,type,
    c_IntDef_Oint: $i > $i ).

thf(tp_c_Inter,type,
    c_Inter: $i > $i > $i ).

thf(tp_c_List_Ochar_OChar,type,
    c_List_Ochar_OChar: $i > $i > $i ).

thf(tp_c_List_Odistinct,type,
    c_List_Odistinct: $i > $i > $o ).

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_Olist_OCons,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(tp_c_List_Olist_ONil,type,
    c_List_Olist_ONil: $i ).

thf(tp_c_List_Olistrel,type,
    c_List_Olistrel: $i > $i > $i ).

thf(tp_c_List_Olists,type,
    c_List_Olists: $i > $i > $i ).

thf(tp_c_List_Oremdups,type,
    c_List_Oremdups: $i > $i > $i ).

thf(tp_c_List_Orev,type,
    c_List_Orev: $i > $i > $i ).

thf(tp_c_List_Oset,type,
    c_List_Oset: $i > $i > $i ).

thf(tp_c_Main_ODomainE__1,type,
    c_Main_ODomainE__1: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OIdE__1,type,
    c_Main_OIdE__1: $i > $i > $i ).

thf(tp_c_Main_OImageE__1,type,
    c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OInterI__1,type,
    c_Main_OInterI__1: $i > $i > $i > $i ).

thf(tp_c_Main_OPlusE__1,type,
    c_Main_OPlusE__1: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OPlusE__2,type,
    c_Main_OPlusE__2: $i > $i > $i > $i > $i ).

thf(tp_c_Main_ORangeE__1,type,
    c_Main_ORangeE__1: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OUnionE__1,type,
    c_Main_OUnionE__1: $i > $i > $i > $i ).

thf(tp_c_Main_OconverseE__1,type,
    c_Main_OconverseE__1: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OconverseE__2,type,
    c_Main_OconverseE__2: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdiagE__1,type,
    c_Main_OdiagE__1: $i > $i > $i > $i ).

thf(tp_c_Main_OdprodE__1,type,
    c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdprodE__2,type,
    c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdprodE__3,type,
    c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdprodE__4,type,
    c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdsumE__1,type,
    c_Main_OdsumE__1: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdsumE__2,type,
    c_Main_OdsumE__2: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdsumE__3,type,
    c_Main_OdsumE__3: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OdsumE__4,type,
    c_Main_OdsumE__4: $i > $i > $i > $i > $i ).

thf(tp_c_Main_Ofinite__Union__1,type,
    c_Main_Ofinite__Union__1: $i > $i > $i ).

thf(tp_c_Main_Oin__listsI__1,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $i ).

thf(tp_c_Main_Olistrel__Cons1__1,type,
    c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_Olistrel__Cons1__2,type,
    c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_Olistrel__Cons2__1,type,
    c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_Olistrel__Cons2__2,type,
    c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_Omod__eq__0D__dest__1,type,
    c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).

thf(tp_c_Main_Onot__None__eq__iff1__1,type,
    c_Main_Onot__None__eq__iff1__1: $i > $i > $i ).

thf(tp_c_Main_Onot__Some__eq__iff1__1,type,
    c_Main_Onot__Some__eq__iff1__1: $i > $i > $i ).

thf(tp_c_Main_Orel__compE__1,type,
    c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_Orel__compE__2,type,
    c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_Orel__compE__3,type,
    c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OsubsetI__1,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(tp_c_Main_OuprodE__1,type,
    c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OuprodE__2,type,
    c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Main_OusumE__1,type,
    c_Main_OusumE__1: $i > $i > $i > $i > $i ).

thf(tp_c_Main_OusumE__2,type,
    c_Main_OusumE__2: $i > $i > $i > $i > $i ).

thf(tp_c_Main_Ozmod__eq__0D__dest__1,type,
    c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).

thf(tp_c_Message_Oagent_OFriend,type,
    c_Message_Oagent_OFriend: $i > $i ).

thf(tp_c_Message_Oagent_OServer,type,
    c_Message_Oagent_OServer: $i ).

thf(tp_c_Message_Oagent_OSpy,type,
    c_Message_Oagent_OSpy: $i ).

thf(tp_c_Message_Oanalz,type,
    c_Message_Oanalz: $i > $i ).

thf(tp_c_Message_OinvKey,type,
    c_Message_OinvKey: $i > $i ).

thf(tp_c_Message_Omsg_OAgent,type,
    c_Message_Omsg_OAgent: $i > $i ).

thf(tp_c_Message_Omsg_OCrypt,type,
    c_Message_Omsg_OCrypt: $i > $i > $i ).

thf(tp_c_Message_Omsg_OHash,type,
    c_Message_Omsg_OHash: $i > $i ).

thf(tp_c_Message_Omsg_OKey,type,
    c_Message_Omsg_OKey: $i > $i ).

thf(tp_c_Message_Omsg_OMPair,type,
    c_Message_Omsg_OMPair: $i > $i > $i ).

thf(tp_c_Message_Omsg_ONonce,type,
    c_Message_Omsg_ONonce: $i > $i ).

thf(tp_c_Message_Omsg_ONumber,type,
    c_Message_Omsg_ONumber: $i > $i ).

thf(tp_c_Message_Oparts,type,
    c_Message_Oparts: $i > $i ).

thf(tp_c_Message_Osynth,type,
    c_Message_Osynth: $i > $i ).

thf(tp_c_Nat_Osize,type,
    c_Nat_Osize: $i > $i > $i ).

thf(tp_c_Numeral_Obit_OB0,type,
    c_Numeral_Obit_OB0: $i ).

thf(tp_c_Numeral_Obit_OB1,type,
    c_Numeral_Obit_OB1: $i ).

thf(tp_c_Pair,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(tp_c_Pow,type,
    c_Pow: $i > $i > $i ).

thf(tp_c_Relation_ODomain,type,
    c_Relation_ODomain: $i > $i > $i > $i ).

thf(tp_c_Relation_OId,type,
    c_Relation_OId: $i ).

thf(tp_c_Relation_OImage,type,
    c_Relation_OImage: $i > $i > $i > $i > $i ).

thf(tp_c_Relation_ORange,type,
    c_Relation_ORange: $i > $i > $i > $i ).

thf(tp_c_Relation_Oconverse,type,
    c_Relation_Oconverse: $i > $i > $i > $i ).

thf(tp_c_Relation_Odiag,type,
    c_Relation_Odiag: $i > $i > $i ).

thf(tp_c_Relation_Orel__comp,type,
    c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).

thf(tp_c_Relation_Otrans,type,
    c_Relation_Otrans: $i > $i > $o ).

thf(tp_c_SetInterval_OatLeast,type,
    c_SetInterval_OatLeast: $i > $i > $i ).

thf(tp_c_SetInterval_OatLeastAtMost,type,
    c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).

thf(tp_c_SetInterval_OatLeastLessThan,type,
    c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).

thf(tp_c_SetInterval_OatMost,type,
    c_SetInterval_OatMost: $i > $i > $i ).

thf(tp_c_SetInterval_OgreaterThan,type,
    c_SetInterval_OgreaterThan: $i > $i > $i ).

thf(tp_c_SetInterval_OgreaterThanAtMost,type,
    c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).

thf(tp_c_SetInterval_OgreaterThanLessThan,type,
    c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).

thf(tp_c_SetInterval_OlessThan,type,
    c_SetInterval_OlessThan: $i > $i > $i ).

thf(tp_c_Suc,type,
    c_Suc: $i > $i ).

thf(tp_c_Sum__Type_OInl,type,
    c_Sum__Type_OInl: $i > $i > $i > $i ).

thf(tp_c_Sum__Type_OInr,type,
    c_Sum__Type_OInr: $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_UNIV,type,
    c_UNIV: $i ).

thf(tp_c_Union,type,
    c_Union: $i > $i > $i ).

thf(tp_c_Wellfounded__Recursion_Oacyclic,type,
    c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).

thf(tp_c_Wellfounded__Recursion_Owf,type,
    c_Wellfounded__Recursion_Owf: $i > $i > $o ).

thf(tp_c_Wellfounded__Relations_Oless__than,type,
    c_Wellfounded__Relations_Oless__than: $i ).

thf(tp_c_Wellfounded__Relations_Olex__prod,type,
    c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).

thf(tp_c_append,type,
    c_append: $i > $i > $i > $i ).

thf(tp_c_emptyset,type,
    c_emptyset: $i ).

thf(tp_c_in,type,
    c_in: $i > $i > $i > $o ).

thf(tp_c_insert,type,
    c_insert: $i > $i > $i > $i ).

thf(tp_c_inter,type,
    c_inter: $i > $i > $i > $i ).

thf(tp_c_less,type,
    c_less: $i > $i > $i > $o ).

thf(tp_c_lessequals,type,
    c_lessequals: $i > $i > $i > $o ).

thf(tp_c_minus,type,
    c_minus: $i > $i > $i > $i ).

thf(tp_c_plus,type,
    c_plus: $i > $i > $i > $i ).

thf(tp_c_times,type,
    c_times: $i > $i > $i > $i ).

thf(tp_c_uminus,type,
    c_uminus: $i > $i > $i ).

thf(tp_c_union,type,
    c_union: $i > $i > $i > $i ).

thf(tp_class_Divides_Odiv,type,
    class_Divides_Odiv: $i > $o ).

thf(tp_class_Finite__Set_Ofinite,type,
    class_Finite__Set_Ofinite: $i > $o ).

thf(tp_class_HOL_Oinverse,type,
    class_HOL_Oinverse: $i > $o ).

thf(tp_class_HOL_Ominus,type,
    class_HOL_Ominus: $i > $o ).

thf(tp_class_HOL_Oone,type,
    class_HOL_Oone: $i > $o ).

thf(tp_class_HOL_Oplus,type,
    class_HOL_Oplus: $i > $o ).

thf(tp_class_HOL_Otimes,type,
    class_HOL_Otimes: $i > $o ).

thf(tp_class_HOL_Ozero,type,
    class_HOL_Ozero: $i > $o ).

thf(tp_class_LOrder_Ojoin__semilorder,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

thf(tp_class_LOrder_Olorder,type,
    class_LOrder_Olorder: $i > $o ).

thf(tp_class_LOrder_Omeet__semilorder,type,
    class_LOrder_Omeet__semilorder: $i > $o ).

thf(tp_class_Nat_Opower,type,
    class_Nat_Opower: $i > $o ).

thf(tp_class_Numeral_Onumber,type,
    class_Numeral_Onumber: $i > $o ).

thf(tp_class_Numeral_Onumber__ring,type,
    class_Numeral_Onumber__ring: $i > $o ).

thf(tp_class_OrderedGroup_Oab__group__add,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

thf(tp_class_OrderedGroup_Oab__semigroup__mult,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

thf(tp_class_OrderedGroup_Ocomm__monoid__mult,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

thf(tp_class_OrderedGroup_Olordered__ab__group,type,
    class_OrderedGroup_Olordered__ab__group: $i > $o ).

thf(tp_class_OrderedGroup_Olordered__ab__group__abs,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).

thf(tp_class_OrderedGroup_Olordered__ab__group__join,type,
    class_OrderedGroup_Olordered__ab__group__join: $i > $o ).

thf(tp_class_OrderedGroup_Olordered__ab__group__meet,type,
    class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).

thf(tp_class_OrderedGroup_Omonoid__mult,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

thf(tp_class_OrderedGroup_Oordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).

thf(tp_class_OrderedGroup_Opordered__ab__group__add,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

thf(tp_class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

thf(tp_class_OrderedGroup_Osemigroup__add,type,
    class_OrderedGroup_Osemigroup__add: $i > $o ).

thf(tp_class_OrderedGroup_Osemigroup__mult,type,
    class_OrderedGroup_Osemigroup__mult: $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_Parity_Oeven__odd,type,
    class_Parity_Oeven__odd: $i > $o ).

thf(tp_class_Power_Orecpower,type,
    class_Power_Orecpower: $i > $o ).

thf(tp_class_Ring__and__Field_Oaxclass__0__neq__1,type,
    class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).

thf(tp_class_Ring__and__Field_Oaxclass__abs__if,type,
    class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).

thf(tp_class_Ring__and__Field_Oaxclass__no__zero__divisors,type,
    class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).

thf(tp_class_Ring__and__Field_Ocomm__ring,type,
    class_Ring__and__Field_Ocomm__ring: $i > $o ).

thf(tp_class_Ring__and__Field_Ocomm__ring__1,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

thf(tp_class_Ring__and__Field_Ocomm__semiring,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

thf(tp_class_Ring__and__Field_Ocomm__semiring__0,type,
    class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).

thf(tp_class_Ring__and__Field_Ocomm__semiring__0__cancel,type,
    class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).

thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

thf(tp_class_Ring__and__Field_Ocomm__semiring__1__cancel,type,
    class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).

thf(tp_class_Ring__and__Field_Odivision__by__zero,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

thf(tp_class_Ring__and__Field_Ofield,type,
    class_Ring__and__Field_Ofield: $i > $o ).

thf(tp_class_Ring__and__Field_Oidom,type,
    class_Ring__and__Field_Oidom: $i > $o ).

thf(tp_class_Ring__and__Field_Olordered__ring,type,
    class_Ring__and__Field_Olordered__ring: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__comm__semiring__strict,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__field,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__idom,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__ring__strict,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__semidom,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

thf(tp_class_Ring__and__Field_Oordered__semiring__strict,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

thf(tp_class_Ring__and__Field_Opordered__cancel__comm__semiring,type,
    class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).

thf(tp_class_Ring__and__Field_Opordered__cancel__semiring,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

thf(tp_class_Ring__and__Field_Opordered__comm__ring,type,
    class_Ring__and__Field_Opordered__comm__ring: $i > $o ).

thf(tp_class_Ring__and__Field_Opordered__comm__semiring,type,
    class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).

thf(tp_class_Ring__and__Field_Opordered__ring,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

thf(tp_class_Ring__and__Field_Opordered__semiring,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

thf(tp_class_Ring__and__Field_Oring,type,
    class_Ring__and__Field_Oring: $i > $o ).

thf(tp_class_Ring__and__Field_Oring__1,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

thf(tp_class_Ring__and__Field_Osemiring,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

thf(tp_class_Ring__and__Field_Osemiring__0,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

thf(tp_class_Ring__and__Field_Osemiring__0__cancel,type,
    class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).

thf(tp_class_Ring__and__Field_Osemiring__1,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

thf(tp_class_Ring__and__Field_Osemiring__1__cancel,type,
    class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).

thf(tp_class_Wellfounded__Recursion_Owellorder,type,
    class_Wellfounded__Recursion_Owellorder: $i > $o ).

thf(tp_tc_Datatype_Ooption,type,
    tc_Datatype_Ooption: $i > $i ).

thf(tp_tc_Datatype__Universe_Onode,type,
    tc_Datatype__Universe_Onode: $i > $i > $i ).

thf(tp_tc_IntDef_Oint,type,
    tc_IntDef_Oint: $i ).

thf(tp_tc_List_Olist,type,
    tc_List_Olist: $i > $i ).

thf(tp_tc_Message_Omsg,type,
    tc_Message_Omsg: $i ).

thf(tp_tc_Product__Type_Ounit,type,
    tc_Product__Type_Ounit: $i ).

thf(tp_tc_bool,type,
    tc_bool: $i ).

thf(tp_tc_fun,type,
    tc_fun: $i > $i > $i ).

thf(tp_tc_nat,type,
    tc_nat: $i ).

thf(tp_tc_prod,type,
    tc_prod: $i > $i > $i ).

thf(tp_tc_set,type,
    tc_set: $i > $i ).

thf(tp_tc_sum,type,
    tc_sum: $i > $i > $i ).

thf(tp_v_G,type,
    v_G: $i ).

thf(tp_v_H,type,
    v_H: $i ).

thf(1,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Osynth @ V_H ) ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).

thf(2,axiom,
    ! [V_H: $i,V_H_H: $i,V_G: $i,V_G_H: $i] :
      ( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_H ) @ ( c_Message_Oanalz @ V_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
      | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ V_G_H @ V_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__cong_0) ).

thf(3,axiom,
    ! [V_n: $i,V_H: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ V_n ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_ONumber_0) ).

thf(4,axiom,
    ! [V_Y: $i,V_H: $i,V_X: $i] :
      ( ~ ( c_in @ V_Y @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).

thf(5,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).

thf(6,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).

thf(7,axiom,
    ! [V_X: $i,V_H: $i,V_K: $i] :
      ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).

thf(8,axiom,
    ! [V_agt: $i,V_H: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ V_agt ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OAgent_0) ).

thf(9,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ V_X @ ( c_Message_Oparts @ ( c_Message_Oparts @ V_H ) ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).

thf(10,axiom,
    ! [V_X: $i] :
      ~ ( c_in @ V_X @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).

thf(11,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

thf(12,axiom,
    ! [V_nat: $i,V_msg: $i,V_nat_H: $i,V_msg_H: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
       != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
      | ( V_msg = V_msg_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).

thf(13,axiom,
    ! [V_nat: $i,V_msg: $i,V_nat_H: $i,V_msg_H: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
       != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
      | ( V_nat = V_nat_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).

thf(14,axiom,
    ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i,V_msg2_H: $i] :
      ( ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
       != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
      | ( V_msg2 = V_msg2_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).

thf(15,axiom,
    ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i,V_msg2_H: $i] :
      ( ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
       != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
      | ( V_msg1 = V_msg1_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).

thf(16,axiom,
    ! [V_msg: $i,V_msg_H: $i] :
      ( ( ( c_Message_Omsg_OHash @ V_msg )
       != ( c_Message_Omsg_OHash @ V_msg_H ) )
      | ( V_msg = V_msg_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).

thf(17,axiom,
    ! [V_nat: $i,V_nat_H: $i] :
      ( ( ( c_Message_Omsg_OKey @ V_nat )
       != ( c_Message_Omsg_OKey @ V_nat_H ) )
      | ( V_nat = V_nat_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).

thf(18,axiom,
    ! [V_nat: $i,V_nat_H: $i] :
      ( ( ( c_Message_Omsg_ONonce @ V_nat )
       != ( c_Message_Omsg_ONonce @ V_nat_H ) )
      | ( V_nat = V_nat_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).

thf(19,axiom,
    ! [V_nat: $i,V_nat_H: $i] :
      ( ( ( c_Message_Omsg_ONumber @ V_nat )
       != ( c_Message_Omsg_ONumber @ V_nat_H ) )
      | ( V_nat = V_nat_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).

thf(20,axiom,
    ! [V_agent: $i,V_agent_H: $i] :
      ( ( ( c_Message_Omsg_OAgent @ V_agent )
       != ( c_Message_Omsg_OAgent @ V_agent_H ) )
      | ( V_agent = V_agent_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).

thf(21,axiom,
    ! [V_c: $i,V_G: $i,V_H: $i] :
      ( ~ ( c_in @ V_c @ ( c_Message_Oparts @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ( c_in @ V_c @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_c @ ( c_Message_Oparts @ V_G ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).

thf(22,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ V_X @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).

thf(23,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).

thf(24,axiom,
    ! [V_K: $i,V_X: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ V_K ) ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).

thf(25,axiom,
    ! [V_nat: $i,V_nat_H: $i] :
      ( ( ( c_Message_Oagent_OFriend @ V_nat )
       != ( c_Message_Oagent_OFriend @ V_nat_H ) )
      | ( V_nat = V_nat_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject__iff1_0) ).

thf(26,axiom,
    ! [V_nat: $i] :
      ( c_Message_Oagent_OSpy
     != ( c_Message_Oagent_OFriend @ V_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6__iff1_0) ).

thf(27,axiom,
    ! [V_nat: $i] :
      ( ( c_Message_Oagent_OFriend @ V_nat )
     != c_Message_Oagent_OSpy ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5__iff1_0) ).

thf(28,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).

thf(29,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).

thf(30,axiom,
    ! [V_nat_H: $i] :
      ( ( c_Message_Oagent_OFriend @ V_nat_H )
     != c_Message_Oagent_OServer ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2__iff1_0) ).

thf(31,axiom,
    ! [V_nat_H: $i] :
      ( c_Message_Oagent_OServer
     != ( c_Message_Oagent_OFriend @ V_nat_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1__iff1_0) ).

thf(32,axiom,
    ! [V_n: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_n ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ V_n ) @ V_H @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth_0) ).

thf(33,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ V_H @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).

thf(34,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_Y @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ V_H @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).

thf(35,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).

thf(36,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_Y @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).

thf(37,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).

thf(38,axiom,
    ! [V_X: $i,V_Y: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).

thf(39,axiom,
    ! [V_K: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).

thf(40,axiom,
    ! [V_X: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ V_H @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).

thf(41,axiom,
    ! [V_K: $i,V_X: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).

thf(42,axiom,
    ! [V_K: $i,V_X: $i,V_H: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).

thf(43,axiom,
    ! [V_x: $i,V_y: $i] :
      ( ~ ( c_less @ V_x @ V_y @ tc_nat )
      | ( c_in @ ( c_Pair @ V_x @ V_y @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

thf(44,axiom,
    ! [V_x: $i,V_y: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
      | ( c_less @ V_x @ V_y @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

thf(45,axiom,
    ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
      | ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
      | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

thf(46,axiom,
    ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
      | ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

thf(47,axiom,
    ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
      | ( c_Wellfounded__Recursion_Owf @ V_r @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

thf(48,axiom,
    ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a )
      | ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
      | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

thf(49,axiom,
    ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
      | ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

thf(50,axiom,
    ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
      | ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

thf(51,axiom,
    ! [V_r: $i,T_a: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a )
      | ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

thf(52,axiom,
    ! [V_r: $i,T_a: $i] :
      ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
      | ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

thf(53,axiom,
    ! [V_b: $i,T_b: $i,T_a: $i,V_a: $i] :
      ( ( c_Sum__Type_OInr @ V_b @ T_b @ T_a )
     != ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

thf(54,axiom,
    ! [V_x: $i,T_b: $i,T_a: $i,V_y: $i] :
      ( ( ( c_Sum__Type_OInr @ V_x @ T_b @ T_a )
       != ( c_Sum__Type_OInr @ V_y @ T_b @ T_a ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).

thf(55,axiom,
    ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
      ( ( c_Sum__Type_OInl @ V_a @ T_a @ T_b )
     != ( c_Sum__Type_OInr @ V_b @ T_b @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

thf(56,axiom,
    ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
      ( ( ( c_Sum__Type_OInl @ V_x @ T_a @ T_b )
       != ( c_Sum__Type_OInl @ V_y @ T_a @ T_b ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).

thf(57,axiom,
    ! [V_A: $i,V_x: $i,T_a: $i] :
      ( ~ ( c_lessequals @ V_A @ ( c_insert @ V_x @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) )
      | ( ( c_insert @ V_x @ c_emptyset @ T_a )
        = ( c_insert @ V_x @ V_A @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

thf(58,axiom,
    ! [V_b: $i,T_a: $i,V_a: $i,V_A: $i] :
      ( ( ( c_insert @ V_b @ c_emptyset @ T_a )
       != ( c_insert @ V_a @ V_A @ T_a ) )
      | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

thf(59,axiom,
    ! [V_b: $i,T_a: $i,V_a: $i,V_A: $i] :
      ( ( ( c_insert @ V_b @ c_emptyset @ T_a )
       != ( c_insert @ V_a @ V_A @ T_a ) )
      | ( V_a = V_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

thf(60,axiom,
    ! [V_A: $i,V_x: $i,T_a: $i] :
      ( ~ ( c_lessequals @ V_A @ ( c_insert @ V_x @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) )
      | ( ( c_insert @ V_x @ V_A @ T_a )
        = ( c_insert @ V_x @ c_emptyset @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

thf(61,axiom,
    ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
      ( ( ( c_insert @ V_a @ V_A @ T_a )
       != ( c_insert @ V_b @ c_emptyset @ T_a ) )
      | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

thf(62,axiom,
    ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
      ( ( ( c_insert @ V_a @ V_A @ T_a )
       != ( c_insert @ V_b @ c_emptyset @ T_a ) )
      | ( V_a = V_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

thf(63,axiom,
    ! [V_A: $i,T_a: $i] :
      ~ ( c_less @ V_A @ c_emptyset @ ( tc_set @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).

thf(64,axiom,
    ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
      | ( c_in @ V_a @ V_A @ T_a )
      | ( V_a = V_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(65,axiom,
    ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(66,axiom,
    ! [V_a: $i,V_B: $i,T_a: $i,V_b: $i] :
      ( ~ ( c_in @ V_a @ V_B @ T_a )
      | ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).

thf(67,axiom,
    ! [V_a: $i,T_a: $i] :
      ~ ( c_in @ V_a @ c_emptyset @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(68,axiom,
    ! [V_A: $i,V_X: $i,T_a: $i,V_C: $i] :
      ( ~ ( c_in @ V_A @ V_X @ T_a )
      | ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
      | ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).

thf(69,axiom,
    ! [T_a: $i] :
      ( ( c_union @ c_emptyset @ c_emptyset @ T_a )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).

thf(70,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ( ( c_union @ V_A @ V_B @ T_a )
       != c_emptyset )
      | ( V_B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).

thf(71,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ( ( c_union @ V_A @ V_B @ T_a )
       != c_emptyset )
      | ( V_A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).

thf(72,axiom,
    ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
      | ( c_in @ V_c @ V_B @ T_a )
      | ( c_in @ V_c @ V_A @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(73,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
      ( ~ ( c_in @ V_c @ V_A @ T_a )
      | ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(74,axiom,
    ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ V_c @ V_B @ T_a )
      | ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(75,axiom,
    c_UNIV != c_emptyset,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).

thf(76,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( c_in @ V_A @ ( c_Pow @ V_B @ T_a ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).

thf(77,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_in @ V_A @ ( c_Pow @ V_B @ T_a ) @ ( tc_set @ T_a ) )
      | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).

thf(78,axiom,
    ! [V_X: $i,V_C: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
      | ~ ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a )
      | ( c_in @ V_A @ V_X @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).

thf(79,axiom,
    ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ V_c @ V_B @ T_a )
      | ~ ( c_in @ V_c @ V_A @ T_a )
      | ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).

thf(80,axiom,
    ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
      | ( c_in @ V_c @ V_A @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).

thf(81,axiom,
    ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
      | ( c_in @ V_c @ V_B @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).

thf(82,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
      ( ~ ( c_in @ V_c @ V_A @ T_a )
      | ( c_in @ V_c @ V_B @ T_a )
      | ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(83,axiom,
    ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a )
      | ( c_in @ V_c @ V_A @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).

thf(84,axiom,
    ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ V_c @ V_B @ T_a )
      | ~ ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).

thf(85,axiom,
    ! [V_B: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
      | ( c_lessequals @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

thf(86,axiom,
    ! [V_A: $i,T_a: $i,V_B: $i] :
      ( ~ ( c_lessequals @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
      | ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

thf(87,axiom,
    ! [V_A: $i,T_a: $i,V_B: $i] :
      ( ( ( c_uminus @ V_A @ ( tc_set @ T_a ) )
       != ( c_uminus @ V_B @ ( tc_set @ T_a ) ) )
      | ( V_A = V_B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

thf(88,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i] :
      ( ( c_in @ V_c @ V_A @ T_a )
      | ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).

thf(89,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ V_A @ T_a )
      | ~ ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).

thf(90,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ~ ( c_lessequals @ V_x @ V_y @ T_a )
      | ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

thf(91,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
      | ( c_lessequals @ V_x @ V_y @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

thf(92,axiom,
    ! [T_a: $i,V_i: $i,V_k: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_less @ V_i @ V_k @ T_a )
      | ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).

thf(93,axiom,
    ! [T_a: $i,V_i: $i,V_k: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a )
      | ( c_less @ V_i @ V_k @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).

thf(94,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ( ( c_SetInterval_OlessThan @ V_x @ T_a )
       != ( c_SetInterval_OlessThan @ V_y @ T_a ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

thf(95,axiom,
    ! [T_a: $i,V_y: $i,V_x: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ~ ( c_lessequals @ V_y @ V_x @ T_a )
      | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

thf(96,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
      | ( c_lessequals @ V_y @ V_x @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

thf(97,axiom,
    ! [T_a: $i,V_k: $i,V_i: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_less @ V_k @ V_i @ T_a )
      | ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

thf(98,axiom,
    ! [T_a: $i,V_i: $i,V_k: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a )
      | ( c_less @ V_k @ V_i @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

thf(99,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ( ( c_SetInterval_OgreaterThan @ V_x @ T_a )
       != ( c_SetInterval_OgreaterThan @ V_y @ T_a ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

thf(100,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_lessequals @ V_x @ V_y @ T_a )
      | ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

thf(101,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) )
      | ( c_lessequals @ V_x @ V_y @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

thf(102,axiom,
    ! [T_a: $i,V_i: $i,V_k: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_lessequals @ V_i @ V_k @ T_a )
      | ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).

thf(103,axiom,
    ! [T_a: $i,V_i: $i,V_k: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a )
      | ( c_lessequals @ V_i @ V_k @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).

thf(104,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ( ( c_SetInterval_OatMost @ V_x @ T_a )
       != ( c_SetInterval_OatMost @ V_y @ T_a ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

thf(105,axiom,
    ! [T_a: $i,V_y: $i,V_x: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_lessequals @ V_y @ V_x @ T_a )
      | ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

thf(106,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) )
      | ( c_lessequals @ V_y @ V_x @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

thf(107,axiom,
    ! [T_a: $i,V_k: $i,V_i: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_lessequals @ V_k @ V_i @ T_a )
      | ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).

thf(108,axiom,
    ! [T_a: $i,V_i: $i,V_k: $i] :
      ( ~ ( class_Orderings_Oord @ T_a )
      | ~ ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a )
      | ( c_lessequals @ V_k @ V_i @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).

thf(109,axiom,
    ! [T_a: $i,V_x: $i,V_y: $i] :
      ( ~ ( class_Orderings_Olinorder @ T_a )
      | ( ( c_SetInterval_OatLeast @ V_x @ T_a )
       != ( c_SetInterval_OatLeast @ V_y @ T_a ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

thf(110,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
      | ( V_a = V_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).

thf(111,axiom,
    ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
      | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).

thf(112,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).

thf(113,axiom,
    ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
      | ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_insert @ V_a @ c_emptyset @ T_b ) @ T_b @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).

thf(114,axiom,
    ! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_insert @ V_a @ c_emptyset @ T_b ) @ T_b @ T_a ) @ T_a )
      | ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).

thf(115,axiom,
    ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).

thf(116,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
      ( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
       != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
      | ( V_b = V_b_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).

thf(117,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
      ( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
       != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
      | ( V_a = V_a_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).

thf(118,axiom,
    ! [T_a: $i,V_x: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_less @ V_x @ V_x @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

thf(119,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2__iff1_0) ).

thf(120,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1__iff1_0) ).

thf(121,axiom,
    ! [V_n: $i] :
      ~ ( c_less @ V_n @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).

thf(122,axiom,
    ! [V_j: $i,V_i: $i] :
      ~ ( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).

thf(123,axiom,
    ! [V_i: $i,V_j: $i] :
      ~ ( c_less @ ( c_plus @ V_i @ V_j @ tc_nat ) @ V_i @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).

thf(124,axiom,
    ~ ( c_less @ c_0 @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).

thf(125,axiom,
    ! [V_n: $i] :
      ( ( c_less @ c_0 @ V_n @ tc_nat )
      | ( V_n = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).

thf(126,axiom,
    c_less @ c_0 @ c_1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).

thf(127,axiom,
    ! [V_n: $i] :
      ( ~ ( c_less @ V_n @ c_1 @ tc_nat )
      | ( V_n = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).

thf(128,axiom,
    c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).

thf(129,axiom,
    ! [V_n: $i] :
      ( ~ ( c_less @ V_n @ ( c_Suc @ c_0 ) @ tc_nat )
      | ( V_n = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).

thf(130,axiom,
    c_lessequals @ c_0 @ c_0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).

thf(131,axiom,
    ! [V_i: $i] :
      ( ~ ( c_lessequals @ V_i @ c_0 @ tc_nat )
      | ( V_i = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).

thf(132,axiom,
    ( ( c_plus @ c_0 @ c_0 @ tc_nat )
    = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).

thf(133,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ( ( c_plus @ V_m @ V_n @ tc_nat )
       != c_0 )
      | ( V_n = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).

thf(134,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ( ( c_plus @ V_m @ V_n @ tc_nat )
       != c_0 )
      | ( V_m = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).

thf(135,axiom,
    ! [V_n: $i,V_m: $i] :
      ( ~ ( c_less @ c_0 @ V_n @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).

thf(136,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ~ ( c_less @ c_0 @ V_m @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).

thf(137,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ~ ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ V_n @ tc_nat )
      | ( c_less @ c_0 @ V_m @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).

thf(138,axiom,
    ! [V_m: $i] :
      ( c_0
     != ( c_Suc @ V_m ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).

thf(139,axiom,
    ! [V_m: $i] :
      ( ( c_Suc @ V_m )
     != c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).

thf(140,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ~ ( c_less @ V_m @ V_n @ tc_nat )
      | ( c_less @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).

thf(141,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ~ ( c_less @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
      | ( c_less @ V_m @ V_n @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).

thf(142,axiom,
    ! [V_n: $i,V_m: $i] :
      ( ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
      | ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).

thf(143,axiom,
    ! [V_n: $i,V_m: $i] :
      ( ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
      | ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).

thf(144,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ( ( c_Suc @ V_m )
       != ( c_Suc @ V_n ) )
      | ( V_m = V_n ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).

thf(145,axiom,
    ! [T_a: $i] :
      ( ( c_List_Oset @ c_List_Olist_ONil @ T_a )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).

thf(146,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( ( c_List_Oset @ V_xs @ T_a )
       != c_emptyset )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).

thf(147,axiom,
    ! [T_a: $i] :
      ( c_emptyset
      = ( c_List_Oset @ c_List_Olist_ONil @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).

thf(148,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_emptyset
       != ( c_List_Oset @ V_xs @ T_a ) )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).

thf(149,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( V_xs
      = ( c_append @ V_xs @ c_List_Olist_ONil @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).

thf(150,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i] :
      ( ( V_xs
       != ( c_append @ V_xs @ V_ys @ T_a ) )
      | ( V_ys = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).

thf(151,axiom,
    ! [V_ys: $i,T_a: $i] :
      ( V_ys
      = ( c_append @ c_List_Olist_ONil @ V_ys @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).

thf(152,axiom,
    ! [V_ys: $i,V_xs: $i,T_a: $i] :
      ( ( V_ys
       != ( c_append @ V_xs @ V_ys @ T_a ) )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).

thf(153,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
      ( ( ( c_append @ V_xs @ V_ys @ T_a )
       != ( c_append @ V_xs @ V_zs @ T_a ) )
      | ( V_ys = V_zs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).

thf(154,axiom,
    ! [V_xs: $i,T_a: $i,V_ys: $i] :
      ( ( ( c_List_Orev @ V_xs @ T_a )
       != ( c_List_Orev @ V_ys @ T_a ) )
      | ( V_xs = V_ys ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).

thf(155,axiom,
    ! [T_a: $i] :
      ( ( c_List_Orev @ c_List_Olist_ONil @ T_a )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff2_0) ).

thf(156,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( ( c_List_Orev @ V_xs @ T_a )
       != c_List_Olist_ONil )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff1_0) ).

thf(157,axiom,
    ! [V_ys: $i,T_a: $i,V_y: $i] :
      ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
      = ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).

thf(158,axiom,
    ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
      ( ( ( c_List_Orev @ V_xs @ T_a )
       != ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
      | ( V_xs
        = ( c_append @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff1_0) ).

thf(159,axiom,
    ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
      ( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
       != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
      | ( V_list = V_list_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).

thf(160,axiom,
    ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
      ( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
       != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
      | ( V_a = V_a_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).

thf(161,axiom,
    ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
      ( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).

thf(162,axiom,
    ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
      ( c_List_Olist_ONil
     != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).

thf(163,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( ( c_List_Oremdups @ V_xs @ T_a )
       != V_xs )
      | ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
        = ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff2_0) ).

thf(164,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
       != ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
      | ( ( c_List_Oremdups @ V_xs @ T_a )
        = V_xs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).

thf(165,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).

thf(166,axiom,
    ! [T_a: $i] :
      ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).

thf(167,axiom,
    ! [T_a: $i] :
      ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).

thf(168,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
       != c_0 )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).

thf(169,axiom,
    ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i,V_nibble2_H: $i] :
      ( ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
       != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
      | ( V_nibble2 = V_nibble2_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_1) ).

thf(170,axiom,
    ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i,V_nibble2_H: $i] :
      ( ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
       != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
      | ( V_nibble1 = V_nibble1_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_0) ).

thf(171,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_append @ V_xs @ c_List_Olist_ONil @ T_a )
      = V_xs ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).

thf(172,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i] :
      ( ( ( c_append @ V_xs @ V_ys @ T_a )
       != V_xs )
      | ( V_ys = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).

thf(173,axiom,
    ! [V_ys: $i,T_a: $i] :
      ( ( c_append @ c_List_Olist_ONil @ V_ys @ T_a )
      = V_ys ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).

thf(174,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i] :
      ( ( ( c_append @ V_xs @ V_ys @ T_a )
       != V_ys )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).

thf(175,axiom,
    ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
      ( ( ( c_append @ V_ys @ V_xs @ T_a )
       != ( c_append @ V_zs @ V_xs @ T_a ) )
      | ( V_ys = V_zs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).

thf(176,axiom,
    ! [T_a: $i] :
      ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).

thf(177,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i] :
      ( ( ( c_append @ V_xs @ V_ys @ T_a )
       != c_List_Olist_ONil )
      | ( V_ys = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).

thf(178,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i] :
      ( ( ( c_append @ V_xs @ V_ys @ T_a )
       != c_List_Olist_ONil )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).

thf(179,axiom,
    ! [V_ys: $i,V_A: $i,T_a: $i,V_xs: $i] :
      ( ~ ( c_in @ V_ys @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).

thf(180,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ( c_in @ V_ys @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).

thf(181,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).

thf(182,axiom,
    ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
      ( ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
       != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).

thf(183,axiom,
    ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
      ( ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
       != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
      | ( V_xs = V_ys ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).

thf(184,axiom,
    ! [V_ys: $i,T_a: $i,V_r: $i] :
      ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ V_ys @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).

thf(185,axiom,
    ! [T_a: $i] :
      ( c_List_Olist_ONil
      = ( c_List_Orev @ c_List_Olist_ONil @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff2_0) ).

thf(186,axiom,
    ! [V_xs: $i,T_a: $i] :
      ( ( c_List_Olist_ONil
       != ( c_List_Orev @ V_xs @ T_a ) )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff1_0) ).

thf(187,axiom,
    ! [T_a: $i] :
      ( c_List_Olist_ONil
      = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).

thf(188,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ V_xs @ V_ys @ T_a ) )
      | ( V_ys = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).

thf(189,axiom,
    ! [V_xs: $i,V_ys: $i,T_a: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ V_xs @ V_ys @ T_a ) )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).

thf(190,axiom,
    ! [V_xs: $i,T_a: $i,V_r: $i] :
      ~ ( c_in @ ( c_Pair @ V_xs @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).

thf(191,axiom,
    ! [V_z: $i,V_w: $i] :
      ( ~ ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ ( c_uminus @ V_z @ tc_IntDef_Oint ) @ V_w @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

thf(192,axiom,
    ! [V_z: $i,V_w: $i] :
      ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ V_z @ tc_IntDef_Oint ) @ V_w @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

thf(193,axiom,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

thf(194,axiom,
    ! [V_m: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_IntDef_Oint )
      | ( V_m = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

thf(195,axiom,
    ! [V_z: $i,V_w: $i] :
      ( ~ ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ V_z @ ( c_uminus @ V_w @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

thf(196,axiom,
    ! [V_z: $i,V_w: $i] :
      ( ~ ( c_Divides_Oop_Advd @ V_z @ ( c_uminus @ V_w @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      | ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

thf(197,axiom,
    ! [V_m: $i,V_n: $i] :
      ( ( ( c_IntDef_Oint @ V_m )
       != ( c_IntDef_Oint @ V_n ) )
      | ( V_m = V_n ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).

thf(198,axiom,
    ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).

thf(199,axiom,
    ! [V_k: $i,V_n: $i,V_m: $i] :
      ( ~ ( c_Divides_Oop_Advd @ V_k @ V_n @ tc_nat )
      | ~ ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat )
      | ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).

thf(200,axiom,
    ! [V_k: $i,V_m: $i,V_n: $i] :
      ( ~ ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat )
      | ( c_Divides_Oop_Advd @ V_k @ V_n @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).

thf(201,axiom,
    ! [V_k: $i,V_m: $i,V_n: $i] :
      ( ~ ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat )
      | ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).

thf(202,axiom,
    ! [V_r: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_r @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_b @ T_a ) ) )
      | ( c_in @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_a @ T_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).

thf(203,axiom,
    ! [V_r: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_a @ T_b ) ) )
      | ( c_in @ V_r @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_b @ T_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).

thf(204,axiom,
    ! [V_G: $i,T_a: $i,V_F: $i] :
      ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).

thf(205,axiom,
    ! [V_F: $i,V_G: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).

thf(206,axiom,
    ! [V_F: $i,V_G: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).

thf(207,axiom,
    ! [V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_Pow @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

thf(208,axiom,
    ! [V_A: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_Pow @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
      | ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

thf(209,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
      ( ~ ( c_in @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_minus @ V_A @ ( c_insert @ V_a @ V_B @ T_a ) @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

thf(210,axiom,
    ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_minus @ V_A @ ( c_insert @ V_a @ V_B @ T_a ) @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

thf(211,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2__iff1_0) ).

thf(212,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).

thf(213,axiom,
    ! [V_r: $i,T_a: $i] :
      ( ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff2_0) ).

thf(214,axiom,
    ! [V_A: $i,V_r: $i,T_a: $i] :
      ( ( ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a )
       != c_emptyset )
      | ( V_A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff1_0) ).

thf(215,axiom,
    ! [V_r: $i,T_a: $i] :
      ( c_emptyset
      = ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff2_0) ).

thf(216,axiom,
    ! [V_A: $i,V_r: $i,T_a: $i] :
      ( ( c_emptyset
       != ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) )
      | ( V_A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff1_0) ).

thf(217,axiom,
    c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).

thf(218,axiom,
    ! [V_m: $i] :
      ( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_nat )
      | ( V_m = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).

thf(219,axiom,
    ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_k: $i] :
      ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
     != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb__iff1_0) ).

thf(220,axiom,
    ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
      ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
     != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf__iff1_0) ).

thf(221,axiom,
    ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
      ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
     != ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).

thf(222,axiom,
    ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i,V_N_H: $i] :
      ( ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
       != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
      | ( V_N = V_N_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

thf(223,axiom,
    ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i,V_N_H: $i] :
      ( ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
       != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
      | ( V_M = V_M_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

thf(224,axiom,
    ! [V_k: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
      ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
     != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons__iff1_0) ).

thf(225,axiom,
    ! [V_k: $i,T_a: $i,T_b: $i,V_a: $i] :
      ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
     != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf__iff1_0) ).

thf(226,axiom,
    ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
      ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
     != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons__iff1_0) ).

thf(227,axiom,
    ! [V_a: $i,T_a: $i,T_b: $i,V_k: $i] :
      ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
     != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).

thf(228,axiom,
    ! [V_N: $i,T_a: $i,T_b: $i,V_M: $i] :
      ( ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b )
     != ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

thf(229,axiom,
    ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
      ( ( ( c_Datatype__Universe_OIn1 @ V_M @ T_a @ T_b )
       != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) )
      | ( V_M = V_N ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

thf(230,axiom,
    ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
      ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
     != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

thf(231,axiom,
    ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
      ( ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
       != ( c_Datatype__Universe_OIn0 @ V_N @ T_a @ T_b ) )
      | ( V_M = V_N ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

thf(232,axiom,
    ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
      ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
     != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons__iff1_0) ).

thf(233,axiom,
    ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
      ( ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
       != ( c_Datatype__Universe_OAtom @ V_b @ T_a @ T_b ) )
      | ( V_a = V_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq__iff1_0) ).

thf(234,axiom,
    ! [V_a: $i,T_a: $i,V_a_H: $i] :
      ( ( ( c_Datatype_Ooption_OSome @ V_a @ T_a )
       != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) )
      | ( V_a = V_a_H ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).

thf(235,axiom,
    ! [V_a_H: $i,T_a: $i] :
      ( ( c_Datatype_Ooption_OSome @ V_a_H @ T_a )
     != c_Datatype_Ooption_ONone ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2__iff1_0) ).

thf(236,axiom,
    ! [V_a_H: $i,T_a: $i] :
      ( c_Datatype_Ooption_ONone
     != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1__iff1_0) ).

thf(237,axiom,
    ! [V_x: $i,T_a: $i] :
      ( ( V_x = c_Datatype_Ooption_ONone )
      | ( V_x
        = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq__iff1_0) ).

thf(238,axiom,
    ! [V_x: $i,T_a: $i] :
      ( ( V_x = c_Datatype_Ooption_ONone )
      | ( V_x
        = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq__iff1_0) ).

thf(239,axiom,
    ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ V_x @ T_a ) @ T_a ) @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).

thf(240,axiom,
    ! [V_x: $i,V_xo: $i,T_a: $i] :
      ( ~ ( c_in @ V_x @ ( c_Datatype_Oo2s @ V_xo @ T_a ) @ T_a )
      | ( V_xo
        = ( c_Datatype_Ooption_OSome @ V_x @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).

thf(241,axiom,
    ! [T: $i] :
      ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).

thf(242,axiom,
    ! [T: $i] :
      ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).

thf(243,axiom,
    ! [T: $i] :
      ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).

thf(244,axiom,
    ! [T: $i] :
      ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).

thf(245,axiom,
    ! [T: $i] :
      ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).

thf(246,axiom,
    ! [T: $i] :
      ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).

thf(247,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

thf(248,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).

thf(249,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).

thf(250,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).

thf(251,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).

thf(252,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

thf(253,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

thf(254,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

thf(255,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

thf(256,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

thf(257,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

thf(258,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).

thf(259,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).

thf(260,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

thf(261,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

thf(262,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).

thf(263,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).

thf(264,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).

thf(265,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).

thf(266,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).

thf(267,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).

thf(268,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).

thf(269,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).

thf(270,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).

thf(271,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).

thf(272,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).

thf(273,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).

thf(274,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).

thf(275,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

thf(276,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).

thf(277,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).

thf(278,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).

thf(279,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).

thf(280,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

thf(281,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).

thf(282,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).

thf(283,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

thf(284,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

thf(285,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

thf(286,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).

thf(287,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).

thf(288,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).

thf(289,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).

thf(290,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).

thf(291,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).

thf(292,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).

thf(293,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).

thf(294,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).

thf(295,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).

thf(296,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).

thf(297,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).

thf(298,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).

thf(299,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).

thf(300,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).

thf(301,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).

thf(302,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).

thf(303,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).

thf(304,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).

thf(305,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).

thf(306,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).

thf(307,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).

thf(308,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).

thf(309,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).

thf(310,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).

thf(311,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).

thf(312,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).

thf(313,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).

thf(314,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).

thf(315,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).

thf(316,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).

thf(317,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).

thf(318,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).

thf(319,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).

thf(320,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).

thf(321,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).

thf(322,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).

thf(323,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).

thf(324,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).

thf(325,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).

thf(326,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).

thf(327,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).

thf(328,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).

thf(329,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).

thf(330,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).

thf(331,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).

thf(332,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).

thf(333,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).

thf(334,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).

thf(335,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).

thf(336,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).

thf(337,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).

thf(338,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).

thf(339,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).

thf(340,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).

thf(341,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).

thf(342,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

thf(343,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).

thf(344,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).

thf(345,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).

thf(346,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).

thf(347,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).

thf(348,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).

thf(349,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).

thf(350,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).

thf(351,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).

thf(352,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).

thf(353,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).

thf(354,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).

thf(355,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).

thf(356,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).

thf(357,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).

thf(358,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).

thf(359,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).

thf(360,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).

thf(361,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).

thf(362,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).

thf(363,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).

thf(364,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).

thf(365,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).

thf(366,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).

thf(367,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).

thf(368,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).

thf(369,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).

thf(370,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).

thf(371,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).

thf(372,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).

thf(373,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

thf(374,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

thf(375,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

thf(376,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

thf(377,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

thf(378,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

thf(379,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

thf(380,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).

thf(381,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).

thf(382,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

thf(383,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

thf(384,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_9) ).

thf(385,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_8) ).

thf(386,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_7) ).

thf(387,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_6) ).

thf(388,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_5) ).

thf(389,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_4) ).

thf(390,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_3) ).

thf(391,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_24) ).

thf(392,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_23) ).

thf(393,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_22) ).

thf(394,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_21) ).

thf(395,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_20) ).

thf(396,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_2) ).

thf(397,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_19) ).

thf(398,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_18) ).

thf(399,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_17) ).

thf(400,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_16) ).

thf(401,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_15) ).

thf(402,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_14) ).

thf(403,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_13) ).

thf(404,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_12) ).

thf(405,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_11) ).

thf(406,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_10) ).

thf(407,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_1) ).

thf(408,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
      | ( class_Ring__and__Field_Ocomm__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_0) ).

thf(409,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).

thf(410,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).

thf(411,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

thf(412,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).

thf(413,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

thf(414,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).

thf(415,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).

thf(416,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

thf(417,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

thf(418,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

thf(419,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

thf(420,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

thf(421,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

thf(422,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).

thf(423,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

thf(424,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

thf(425,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).

thf(426,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

thf(427,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).

thf(428,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).

thf(429,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

thf(430,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

thf(431,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).

thf(432,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

thf(433,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

thf(434,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

thf(435,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

thf(436,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

thf(437,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

thf(438,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

thf(439,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

thf(440,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).

thf(441,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).

thf(442,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).

thf(443,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

thf(444,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

thf(445,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

thf(446,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

thf(447,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).

thf(448,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).

thf(449,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).

thf(450,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).

thf(451,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

thf(452,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).

thf(453,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

thf(454,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

thf(455,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

thf(456,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

thf(457,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).

thf(458,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

thf(459,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

thf(460,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

thf(461,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

thf(462,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

thf(463,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

thf(464,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

thf(465,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

thf(466,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

thf(467,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

thf(468,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

thf(469,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

thf(470,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).

thf(471,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).

thf(472,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).

thf(473,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).

thf(474,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).

thf(475,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).

thf(476,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).

thf(477,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

thf(478,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).

thf(479,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

thf(480,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).

thf(481,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

thf(482,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).

thf(483,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

thf(484,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).

thf(485,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

thf(486,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).

thf(487,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

thf(488,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

thf(489,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).

thf(490,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

thf(491,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).

thf(492,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).

thf(493,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).

thf(494,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).

thf(495,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).

thf(496,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).

thf(497,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).

thf(498,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).

thf(499,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).

thf(500,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).

thf(501,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).

thf(502,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).

thf(503,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).

thf(504,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).

thf(505,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).

thf(506,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).

thf(507,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).

thf(508,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).

thf(509,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).

thf(510,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).

thf(511,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).

thf(512,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).

thf(513,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).

thf(514,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).

thf(515,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).

thf(516,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).

thf(517,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

thf(518,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

thf(519,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

thf(520,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Opordered__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

thf(521,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Olordered__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

thf(522,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

thf(523,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

thf(524,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Olordered__ab__group @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

thf(525,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

thf(526,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

thf(527,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

thf(528,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

thf(529,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

thf(530,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

thf(531,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

thf(532,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

thf(533,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

thf(534,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).

thf(535,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

thf(536,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

thf(537,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

thf(538,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

thf(539,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

thf(540,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).

thf(541,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).

thf(542,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).

thf(543,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).

thf(544,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).

thf(545,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).

thf(546,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

thf(547,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).

thf(548,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).

thf(549,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).

thf(550,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).

thf(551,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oidom @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).

thf(552,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).

thf(553,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oordered__semidom @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).

thf(554,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

thf(555,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Olordered__ab__group @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).

thf(556,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).

thf(557,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).

thf(558,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

thf(559,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).

thf(560,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Opordered__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).

thf(561,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Olordered__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).

thf(562,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oordered__ring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).

thf(563,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).

thf(564,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).

thf(565,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

thf(566,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).

thf(567,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(568,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).

thf(569,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

thf(570,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

thf(571,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).

thf(572,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).

thf(573,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).

thf(574,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).

thf(575,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

thf(576,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).

thf(577,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

thf(578,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).

thf(579,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).

thf(580,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).

thf(581,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).

thf(582,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).

thf(583,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).

thf(584,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).

thf(585,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).

thf(586,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).

thf(587,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).

thf(588,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

thf(589,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).

thf(590,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).

thf(591,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).

thf(592,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).

thf(593,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).

thf(594,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).

thf(595,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).

thf(596,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).

thf(597,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).

thf(598,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).

thf(599,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).

thf(600,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).

thf(601,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).

thf(602,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).

thf(603,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Ocomm__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).

thf(604,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).

thf(605,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_9) ).

thf(606,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_8) ).

thf(607,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_7) ).

thf(608,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oordered__semidom @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_60) ).

thf(609,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_6) ).

thf(610,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_59) ).

thf(611,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).

thf(612,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_57) ).

thf(613,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_56) ).

thf(614,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_55) ).

thf(615,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_54) ).

thf(616,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_53) ).

thf(617,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_52) ).

thf(618,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_51) ).

thf(619,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Olordered__ab__group @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_50) ).

thf(620,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_5) ).

thf(621,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_49) ).

thf(622,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_48) ).

thf(623,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).

thf(624,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).

thf(625,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_45) ).

thf(626,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Opordered__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_44) ).

thf(627,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Olordered__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_43) ).

thf(628,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_42) ).

thf(629,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_41) ).

thf(630,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_40) ).

thf(631,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ocomm__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_4) ).

thf(632,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_39) ).

thf(633,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oordered__ring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_38) ).

thf(634,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_37) ).

thf(635,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_36) ).

thf(636,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_35) ).

thf(637,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oordered__idom @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).

thf(638,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_33) ).

thf(639,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_32) ).

thf(640,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_31) ).

thf(641,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_30) ).

thf(642,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_3) ).

thf(643,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_29) ).

thf(644,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_28) ).

thf(645,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_27) ).

thf(646,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_26) ).

thf(647,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_25) ).

thf(648,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_24) ).

thf(649,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_23) ).

thf(650,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_22) ).

thf(651,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_21) ).

thf(652,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_20) ).

thf(653,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oidom @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_2) ).

thf(654,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_19) ).

thf(655,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_18) ).

thf(656,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_17) ).

thf(657,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_16) ).

thf(658,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_15) ).

thf(659,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_14) ).

thf(660,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_13) ).

thf(661,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_12) ).

thf(662,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_11) ).

thf(663,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_10) ).

thf(664,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_HOL_Oinverse @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_1) ).

thf(665,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ T )
      | ( class_Ring__and__Field_Ofield @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).

thf(666,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).

thf(667,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).

thf(668,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

thf(669,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).

thf(670,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).

thf(671,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

thf(672,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

thf(673,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

thf(674,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

thf(675,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

thf(676,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

thf(677,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

thf(678,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

thf(679,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

thf(680,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

thf(681,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

thf(682,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

thf(683,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).

thf(684,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

thf(685,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

thf(686,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

thf(687,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

thf(688,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

thf(689,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

thf(690,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

thf(691,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

thf(692,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).

thf(693,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).

thf(694,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

thf(695,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

thf(696,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).

thf(697,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Ring__and__Field_Opordered__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).

thf(698,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).

thf(699,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).

thf(700,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).

thf(701,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).

thf(702,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).

thf(703,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).

thf(704,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).

thf(705,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).

thf(706,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).

thf(707,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).

thf(708,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Olordered__ab__group @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).

thf(709,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).

thf(710,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).

thf(711,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).

thf(712,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).

thf(713,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).

thf(714,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).

thf(715,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).

thf(716,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).

thf(717,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).

thf(718,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).

thf(719,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).

thf(720,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).

thf(721,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).

thf(722,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).

thf(723,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).

thf(724,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).

thf(725,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).

thf(726,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
      | ( class_Ring__and__Field_Opordered__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).

thf(727,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).

thf(728,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).

thf(729,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).

thf(730,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).

thf(731,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).

thf(732,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).

thf(733,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).

thf(734,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).

thf(735,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).

thf(736,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).

thf(737,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).

thf(738,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).

thf(739,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).

thf(740,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).

thf(741,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).

thf(742,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).

thf(743,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).

thf(744,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).

thf(745,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Oring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).

thf(746,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).

thf(747,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).

thf(748,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).

thf(749,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).

thf(750,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).

thf(751,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).

thf(752,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).

thf(753,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).

thf(754,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).

thf(755,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).

thf(756,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Ocomm__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).

thf(757,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ T )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).

thf(758,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_9) ).

thf(759,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).

thf(760,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_7) ).

thf(761,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_6) ).

thf(762,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).

thf(763,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_4) ).

thf(764,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).

thf(765,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Oidom @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_31) ).

thf(766,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_HOL_Oinverse @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_30) ).

thf(767,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_3) ).

thf(768,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_29) ).

thf(769,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_28) ).

thf(770,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_27) ).

thf(771,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_26) ).

thf(772,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_25) ).

thf(773,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_24) ).

thf(774,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_23) ).

thf(775,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_22) ).

thf(776,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).

thf(777,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_20) ).

thf(778,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Oring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_2) ).

thf(779,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_19) ).

thf(780,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).

thf(781,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).

thf(782,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_16) ).

thf(783,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_15) ).

thf(784,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_14) ).

thf(785,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_13) ).

thf(786,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).

thf(787,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).

thf(788,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_10) ).

thf(789,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Ocomm__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_1) ).

thf(790,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ T )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_0) ).

thf(791,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
      | ( class_HOL_Oinverse @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Odivision__by__zero_1) ).

thf(792,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Odivision__by__zero_0) ).

thf(793,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).

thf(794,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

thf(795,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

thf(796,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

thf(797,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

thf(798,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).

thf(799,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

thf(800,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

thf(801,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

thf(802,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

thf(803,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

thf(804,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

thf(805,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).

thf(806,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).

thf(807,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).

thf(808,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

thf(809,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

thf(810,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).

thf(811,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).

thf(812,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).

thf(813,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).

thf(814,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

thf(815,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).

thf(816,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).

thf(817,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).

thf(818,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

thf(819,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

thf(820,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).

thf(821,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

thf(822,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).

thf(823,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

thf(824,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

thf(825,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

thf(826,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

thf(827,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).

thf(828,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).

thf(829,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).

thf(830,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

thf(831,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).

thf(832,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

thf(833,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).

thf(834,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).

thf(835,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

thf(836,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).

thf(837,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).

thf(838,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

thf(839,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

thf(840,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).

thf(841,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

thf(842,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

thf(843,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

thf(844,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).

thf(845,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).

thf(846,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

thf(847,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

thf(848,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).

thf(849,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

thf(850,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).

thf(851,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).

thf(852,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).

thf(853,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).

thf(854,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).

thf(855,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

thf(856,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

thf(857,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).

thf(858,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

thf(859,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

thf(860,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).

thf(861,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).

thf(862,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).

thf(863,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).

thf(864,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).

thf(865,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).

thf(866,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).

thf(867,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).

thf(868,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).

thf(869,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).

thf(870,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).

thf(871,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).

thf(872,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).

thf(873,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).

thf(874,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).

thf(875,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Oring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).

thf(876,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).

thf(877,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).

thf(878,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).

thf(879,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).

thf(880,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).

thf(881,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).

thf(882,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).

thf(883,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).

thf(884,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).

thf(885,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).

thf(886,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).

thf(887,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).

thf(888,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).

thf(889,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).

thf(890,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).

thf(891,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).

thf(892,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).

thf(893,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).

thf(894,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
      | ( class_Ring__and__Field_Ocomm__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).

thf(895,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).

thf(896,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).

thf(897,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).

thf(898,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).

thf(899,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).

thf(900,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).

thf(901,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).

thf(902,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).

thf(903,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).

thf(904,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).

thf(905,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).

thf(906,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).

thf(907,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).

thf(908,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).

thf(909,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).

thf(910,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).

thf(911,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).

thf(912,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).

thf(913,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).

thf(914,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).

thf(915,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).

thf(916,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).

thf(917,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

thf(918,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).

thf(919,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

thf(920,axiom,
    ! [T: $i] :
      ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).

thf(921,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).

thf(922,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).

thf(923,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).

thf(924,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).

thf(925,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).

thf(926,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).

thf(927,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).

thf(928,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).

thf(929,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).

thf(930,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).

thf(931,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).

thf(932,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).

thf(933,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).

thf(934,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).

thf(935,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).

thf(936,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).

thf(937,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).

thf(938,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

thf(939,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).

thf(940,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).

thf(941,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).

thf(942,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).

thf(943,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).

thf(944,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).

thf(945,axiom,
    ! [T: $i] :
      ( ~ ( class_Power_Orecpower @ T )
      | ( class_Nat_Opower @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).

thf(946,axiom,
    ! [T: $i] :
      ( ~ ( class_Orderings_Oorder @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

thf(947,axiom,
    ! [T: $i] :
      ( ~ ( class_Orderings_Olinorder @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(948,axiom,
    ! [T: $i] :
      ( ~ ( class_Orderings_Olinorder @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

thf(949,axiom,
    ! [T: $i] :
      ( ~ ( class_Orderings_Olinorder @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

thf(950,axiom,
    ! [T: $i] :
      ( ~ ( class_Orderings_Olinorder @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

thf(951,axiom,
    ! [T: $i] :
      ( ~ ( class_Orderings_Olinorder @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

thf(952,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__mult @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).

thf(953,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).

thf(954,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

thf(955,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

thf(956,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).

thf(957,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).

thf(958,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).

thf(959,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

thf(960,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

thf(961,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

thf(962,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).

thf(963,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).

thf(964,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

thf(965,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).

thf(966,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

thf(967,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

thf(968,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

thf(969,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

thf(970,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

thf(971,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).

thf(972,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).

thf(973,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).

thf(974,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

thf(975,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

thf(976,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

thf(977,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).

thf(978,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).

thf(979,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).

thf(980,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).

thf(981,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).

thf(982,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).

thf(983,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).

thf(984,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

thf(985,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

thf(986,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

thf(987,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

thf(988,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).

thf(989,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).

thf(990,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_Orderings_Olinorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

thf(991,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).

thf(992,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).

thf(993,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

thf(994,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).

thf(995,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

thf(996,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

thf(997,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

thf(998,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

thf(999,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

thf(1000,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

thf(1001,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

thf(1002,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

thf(1003,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

thf(1004,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).

thf(1005,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).

thf(1006,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).

thf(1007,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

thf(1008,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

thf(1009,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

thf(1010,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

thf(1011,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

thf(1012,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).

thf(1013,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).

thf(1014,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).

thf(1015,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

thf(1016,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

thf(1017,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Olordered__ab__group @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

thf(1018,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

thf(1019,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).

thf(1020,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).

thf(1021,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).

thf(1022,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).

thf(1023,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).

thf(1024,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).

thf(1025,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

thf(1026,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

thf(1027,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

thf(1028,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

thf(1029,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

thf(1030,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

thf(1031,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).

thf(1032,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).

thf(1033,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).

thf(1034,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

thf(1035,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

thf(1036,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Olordered__ab__group @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

thf(1037,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

thf(1038,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).

thf(1039,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).

thf(1040,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).

thf(1041,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).

thf(1042,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).

thf(1043,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).

thf(1044,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

thf(1045,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).

thf(1046,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

thf(1047,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

thf(1048,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

thf(1049,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).

thf(1050,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).

thf(1051,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).

thf(1052,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).

thf(1053,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

thf(1054,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

thf(1055,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

thf(1056,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

thf(1057,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

thf(1058,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).

thf(1059,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).

thf(1060,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).

thf(1061,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).

thf(1062,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

thf(1063,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
      | ( class_OrderedGroup_Olordered__ab__group @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

thf(1064,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).

thf(1065,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).

thf(1066,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).

thf(1067,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).

thf(1068,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).

thf(1069,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).

thf(1070,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).

thf(1071,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).

thf(1072,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).

thf(1073,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).

thf(1074,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_LOrder_Olorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).

thf(1075,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).

thf(1076,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).

thf(1077,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).

thf(1078,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).

thf(1079,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).

thf(1080,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).

thf(1081,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
      | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).

thf(1082,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

thf(1083,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).

thf(1084,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).

thf(1085,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

thf(1086,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

thf(1087,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).

thf(1088,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).

thf(1089,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).

thf(1090,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).

thf(1091,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).

thf(1092,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).

thf(1093,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

thf(1094,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).

thf(1095,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).

thf(1096,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).

thf(1097,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).

thf(1098,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).

thf(1099,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).

thf(1100,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).

thf(1101,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).

thf(1102,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).

thf(1103,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).

thf(1104,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).

thf(1105,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).

thf(1106,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).

thf(1107,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).

thf(1108,axiom,
    ! [T: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).

thf(1109,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).

thf(1110,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_HOL_Ozero @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).

thf(1111,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).

thf(1112,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Osemiring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).

thf(1113,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).

thf(1114,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Osemigroup__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).

thf(1115,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Numeral_Onumber @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).

thf(1116,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_HOL_Otimes @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).

thf(1117,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).

thf(1118,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).

thf(1119,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Oring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).

thf(1120,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).

thf(1121,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).

thf(1122,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Osemiring__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).

thf(1123,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).

thf(1124,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Omonoid__mult @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).

thf(1125,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).

thf(1126,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_HOL_Oone @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).

thf(1127,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).

thf(1128,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Ocomm__ring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).

thf(1129,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).

thf(1130,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Oring @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).

thf(1131,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).

thf(1132,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Oab__group__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).

thf(1133,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).

thf(1134,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).

thf(1135,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_HOL_Ominus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).

thf(1136,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).

thf(1137,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_Ring__and__Field_Osemiring__0 @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).

thf(1138,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_OrderedGroup_Osemigroup__add @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).

thf(1139,axiom,
    ! [T: $i] :
      ( ~ ( class_Numeral_Onumber__ring @ T )
      | ( class_HOL_Oplus @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).

thf(1140,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

thf(1141,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Omeet__semilorder @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).

thf(1142,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Olorder @ T )
      | ( class_LOrder_Ojoin__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

thf(1143,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Olorder @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

thf(1144,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Olorder @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

thf(1145,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Olorder @ T )
      | ( class_LOrder_Omeet__semilorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

thf(1146,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ T )
      | ( class_Orderings_Oorder @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

thf(1147,axiom,
    ! [T: $i] :
      ( ~ ( class_LOrder_Ojoin__semilorder @ T )
      | ( class_Orderings_Oord @ T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).

thf(1148,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Finite__Set_Ofinite @ ( tc_sum @ T_2 @ T_1 ) )
      | ~ ( class_Finite__Set_Ofinite @ T_1 )
      | ~ ( class_Finite__Set_Ofinite @ T_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).

thf(1149,axiom,
    ! [T_1: $i] : ( class_Nat_Opower @ ( tc_set @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).

thf(1150,axiom,
    ! [T_1: $i] :
      ( ( class_Finite__Set_Ofinite @ ( tc_set @ T_1 ) )
      | ~ ( class_Finite__Set_Ofinite @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).

thf(1151,axiom,
    ! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).

thf(1152,axiom,
    ! [T_1: $i] : ( class_Orderings_Oord @ ( tc_set @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).

thf(1153,axiom,
    ! [T_1: $i] : ( class_HOL_Ominus @ ( tc_set @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).

thf(1154,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Finite__Set_Ofinite @ ( tc_prod @ T_2 @ T_1 ) )
      | ~ ( class_Finite__Set_Ofinite @ T_1 )
      | ~ ( class_Finite__Set_Ofinite @ T_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).

thf(1155,axiom,
    class_HOL_Ominus @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).

thf(1156,axiom,
    class_Wellfounded__Recursion_Owellorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).

thf(1157,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).

thf(1158,axiom,
    class_LOrder_Olorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).

thf(1159,axiom,
    class_LOrder_Ojoin__semilorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).

thf(1160,axiom,
    class_Parity_Oeven__odd @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).

thf(1161,axiom,
    class_Numeral_Onumber @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).

thf(1162,axiom,
    class_Power_Orecpower @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).

thf(1163,axiom,
    class_Divides_Odiv @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).

thf(1164,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).

thf(1165,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).

thf(1166,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).

thf(1167,axiom,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).

thf(1168,axiom,
    class_LOrder_Omeet__semilorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).

thf(1169,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).

thf(1170,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).

thf(1171,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).

thf(1172,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).

thf(1173,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).

thf(1174,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).

thf(1175,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).

thf(1176,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).

thf(1177,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).

thf(1178,axiom,
    class_Ring__and__Field_Osemiring__1__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).

thf(1179,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(1180,axiom,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).

thf(1181,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).

thf(1182,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).

thf(1183,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).

thf(1184,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).

thf(1185,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(1186,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).

thf(1187,axiom,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).

thf(1188,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).

thf(1189,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).

thf(1190,axiom,
    class_Orderings_Oord @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).

thf(1191,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).

thf(1192,axiom,
    class_Ring__and__Field_Osemiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).

thf(1193,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).

thf(1194,axiom,
    class_OrderedGroup_Osemigroup__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_16) ).

thf(1195,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_15) ).

thf(1196,axiom,
    class_OrderedGroup_Osemigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_14) ).

thf(1197,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).

thf(1198,axiom,
    class_Nat_Opower @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(1199,axiom,
    class_HOL_Otimes @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_11) ).

thf(1200,axiom,
    class_HOL_Oplus @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_10) ).

thf(1201,axiom,
    class_HOL_Ozero @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_1) ).

thf(1202,axiom,
    class_HOL_Oone @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).

thf(1203,axiom,
    ! [T_2: $i,T_1: $i] : ( class_Nat_Opower @ ( tc_fun @ T_2 @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_1) ).

thf(1204,axiom,
    ! [T_2: $i,T_1: $i] :
      ( ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
      | ~ ( class_Finite__Set_Ofinite @ T_1 )
      | ~ ( class_Finite__Set_Ofinite @ T_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).

thf(1205,axiom,
    class_Finite__Set_Ofinite @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).

thf(1206,axiom,
    class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

thf(1207,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).

thf(1208,axiom,
    class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).

thf(1209,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).

thf(1210,axiom,
    class_Parity_Oeven__odd @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).

thf(1211,axiom,
    class_Power_Orecpower @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

thf(1212,axiom,
    class_Nat_Opower @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).

thf(1213,axiom,
    class_Divides_Odiv @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).

thf(1214,axiom,
    class_Numeral_Onumber__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).

thf(1215,axiom,
    class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).

thf(1216,axiom,
    class_Numeral_Onumber @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

thf(1217,axiom,
    class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).

thf(1218,axiom,
    class_Ring__and__Field_Oidom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).

thf(1219,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

thf(1220,axiom,
    class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).

thf(1221,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).

thf(1222,axiom,
    class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).

thf(1223,axiom,
    class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).

thf(1224,axiom,
    class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).

thf(1225,axiom,
    class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).

thf(1226,axiom,
    class_Orderings_Oord @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

thf(1227,axiom,
    class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).

thf(1228,axiom,
    class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).

thf(1229,axiom,
    class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).

thf(1230,axiom,
    class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).

thf(1231,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

thf(1232,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

thf(1233,axiom,
    class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

thf(1234,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

thf(1235,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

thf(1236,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

thf(1237,axiom,
    class_HOL_Ozero @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).

thf(1238,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

thf(1239,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

thf(1240,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

thf(1241,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

thf(1242,axiom,
    class_Orderings_Olinorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

thf(1243,axiom,
    class_LOrder_Olorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

thf(1244,axiom,
    class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

thf(1245,axiom,
    class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

thf(1246,axiom,
    class_Orderings_Oorder @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

thf(1247,axiom,
    class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).

thf(1248,axiom,
    class_HOL_Otimes @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).

thf(1249,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).

thf(1250,axiom,
    class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).

thf(1251,axiom,
    class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).

thf(1252,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).

thf(1253,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).

thf(1254,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

thf(1255,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

thf(1256,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

thf(1257,axiom,
    class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).

thf(1258,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).

thf(1259,axiom,
    class_HOL_Oplus @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).

thf(1260,axiom,
    class_Ring__and__Field_Oring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).

thf(1261,axiom,
    class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

thf(1262,axiom,
    class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).

thf(1263,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).

thf(1264,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).

thf(1265,axiom,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).

thf(1266,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).

thf(1267,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).

thf(1268,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).

thf(1269,axiom,
    class_Ring__and__Field_Osemiring @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).

thf(1270,axiom,
    class_HOL_Oone @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).

thf(1271,axiom,
    class_HOL_Ominus @ tc_IntDef_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).

thf(1272,axiom,
    ! [T_1: $i] :
      ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ T_1 ) )
      | ~ ( class_Finite__Set_Ofinite @ T_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).

thf(1273,axiom,
    ! [V_rb: $i,T_b: $i,V_ra: $i,T_a: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ V_rb @ T_b )
      | ~ ( c_Wellfounded__Recursion_Owf @ V_ra @ T_a )
      | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ V_ra @ V_rb @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

thf(1274,axiom,
    c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(1275,axiom,
    ! [V_R2: $i,T_b: $i,V_R1: $i,T_a: $i] :
      ( ~ ( c_Relation_Otrans @ V_R2 @ T_b )
      | ~ ( c_Relation_Otrans @ V_R1 @ T_a )
      | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ V_R1 @ V_R2 @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

thf(1276,axiom,
    c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).

thf(1277,axiom,
    ! [T_a: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(1278,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
      | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

thf(1279,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
      | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

thf(1280,axiom,
    ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

thf(1281,axiom,
    ! [V_p: $i,V_r: $i,T_a: $i] :
      ( ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) )
      | ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

thf(1282,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
      | ( c_in @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ T_a )
      | ( c_in @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ V_B @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

thf(1283,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
      | ( c_in @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ T_a )
      | ( V_u
        = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

thf(1284,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
      | ( c_in @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ V_B @ T_b )
      | ( V_u
        = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

thf(1285,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
      | ( V_u
        = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
      | ( V_u
        = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

thf(1286,axiom,
    ! [V_b: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
      ( ~ ( c_in @ V_b @ V_B @ T_a )
      | ( c_in @ ( c_Sum__Type_OInr @ V_b @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_b @ T_a ) @ ( tc_sum @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

thf(1287,axiom,
    ! [V_a: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
      ( ~ ( c_in @ V_a @ V_A @ T_a )
      | ( c_in @ ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

thf(1288,axiom,
    ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(1289,axiom,
    ! [V_B: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
      | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( V_A = V_B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(1290,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a )
      | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(1291,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
      | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(1292,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
      ( ~ ( c_in @ V_c @ V_A @ T_a )
      | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( c_in @ V_c @ V_B @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(1293,axiom,
    ! [V_a: $i,T_a: $i,V_b: $i] :
      ( ( ( c_insert @ V_a @ c_emptyset @ T_a )
       != ( c_insert @ V_b @ c_emptyset @ T_a ) )
      | ( V_a = V_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(1294,axiom,
    ! [V_a: $i,T_a: $i] : ( c_in @ V_a @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(1295,axiom,
    ! [V_b: $i,V_a: $i,T_a: $i] :
      ( ~ ( c_in @ V_b @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a )
      | ( V_b = V_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(1296,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( V_A = V_B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

thf(1297,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

thf(1298,axiom,
    ! [V_A: $i,V_B: $i,T_a: $i] :
      ( ~ ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

thf(1299,axiom,
    ! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(1300,axiom,
    ! [V_A: $i,V_C: $i,T_a: $i] :
      ( ~ ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a )
      | ( c_in @ V_A @ ( c_Main_OUnionE__1 @ V_A @ V_C @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

thf(1301,axiom,
    ! [V_A: $i,V_C: $i,T_a: $i] :
      ( ~ ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a )
      | ( c_in @ ( c_Main_OUnionE__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

thf(1302,axiom,
    ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ c_UNIV @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

thf(1303,axiom,
    ! [V_A: $i,V_C: $i,T_a: $i] :
      ( ~ ( c_in @ V_A @ ( c_Main_OInterI__1 @ V_A @ V_C @ T_a ) @ T_a )
      | ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

thf(1304,axiom,
    ! [V_A: $i,V_C: $i,T_a: $i] :
      ( ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a )
      | ( c_in @ ( c_Main_OInterI__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

thf(1305,axiom,
    ! [V_k: $i] : ( c_in @ ( c_SetInterval_OlessThan @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

thf(1306,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

thf(1307,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

thf(1308,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

thf(1309,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

thf(1310,axiom,
    ! [V_k: $i] : ( c_in @ ( c_SetInterval_OatMost @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

thf(1311,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

thf(1312,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

thf(1313,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

thf(1314,axiom,
    ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

thf(1315,axiom,
    ! [V_b: $i,V_c: $i,T_b: $i,T_c: $i,V_r: $i,V_a: $i,T_a: $i,V_s: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_r @ ( tc_prod @ T_b @ T_c ) )
      | ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_s @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ ( tc_prod @ T_a @ T_c ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

thf(1316,axiom,
    ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
      | ( V_xz
        = ( c_Pair @ ( c_Main_Orel__compE__1 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__3 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

thf(1317,axiom,
    ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__2 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_a @ T_c ) @ V_s @ ( tc_prod @ T_a @ T_c ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

thf(1318,axiom,
    ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__3 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_c @ T_b ) @ V_r @ ( tc_prod @ T_c @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

thf(1319,axiom,
    ! [V_a: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_a @ V_A @ T_a )
      | ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

thf(1320,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
      | ( c_in @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

thf(1321,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_c @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
      | ( V_c
        = ( c_Pair @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

thf(1322,axiom,
    ! [V_yx: $i,V_r: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_yx @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
      | ( V_yx
        = ( c_Pair @ ( c_Main_OconverseE__2 @ V_r @ V_yx @ T_b @ T_a ) @ ( c_Main_OconverseE__1 @ V_r @ V_yx @ T_b @ T_a ) @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

thf(1323,axiom,
    ! [V_yx: $i,V_r: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_yx @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ V_r @ V_yx @ T_b @ T_a ) @ ( c_Main_OconverseE__2 @ V_r @ V_yx @ T_b @ T_a ) @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

thf(1324,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

thf(1325,axiom,
    ! [V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
      | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

thf(1326,axiom,
    ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,T_b: $i,V_r: $i] :
      ( ~ ( c_in @ V_a @ V_A @ T_a )
      | ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

thf(1327,axiom,
    ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
      | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

thf(1328,axiom,
    ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
      ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
      | ( c_in @ ( c_Main_OImageE__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

thf(1329,axiom,
    ! [V_p: $i,T_a: $i] :
      ( ~ ( c_in @ V_p @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
      | ( V_p
        = ( c_Pair @ ( c_Main_OIdE__1 @ V_p @ T_a ) @ ( c_Main_OIdE__1 @ V_p @ T_a ) @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

thf(1330,axiom,
    ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
      | ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

thf(1331,axiom,
    ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
      | ( c_in @ ( c_Pair @ V_a @ ( c_Main_ODomainE__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

thf(1332,axiom,
    ! [T_a: $i,V_x: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ( c_lessequals @ V_x @ V_x @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(1333,axiom,
    ! [V_n: $i] : ( c_less @ c_0 @ ( c_Suc @ V_n ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

thf(1334,axiom,
    ! [V_n: $i] :
      ~ ( c_less @ V_n @ V_n @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(1335,axiom,
    ! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(1336,axiom,
    ! [V_n: $i] : ( c_lessequals @ c_0 @ V_n @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(1337,axiom,
    ! [V_r: $i,T_a: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
      | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

thf(1338,axiom,
    ! [V_r: $i,T_a: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
      | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

thf(1339,axiom,
    ! [V_A: $i,T_a: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(1340,axiom,
    ! [V_a: $i,V_A: $i,T_a: $i,V_l: $i] :
      ( ~ ( c_in @ V_a @ V_A @ T_a )
      | ~ ( c_in @ V_l @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ( c_in @ ( c_List_Olist_OCons @ V_a @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(1341,axiom,
    ! [V_x: $i,V_l: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ( c_in @ V_x @ V_A @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(1342,axiom,
    ! [V_x: $i,V_l: $i,T_a: $i,V_A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ( c_in @ V_l @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(1343,axiom,
    ! [V_xs: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_xs @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

thf(1344,axiom,
    ! [V_xs: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( V_xs = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

thf(1345,axiom,
    ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).

thf(1346,axiom,
    ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ V_ys @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).

thf(1347,axiom,
    ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( V_xs
        = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( c_Main_Olistrel__Cons2__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).

thf(1348,axiom,
    ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( c_in @ ( c_Pair @ V_y @ ( c_Main_Olistrel__Cons1__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).

thf(1349,axiom,
    ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( c_in @ ( c_Pair @ V_ys @ ( c_Main_Olistrel__Cons1__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).

thf(1350,axiom,
    ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
      | ( V_xs
        = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( c_Main_Olistrel__Cons1__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).

thf(1351,axiom,
    ! [V_xs: $i,T_a: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).

thf(1352,axiom,
    ! [V_A: $i,V_xs: $i,T_a: $i] :
      ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ V_A @ V_xs @ T_a ) @ V_A @ T_a )
      | ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(1353,axiom,
    ! [V_xs: $i,V_A: $i,T_a: $i] :
      ( ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ( c_in @ ( c_Main_Oin__listsI__1 @ V_A @ V_xs @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(1354,axiom,
    ! [V_xs: $i,V_A: $i,T_a: $i,V_U: $i] :
      ( ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
      | ~ ( c_in @ V_U @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
      | ( c_in @ V_U @ V_A @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(1355,axiom,
    ! [V_xs: $i,T_a: $i] : ( c_in @ ( c_List_Oset @ V_xs @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

thf(1356,axiom,
    ! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).

thf(1357,axiom,
    ! [V_m: $i,V_d: $i] :
      ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_IntDef_Oint )
       != c_0 )
      | ( V_m
        = ( c_times @ V_d @ ( c_Main_Ozmod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_IntDef_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

thf(1358,axiom,
    ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_m @ V_k @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

thf(1359,axiom,
    ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_k @ V_m @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

thf(1360,axiom,
    ! [V_m: $i] : ( c_Divides_Oop_Advd @ c_1 @ V_m @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

thf(1361,axiom,
    ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

thf(1362,axiom,
    ! [V_n: $i,V_m: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ V_n ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ V_m ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

thf(1363,axiom,
    ! [V_n: $i,V_m: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ V_n ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ V_m ) @ tc_IntDef_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

thf(1364,axiom,
    ! [V_S: $i,T_a: $i,V_y: $i,V_x: $i] :
      ( ~ ( c_Infinite__Set_Oatmost__one @ V_S @ T_a )
      | ~ ( c_in @ V_y @ V_S @ T_a )
      | ~ ( c_in @ V_x @ V_S @ T_a )
      | ( V_y = V_x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(1365,axiom,
    ! [V_m: $i,V_n: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ V_n @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).

thf(1366,axiom,
    ! [V_m: $i,V_n: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ V_m @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).

thf(1367,axiom,
    ! [V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
      | ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_Union @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

thf(1368,axiom,
    ! [V_A: $i,T_a: $i] :
      ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
      | ( c_in @ ( c_Main_Ofinite__Union__1 @ V_A @ T_a ) @ V_A @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_Union @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

thf(1369,axiom,
    ! [V_G: $i,T_a: $i,V_F: $i] :
      ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(1370,axiom,
    ! [V_F: $i,T_a: $i,V_G: $i] :
      ( ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

thf(1371,axiom,
    ! [V_A: $i,T_a: $i,V_a: $i] :
      ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_insert @ V_a @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

thf(1372,axiom,
    ! [T_a: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

thf(1373,axiom,
    ! [V_m: $i,V_d: $i] :
      ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_nat )
       != c_0 )
      | ( V_m
        = ( c_times @ V_d @ ( c_Main_Omod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

thf(1374,axiom,
    ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_m @ V_k @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).

thf(1375,axiom,
    ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_k @ V_m @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

thf(1376,axiom,
    ! [V_k: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ V_k @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

thf(1377,axiom,
    ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

thf(1378,axiom,
    ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
      ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).

thf(1379,axiom,
    ! [V_M: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
      ( ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).

thf(1380,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).

thf(1381,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( V_u
        = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).

thf(1382,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( V_u
        = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).

thf(1383,axiom,
    ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( V_u
        = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
      | ( V_u
        = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).

thf(1384,axiom,
    ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i,V_M: $i,V_A: $i] :
      ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

thf(1385,axiom,
    ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Main_OuprodE__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

thf(1386,axiom,
    ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( c_in @ ( c_Main_OuprodE__2 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

thf(1387,axiom,
    ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
      | ( V_c
        = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ ( c_Main_OuprodE__2 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ T_a @ T_b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

thf(1388,axiom,
    ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

thf(1389,axiom,
    ! [V_M: $i,V_M_H: $i,T_a: $i,T_b: $i,V_r: $i,V_s: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ V_M_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

thf(1390,axiom,
    ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).

thf(1391,axiom,
    ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( V_w
        = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).

thf(1392,axiom,
    ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( V_w
        = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).

thf(1393,axiom,
    ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( V_w
        = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( V_w
        = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).

thf(1394,axiom,
    ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i,V_M: $i,V_M_H: $i,V_r: $i] :
      ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

thf(1395,axiom,
    ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__3 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

thf(1396,axiom,
    ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__4 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

thf(1397,axiom,
    ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
      ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
      | ( V_c
        = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__2 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__4 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

thf(1398,axiom,
    ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
      ( ( ( c_Datatype__Universe_ONumb @ V_x @ T_a @ T_b )
       != ( c_Datatype__Universe_ONumb @ V_y @ T_a @ T_b ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).

thf(1399,axiom,
    ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
      ( ( ( c_Datatype__Universe_OLeaf @ V_x @ T_a @ T_b )
       != ( c_Datatype__Universe_OLeaf @ V_y @ T_a @ T_b ) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).

thf(1400,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(1401,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[1400]) ).

thf(1402,negated_conjecture,
    ~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ v_G ) @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1403,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[1401]) ).

thf(1404,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Osynth @ V_H ) ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(1405,plain,
    ( ( ! [V_H: $i,V_H_H: $i,V_G: $i,V_G_H: $i] :
          ( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_H ) @ ( c_Message_Oanalz @ V_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
          | ~ ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
          | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ V_G_H @ V_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(1406,plain,
    ( ( ! [V_n: $i,V_H: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ V_n ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(1407,plain,
    ( ( ! [V_Y: $i,V_H: $i,V_X: $i] :
          ( ~ ( c_in @ V_Y @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(1408,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(1409,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(1410,plain,
    ( ( ! [V_X: $i,V_H: $i,V_K: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(1411,plain,
    ( ( ! [V_agt: $i,V_H: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ V_agt ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(1412,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Oparts @ ( c_Message_Oparts @ V_H ) ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(1413,plain,
    ( ( ! [V_X: $i] :
          ~ ( c_in @ V_X @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(1414,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(1415,plain,
    ( ( ! [V_nat: $i,V_msg: $i,V_nat_H: $i,V_msg_H: $i] :
          ( ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
           != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
          | ( V_msg = V_msg_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(1416,plain,
    ( ( ! [V_nat: $i,V_msg: $i,V_nat_H: $i,V_msg_H: $i] :
          ( ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
           != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(1417,plain,
    ( ( ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i,V_msg2_H: $i] :
          ( ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
           != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
          | ( V_msg2 = V_msg2_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(1418,plain,
    ( ( ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i,V_msg2_H: $i] :
          ( ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
           != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
          | ( V_msg1 = V_msg1_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(1419,plain,
    ( ( ! [V_msg: $i,V_msg_H: $i] :
          ( ( ( c_Message_Omsg_OHash @ V_msg )
           != ( c_Message_Omsg_OHash @ V_msg_H ) )
          | ( V_msg = V_msg_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(1420,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_OKey @ V_nat )
           != ( c_Message_Omsg_OKey @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(1421,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_ONonce @ V_nat )
           != ( c_Message_Omsg_ONonce @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(1422,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_ONumber @ V_nat )
           != ( c_Message_Omsg_ONumber @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(1423,plain,
    ( ( ! [V_agent: $i,V_agent_H: $i] :
          ( ( ( c_Message_Omsg_OAgent @ V_agent )
           != ( c_Message_Omsg_OAgent @ V_agent_H ) )
          | ( V_agent = V_agent_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(1424,plain,
    ( ( ! [V_c: $i,V_G: $i,V_H: $i] :
          ( ~ ( c_in @ V_c @ ( c_Message_Oparts @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
          | ( c_in @ V_c @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_c @ ( c_Message_Oparts @ V_G ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(1425,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(1426,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(1427,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ V_K ) ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(1428,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Oagent_OFriend @ V_nat )
           != ( c_Message_Oagent_OFriend @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(1429,plain,
    ( ( ! [V_nat: $i] :
          ( c_Message_Oagent_OSpy
         != ( c_Message_Oagent_OFriend @ V_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(1430,plain,
    ( ( ! [V_nat: $i] :
          ( ( c_Message_Oagent_OFriend @ V_nat )
         != c_Message_Oagent_OSpy ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(1431,plain,
    ( ( c_Message_Oagent_OSpy != c_Message_Oagent_OServer )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(1432,plain,
    ( ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(1433,plain,
    ( ( ! [V_nat_H: $i] :
          ( ( c_Message_Oagent_OFriend @ V_nat_H )
         != c_Message_Oagent_OServer ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(1434,plain,
    ( ( ! [V_nat_H: $i] :
          ( c_Message_Oagent_OServer
         != ( c_Message_Oagent_OFriend @ V_nat_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(1435,plain,
    ( ( ! [V_n: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_n ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_ONonce @ V_n ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(1436,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(1437,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(1438,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(1439,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(1440,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(1441,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(1442,plain,
    ( ( ! [V_K: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(1443,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(1444,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(1445,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(1446,plain,
    ( ( ! [V_x: $i,V_y: $i] :
          ( ~ ( c_less @ V_x @ V_y @ tc_nat )
          | ( c_in @ ( c_Pair @ V_x @ V_y @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[43]) ).

thf(1447,plain,
    ( ( ! [V_x: $i,V_y: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
          | ( c_less @ V_x @ V_y @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[44]) ).

thf(1448,plain,
    ( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[45]) ).

thf(1449,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[46]) ).

thf(1450,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ V_r @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[47]) ).

thf(1451,plain,
    ( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[48]) ).

thf(1452,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[49]) ).

thf(1453,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[50]) ).

thf(1454,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[51]) ).

thf(1455,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
          | ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[52]) ).

thf(1456,plain,
    ( ( ! [V_b: $i,T_b: $i,T_a: $i,V_a: $i] :
          ( ( c_Sum__Type_OInr @ V_b @ T_b @ T_a )
         != ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[53]) ).

thf(1457,plain,
    ( ( ! [V_x: $i,T_b: $i,T_a: $i,V_y: $i] :
          ( ( ( c_Sum__Type_OInr @ V_x @ T_b @ T_a )
           != ( c_Sum__Type_OInr @ V_y @ T_b @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[54]) ).

thf(1458,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
          ( ( c_Sum__Type_OInl @ V_a @ T_a @ T_b )
         != ( c_Sum__Type_OInr @ V_b @ T_b @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[55]) ).

thf(1459,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Sum__Type_OInl @ V_x @ T_a @ T_b )
           != ( c_Sum__Type_OInl @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[56]) ).

thf(1460,plain,
    ( ( ! [V_A: $i,V_x: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ ( c_insert @ V_x @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) )
          | ( ( c_insert @ V_x @ c_emptyset @ T_a )
            = ( c_insert @ V_x @ V_A @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[57]) ).

thf(1461,plain,
    ( ( ! [V_b: $i,T_a: $i,V_a: $i,V_A: $i] :
          ( ( ( c_insert @ V_b @ c_emptyset @ T_a )
           != ( c_insert @ V_a @ V_A @ T_a ) )
          | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[58]) ).

thf(1462,plain,
    ( ( ! [V_b: $i,T_a: $i,V_a: $i,V_A: $i] :
          ( ( ( c_insert @ V_b @ c_emptyset @ T_a )
           != ( c_insert @ V_a @ V_A @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[59]) ).

thf(1463,plain,
    ( ( ! [V_A: $i,V_x: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ ( c_insert @ V_x @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) )
          | ( ( c_insert @ V_x @ V_A @ T_a )
            = ( c_insert @ V_x @ c_emptyset @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[60]) ).

thf(1464,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ V_A @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[61]) ).

thf(1465,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ V_A @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[62]) ).

thf(1466,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ~ ( c_less @ V_A @ c_emptyset @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[63]) ).

thf(1467,plain,
    ( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
          | ( c_in @ V_a @ V_A @ T_a )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[64]) ).

thf(1468,plain,
    ( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[65]) ).

thf(1469,plain,
    ( ( ! [V_a: $i,V_B: $i,T_a: $i,V_b: $i] :
          ( ~ ( c_in @ V_a @ V_B @ T_a )
          | ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[66]) ).

thf(1470,plain,
    ( ( ! [V_a: $i,T_a: $i] :
          ~ ( c_in @ V_a @ c_emptyset @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[67]) ).

thf(1471,plain,
    ( ( ! [V_A: $i,V_X: $i,T_a: $i,V_C: $i] :
          ( ~ ( c_in @ V_A @ V_X @ T_a )
          | ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
          | ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[68]) ).

thf(1472,plain,
    ( ( ! [T_a: $i] :
          ( ( c_union @ c_emptyset @ c_emptyset @ T_a )
          = c_emptyset ) )
    = $true ),
    inference(unfold_def,[status(thm)],[69]) ).

thf(1473,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ( ( c_union @ V_A @ V_B @ T_a )
           != c_emptyset )
          | ( V_B = c_emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[70]) ).

thf(1474,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ( ( c_union @ V_A @ V_B @ T_a )
           != c_emptyset )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[71]) ).

thf(1475,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
          | ( c_in @ V_c @ V_B @ T_a )
          | ( c_in @ V_c @ V_A @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[72]) ).

thf(1476,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[73]) ).

thf(1477,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[74]) ).

thf(1478,plain,
    ( ( c_UNIV != c_emptyset )
    = $true ),
    inference(unfold_def,[status(thm)],[75]) ).

thf(1479,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( c_in @ V_A @ ( c_Pow @ V_B @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[76]) ).

thf(1480,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Pow @ V_B @ T_a ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[77]) ).

thf(1481,plain,
    ( ( ! [V_X: $i,V_C: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
          | ~ ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a )
          | ( c_in @ V_A @ V_X @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[78]) ).

thf(1482,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ~ ( c_in @ V_c @ V_A @ T_a )
          | ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[79]) ).

thf(1483,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
          | ( c_in @ V_c @ V_A @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[80]) ).

thf(1484,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
          | ( c_in @ V_c @ V_B @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[81]) ).

thf(1485,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ( c_in @ V_c @ V_B @ T_a )
          | ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[82]) ).

thf(1486,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a )
          | ( c_in @ V_c @ V_A @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[83]) ).

thf(1487,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ~ ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[84]) ).

thf(1488,plain,
    ( ( ! [V_B: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
          | ( c_lessequals @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[85]) ).

thf(1489,plain,
    ( ( ! [V_A: $i,T_a: $i,V_B: $i] :
          ( ~ ( c_lessequals @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[86]) ).

thf(1490,plain,
    ( ( ! [V_A: $i,T_a: $i,V_B: $i] :
          ( ( ( c_uminus @ V_A @ ( tc_set @ T_a ) )
           != ( c_uminus @ V_B @ ( tc_set @ T_a ) ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[87]) ).

thf(1491,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ( c_in @ V_c @ V_A @ T_a )
          | ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[88]) ).

thf(1492,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ~ ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[89]) ).

thf(1493,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ~ ( c_lessequals @ V_x @ V_y @ T_a )
          | ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[90]) ).

thf(1494,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_x @ V_y @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[91]) ).

thf(1495,plain,
    ( ( ! [T_a: $i,V_i: $i,V_k: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_less @ V_i @ V_k @ T_a )
          | ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[92]) ).

thf(1496,plain,
    ( ( ! [T_a: $i,V_i: $i,V_k: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a )
          | ( c_less @ V_i @ V_k @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[93]) ).

thf(1497,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ( ( c_SetInterval_OlessThan @ V_x @ T_a )
           != ( c_SetInterval_OlessThan @ V_y @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[94]) ).

thf(1498,plain,
    ( ( ! [T_a: $i,V_y: $i,V_x: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ~ ( c_lessequals @ V_y @ V_x @ T_a )
          | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[95]) ).

thf(1499,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_y @ V_x @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[96]) ).

thf(1500,plain,
    ( ( ! [T_a: $i,V_k: $i,V_i: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_less @ V_k @ V_i @ T_a )
          | ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[97]) ).

thf(1501,plain,
    ( ( ! [T_a: $i,V_i: $i,V_k: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a )
          | ( c_less @ V_k @ V_i @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[98]) ).

thf(1502,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ( ( c_SetInterval_OgreaterThan @ V_x @ T_a )
           != ( c_SetInterval_OgreaterThan @ V_y @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[99]) ).

thf(1503,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_lessequals @ V_x @ V_y @ T_a )
          | ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[100]) ).

thf(1504,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_x @ V_y @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[101]) ).

thf(1505,plain,
    ( ( ! [T_a: $i,V_i: $i,V_k: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_lessequals @ V_i @ V_k @ T_a )
          | ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[102]) ).

thf(1506,plain,
    ( ( ! [T_a: $i,V_i: $i,V_k: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a )
          | ( c_lessequals @ V_i @ V_k @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[103]) ).

thf(1507,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ( ( c_SetInterval_OatMost @ V_x @ T_a )
           != ( c_SetInterval_OatMost @ V_y @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[104]) ).

thf(1508,plain,
    ( ( ! [T_a: $i,V_y: $i,V_x: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_lessequals @ V_y @ V_x @ T_a )
          | ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[105]) ).

thf(1509,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_y @ V_x @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[106]) ).

thf(1510,plain,
    ( ( ! [T_a: $i,V_k: $i,V_i: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_lessequals @ V_k @ V_i @ T_a )
          | ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[107]) ).

thf(1511,plain,
    ( ( ! [T_a: $i,V_i: $i,V_k: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ~ ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a )
          | ( c_lessequals @ V_k @ V_i @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[108]) ).

thf(1512,plain,
    ( ( ! [T_a: $i,V_x: $i,V_y: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ( ( c_SetInterval_OatLeast @ V_x @ T_a )
           != ( c_SetInterval_OatLeast @ V_y @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[109]) ).

thf(1513,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[110]) ).

thf(1514,plain,
    ( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[111]) ).

thf(1515,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[112]) ).

thf(1516,plain,
    ( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
          | ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_insert @ V_a @ c_emptyset @ T_b ) @ T_b @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[113]) ).

thf(1517,plain,
    ( ( ! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_insert @ V_a @ c_emptyset @ T_b ) @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[114]) ).

thf(1518,plain,
    ( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[115]) ).

thf(1519,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
          ( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
           != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
          | ( V_b = V_b_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[116]) ).

thf(1520,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
          ( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
           != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[117]) ).

thf(1521,plain,
    ( ( ! [T_a: $i,V_x: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_less @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[118]) ).

thf(1522,plain,
    ( ( c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0 )
    = $true ),
    inference(unfold_def,[status(thm)],[119]) ).

thf(1523,plain,
    ( ( c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 )
    = $true ),
    inference(unfold_def,[status(thm)],[120]) ).

thf(1524,plain,
    ( ( ! [V_n: $i] :
          ~ ( c_less @ V_n @ c_0 @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[121]) ).

thf(1525,plain,
    ( ( ! [V_j: $i,V_i: $i] :
          ~ ( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[122]) ).

thf(1526,plain,
    ( ( ! [V_i: $i,V_j: $i] :
          ~ ( c_less @ ( c_plus @ V_i @ V_j @ tc_nat ) @ V_i @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[123]) ).

thf(1527,plain,
    ( ( ~ ( c_less @ c_0 @ c_0 @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[124]) ).

thf(1528,plain,
    ( ( ! [V_n: $i] :
          ( ( c_less @ c_0 @ V_n @ tc_nat )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[125]) ).

thf(1529,plain,
    ( ( c_less @ c_0 @ c_1 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[126]) ).

thf(1530,plain,
    ( ( ! [V_n: $i] :
          ( ~ ( c_less @ V_n @ c_1 @ tc_nat )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[127]) ).

thf(1531,plain,
    ( ( c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[128]) ).

thf(1532,plain,
    ( ( ! [V_n: $i] :
          ( ~ ( c_less @ V_n @ ( c_Suc @ c_0 ) @ tc_nat )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[129]) ).

thf(1533,plain,
    ( ( c_lessequals @ c_0 @ c_0 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[130]) ).

thf(1534,plain,
    ( ( ! [V_i: $i] :
          ( ~ ( c_lessequals @ V_i @ c_0 @ tc_nat )
          | ( V_i = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[131]) ).

thf(1535,plain,
    ( ( ( c_plus @ c_0 @ c_0 @ tc_nat )
      = c_0 )
    = $true ),
    inference(unfold_def,[status(thm)],[132]) ).

thf(1536,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_plus @ V_m @ V_n @ tc_nat )
           != c_0 )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[133]) ).

thf(1537,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_plus @ V_m @ V_n @ tc_nat )
           != c_0 )
          | ( V_m = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[134]) ).

thf(1538,plain,
    ( ( ! [V_n: $i,V_m: $i] :
          ( ~ ( c_less @ c_0 @ V_n @ tc_nat )
          | ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[135]) ).

thf(1539,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ~ ( c_less @ c_0 @ V_m @ tc_nat )
          | ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[136]) ).

thf(1540,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ~ ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat )
          | ( c_less @ c_0 @ V_n @ tc_nat )
          | ( c_less @ c_0 @ V_m @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[137]) ).

thf(1541,plain,
    ( ( ! [V_m: $i] :
          ( c_0
         != ( c_Suc @ V_m ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[138]) ).

thf(1542,plain,
    ( ( ! [V_m: $i] :
          ( ( c_Suc @ V_m )
         != c_0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[139]) ).

thf(1543,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ~ ( c_less @ V_m @ V_n @ tc_nat )
          | ( c_less @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[140]) ).

thf(1544,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ~ ( c_less @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
          | ( c_less @ V_m @ V_n @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[141]) ).

thf(1545,plain,
    ( ( ! [V_n: $i,V_m: $i] :
          ( ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
          | ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[142]) ).

thf(1546,plain,
    ( ( ! [V_n: $i,V_m: $i] :
          ( ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
          | ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[143]) ).

thf(1547,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_Suc @ V_m )
           != ( c_Suc @ V_n ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[144]) ).

thf(1548,plain,
    ( ( ! [T_a: $i] :
          ( ( c_List_Oset @ c_List_Olist_ONil @ T_a )
          = c_emptyset ) )
    = $true ),
    inference(unfold_def,[status(thm)],[145]) ).

thf(1549,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_List_Oset @ V_xs @ T_a )
           != c_emptyset )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[146]) ).

thf(1550,plain,
    ( ( ! [T_a: $i] :
          ( c_emptyset
          = ( c_List_Oset @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[147]) ).

thf(1551,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( c_emptyset
           != ( c_List_Oset @ V_xs @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[148]) ).

thf(1552,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( V_xs
          = ( c_append @ V_xs @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[149]) ).

thf(1553,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
          ( ( V_xs
           != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[150]) ).

thf(1554,plain,
    ( ( ! [V_ys: $i,T_a: $i] :
          ( V_ys
          = ( c_append @ c_List_Olist_ONil @ V_ys @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[151]) ).

thf(1555,plain,
    ( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
          ( ( V_ys
           != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[152]) ).

thf(1556,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
          ( ( ( c_append @ V_xs @ V_ys @ T_a )
           != ( c_append @ V_xs @ V_zs @ T_a ) )
          | ( V_ys = V_zs ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[153]) ).

thf(1557,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
          ( ( ( c_List_Orev @ V_xs @ T_a )
           != ( c_List_Orev @ V_ys @ T_a ) )
          | ( V_xs = V_ys ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[154]) ).

thf(1558,plain,
    ( ( ! [T_a: $i] :
          ( ( c_List_Orev @ c_List_Olist_ONil @ T_a )
          = c_List_Olist_ONil ) )
    = $true ),
    inference(unfold_def,[status(thm)],[155]) ).

thf(1559,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_List_Orev @ V_xs @ T_a )
           != c_List_Olist_ONil )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[156]) ).

thf(1560,plain,
    ( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
          ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
          = ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[157]) ).

thf(1561,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
          ( ( ( c_List_Orev @ V_xs @ T_a )
           != ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
          | ( V_xs
            = ( c_append @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[158]) ).

thf(1562,plain,
    ( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
          ( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
           != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
          | ( V_list = V_list_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[159]) ).

thf(1563,plain,
    ( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
          ( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
           != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[160]) ).

thf(1564,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
         != c_List_Olist_ONil ) )
    = $true ),
    inference(unfold_def,[status(thm)],[161]) ).

thf(1565,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( c_List_Olist_ONil
         != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[162]) ).

thf(1566,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_List_Oremdups @ V_xs @ T_a )
           != V_xs )
          | ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
            = ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[163]) ).

thf(1567,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
           != ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
          | ( ( c_List_Oremdups @ V_xs @ T_a )
            = V_xs ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[164]) ).

thf(1568,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( c_less @ c_0 @ ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[165]) ).

thf(1569,plain,
    ( ( ! [T_a: $i] :
          ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[166]) ).

thf(1570,plain,
    ( ( ! [T_a: $i] :
          ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) )
          = c_0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[167]) ).

thf(1571,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
           != c_0 )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[168]) ).

thf(1572,plain,
    ( ( ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i,V_nibble2_H: $i] :
          ( ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
           != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
          | ( V_nibble2 = V_nibble2_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[169]) ).

thf(1573,plain,
    ( ( ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i,V_nibble2_H: $i] :
          ( ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
           != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
          | ( V_nibble1 = V_nibble1_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[170]) ).

thf(1574,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( c_append @ V_xs @ c_List_Olist_ONil @ T_a )
          = V_xs ) )
    = $true ),
    inference(unfold_def,[status(thm)],[171]) ).

thf(1575,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
          ( ( ( c_append @ V_xs @ V_ys @ T_a )
           != V_xs )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[172]) ).

thf(1576,plain,
    ( ( ! [V_ys: $i,T_a: $i] :
          ( ( c_append @ c_List_Olist_ONil @ V_ys @ T_a )
          = V_ys ) )
    = $true ),
    inference(unfold_def,[status(thm)],[173]) ).

thf(1577,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
          ( ( ( c_append @ V_xs @ V_ys @ T_a )
           != V_ys )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[174]) ).

thf(1578,plain,
    ( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
          ( ( ( c_append @ V_ys @ V_xs @ T_a )
           != ( c_append @ V_zs @ V_xs @ T_a ) )
          | ( V_ys = V_zs ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[175]) ).

thf(1579,plain,
    ( ( ! [T_a: $i] :
          ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a )
          = c_List_Olist_ONil ) )
    = $true ),
    inference(unfold_def,[status(thm)],[176]) ).

thf(1580,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
          ( ( ( c_append @ V_xs @ V_ys @ T_a )
           != c_List_Olist_ONil )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[177]) ).

thf(1581,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
          ( ( ( c_append @ V_xs @ V_ys @ T_a )
           != c_List_Olist_ONil )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[178]) ).

thf(1582,plain,
    ( ( ! [V_ys: $i,V_A: $i,T_a: $i,V_xs: $i] :
          ( ~ ( c_in @ V_ys @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[179]) ).

thf(1583,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_ys @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[180]) ).

thf(1584,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[181]) ).

thf(1585,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
          ( ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
           != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[182]) ).

thf(1586,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
          ( ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
           != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
          | ( V_xs = V_ys ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[183]) ).

thf(1587,plain,
    ( ( ! [V_ys: $i,T_a: $i,V_r: $i] :
          ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ V_ys @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[184]) ).

thf(1588,plain,
    ( ( ! [T_a: $i] :
          ( c_List_Olist_ONil
          = ( c_List_Orev @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[185]) ).

thf(1589,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( c_List_Olist_ONil
           != ( c_List_Orev @ V_xs @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[186]) ).

thf(1590,plain,
    ( ( ! [T_a: $i] :
          ( c_List_Olist_ONil
          = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[187]) ).

thf(1591,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
          ( ( c_List_Olist_ONil
           != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[188]) ).

thf(1592,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
          ( ( c_List_Olist_ONil
           != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[189]) ).

thf(1593,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_r: $i] :
          ~ ( c_in @ ( c_Pair @ V_xs @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[190]) ).

thf(1594,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ ( c_uminus @ V_z @ tc_IntDef_Oint ) @ V_w @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[191]) ).

thf(1595,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ V_z @ tc_IntDef_Oint ) @ V_w @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[192]) ).

thf(1596,plain,
    ( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[193]) ).

thf(1597,plain,
    ( ( ! [V_m: $i] :
          ( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_IntDef_Oint )
          | ( V_m = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[194]) ).

thf(1598,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ V_z @ ( c_uminus @ V_w @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[195]) ).

thf(1599,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_z @ ( c_uminus @ V_w @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[196]) ).

thf(1600,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_IntDef_Oint @ V_m )
           != ( c_IntDef_Oint @ V_n ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[197]) ).

thf(1601,plain,
    ( ( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[198]) ).

thf(1602,plain,
    ( ( ! [V_k: $i,V_n: $i,V_m: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_k @ V_n @ tc_nat )
          | ~ ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat )
          | ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[199]) ).

thf(1603,plain,
    ( ( ! [V_k: $i,V_m: $i,V_n: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat )
          | ( c_Divides_Oop_Advd @ V_k @ V_n @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[200]) ).

thf(1604,plain,
    ( ( ! [V_k: $i,V_m: $i,V_n: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat )
          | ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[201]) ).

thf(1605,plain,
    ( ( ! [V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_r @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_b @ T_a ) ) )
          | ( c_in @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[202]) ).

thf(1606,plain,
    ( ( ! [V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_a @ T_b ) ) )
          | ( c_in @ V_r @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_b @ T_a ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[203]) ).

thf(1607,plain,
    ( ( ! [V_G: $i,T_a: $i,V_F: $i] :
          ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[204]) ).

thf(1608,plain,
    ( ( ! [V_F: $i,V_G: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[205]) ).

thf(1609,plain,
    ( ( ! [V_F: $i,V_G: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[206]) ).

thf(1610,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_Pow @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[207]) ).

thf(1611,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Pow @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
          | ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[208]) ).

thf(1612,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
          ( ~ ( c_in @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_minus @ V_A @ ( c_insert @ V_a @ V_B @ T_a ) @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[209]) ).

thf(1613,plain,
    ( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_minus @ V_A @ ( c_insert @ V_a @ V_B @ T_a ) @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[210]) ).

thf(1614,plain,
    ( ( c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft )
    = $true ),
    inference(unfold_def,[status(thm)],[211]) ).

thf(1615,plain,
    ( ( c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight )
    = $true ),
    inference(unfold_def,[status(thm)],[212]) ).

thf(1616,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a )
          = c_emptyset ) )
    = $true ),
    inference(unfold_def,[status(thm)],[213]) ).

thf(1617,plain,
    ( ( ! [V_A: $i,V_r: $i,T_a: $i] :
          ( ( ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a )
           != c_emptyset )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[214]) ).

thf(1618,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( c_emptyset
          = ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[215]) ).

thf(1619,plain,
    ( ( ! [V_A: $i,V_r: $i,T_a: $i] :
          ( ( c_emptyset
           != ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[216]) ).

thf(1620,plain,
    ( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[217]) ).

thf(1621,plain,
    ( ( ! [V_m: $i] :
          ( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_nat )
          | ( V_m = c_0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[218]) ).

thf(1622,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_k: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[219]) ).

thf(1623,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[220]) ).

thf(1624,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[221]) ).

thf(1625,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i,V_N_H: $i] :
          ( ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
           != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
          | ( V_N = V_N_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[222]) ).

thf(1626,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i,V_N_H: $i] :
          ( ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
           != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
          | ( V_M = V_M_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[223]) ).

thf(1627,plain,
    ( ( ! [V_k: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[224]) ).

thf(1628,plain,
    ( ( ! [V_k: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
         != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[225]) ).

thf(1629,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[226]) ).

thf(1630,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_k: $i] :
          ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[227]) ).

thf(1631,plain,
    ( ( ! [V_N: $i,T_a: $i,T_b: $i,V_M: $i] :
          ( ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[228]) ).

thf(1632,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( ( c_Datatype__Universe_OIn1 @ V_M @ T_a @ T_b )
           != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) )
          | ( V_M = V_N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[229]) ).

thf(1633,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
         != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[230]) ).

thf(1634,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
           != ( c_Datatype__Universe_OIn0 @ V_N @ T_a @ T_b ) )
          | ( V_M = V_N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[231]) ).

thf(1635,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[232]) ).

thf(1636,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
          ( ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
           != ( c_Datatype__Universe_OAtom @ V_b @ T_a @ T_b ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[233]) ).

thf(1637,plain,
    ( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
          ( ( ( c_Datatype_Ooption_OSome @ V_a @ T_a )
           != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[234]) ).

thf(1638,plain,
    ( ( ! [V_a_H: $i,T_a: $i] :
          ( ( c_Datatype_Ooption_OSome @ V_a_H @ T_a )
         != c_Datatype_Ooption_ONone ) )
    = $true ),
    inference(unfold_def,[status(thm)],[235]) ).

thf(1639,plain,
    ( ( ! [V_a_H: $i,T_a: $i] :
          ( c_Datatype_Ooption_ONone
         != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[236]) ).

thf(1640,plain,
    ( ( ! [V_x: $i,T_a: $i] :
          ( ( V_x = c_Datatype_Ooption_ONone )
          | ( V_x
            = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[237]) ).

thf(1641,plain,
    ( ( ! [V_x: $i,T_a: $i] :
          ( ( V_x = c_Datatype_Ooption_ONone )
          | ( V_x
            = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[238]) ).

thf(1642,plain,
    ( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ V_x @ T_a ) @ T_a ) @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[239]) ).

thf(1643,plain,
    ( ( ! [V_x: $i,V_xo: $i,T_a: $i] :
          ( ~ ( c_in @ V_x @ ( c_Datatype_Oo2s @ V_xo @ T_a ) @ T_a )
          | ( V_xo
            = ( c_Datatype_Ooption_OSome @ V_x @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[240]) ).

thf(1644,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[241]) ).

thf(1645,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[242]) ).

thf(1646,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[243]) ).

thf(1647,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[244]) ).

thf(1648,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[245]) ).

thf(1649,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[246]) ).

thf(1650,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[247]) ).

thf(1651,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[248]) ).

thf(1652,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[249]) ).

thf(1653,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[250]) ).

thf(1654,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[251]) ).

thf(1655,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[252]) ).

thf(1656,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[253]) ).

thf(1657,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[254]) ).

thf(1658,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[255]) ).

thf(1659,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[256]) ).

thf(1660,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[257]) ).

thf(1661,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[258]) ).

thf(1662,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[259]) ).

thf(1663,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[260]) ).

thf(1664,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[261]) ).

thf(1665,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[262]) ).

thf(1666,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[263]) ).

thf(1667,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[264]) ).

thf(1668,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[265]) ).

thf(1669,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[266]) ).

thf(1670,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[267]) ).

thf(1671,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[268]) ).

thf(1672,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[269]) ).

thf(1673,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[270]) ).

thf(1674,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[271]) ).

thf(1675,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[272]) ).

thf(1676,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[273]) ).

thf(1677,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[274]) ).

thf(1678,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[275]) ).

thf(1679,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[276]) ).

thf(1680,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[277]) ).

thf(1681,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[278]) ).

thf(1682,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[279]) ).

thf(1683,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[280]) ).

thf(1684,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[281]) ).

thf(1685,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[282]) ).

thf(1686,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[283]) ).

thf(1687,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[284]) ).

thf(1688,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[285]) ).

thf(1689,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[286]) ).

thf(1690,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[287]) ).

thf(1691,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[288]) ).

thf(1692,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[289]) ).

thf(1693,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[290]) ).

thf(1694,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[291]) ).

thf(1695,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[292]) ).

thf(1696,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[293]) ).

thf(1697,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[294]) ).

thf(1698,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[295]) ).

thf(1699,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[296]) ).

thf(1700,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[297]) ).

thf(1701,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[298]) ).

thf(1702,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[299]) ).

thf(1703,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[300]) ).

thf(1704,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[301]) ).

thf(1705,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[302]) ).

thf(1706,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[303]) ).

thf(1707,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[304]) ).

thf(1708,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[305]) ).

thf(1709,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[306]) ).

thf(1710,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[307]) ).

thf(1711,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[308]) ).

thf(1712,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[309]) ).

thf(1713,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[310]) ).

thf(1714,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[311]) ).

thf(1715,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[312]) ).

thf(1716,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[313]) ).

thf(1717,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[314]) ).

thf(1718,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[315]) ).

thf(1719,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[316]) ).

thf(1720,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[317]) ).

thf(1721,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[318]) ).

thf(1722,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[319]) ).

thf(1723,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[320]) ).

thf(1724,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[321]) ).

thf(1725,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[322]) ).

thf(1726,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[323]) ).

thf(1727,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[324]) ).

thf(1728,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[325]) ).

thf(1729,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[326]) ).

thf(1730,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[327]) ).

thf(1731,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[328]) ).

thf(1732,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[329]) ).

thf(1733,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[330]) ).

thf(1734,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[331]) ).

thf(1735,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[332]) ).

thf(1736,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[333]) ).

thf(1737,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[334]) ).

thf(1738,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[335]) ).

thf(1739,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[336]) ).

thf(1740,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[337]) ).

thf(1741,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[338]) ).

thf(1742,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[339]) ).

thf(1743,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[340]) ).

thf(1744,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[341]) ).

thf(1745,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[342]) ).

thf(1746,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[343]) ).

thf(1747,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[344]) ).

thf(1748,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[345]) ).

thf(1749,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[346]) ).

thf(1750,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[347]) ).

thf(1751,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[348]) ).

thf(1752,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[349]) ).

thf(1753,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[350]) ).

thf(1754,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[351]) ).

thf(1755,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[352]) ).

thf(1756,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[353]) ).

thf(1757,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[354]) ).

thf(1758,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[355]) ).

thf(1759,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[356]) ).

thf(1760,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[357]) ).

thf(1761,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[358]) ).

thf(1762,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[359]) ).

thf(1763,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[360]) ).

thf(1764,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[361]) ).

thf(1765,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[362]) ).

thf(1766,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[363]) ).

thf(1767,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[364]) ).

thf(1768,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[365]) ).

thf(1769,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[366]) ).

thf(1770,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[367]) ).

thf(1771,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[368]) ).

thf(1772,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[369]) ).

thf(1773,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[370]) ).

thf(1774,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[371]) ).

thf(1775,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[372]) ).

thf(1776,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[373]) ).

thf(1777,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[374]) ).

thf(1778,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[375]) ).

thf(1779,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[376]) ).

thf(1780,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[377]) ).

thf(1781,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[378]) ).

thf(1782,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[379]) ).

thf(1783,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[380]) ).

thf(1784,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[381]) ).

thf(1785,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[382]) ).

thf(1786,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[383]) ).

thf(1787,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[384]) ).

thf(1788,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[385]) ).

thf(1789,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[386]) ).

thf(1790,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[387]) ).

thf(1791,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[388]) ).

thf(1792,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[389]) ).

thf(1793,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[390]) ).

thf(1794,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[391]) ).

thf(1795,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[392]) ).

thf(1796,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[393]) ).

thf(1797,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[394]) ).

thf(1798,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[395]) ).

thf(1799,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[396]) ).

thf(1800,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[397]) ).

thf(1801,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[398]) ).

thf(1802,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[399]) ).

thf(1803,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[400]) ).

thf(1804,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[401]) ).

thf(1805,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[402]) ).

thf(1806,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[403]) ).

thf(1807,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[404]) ).

thf(1808,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[405]) ).

thf(1809,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[406]) ).

thf(1810,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[407]) ).

thf(1811,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[408]) ).

thf(1812,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[409]) ).

thf(1813,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[410]) ).

thf(1814,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[411]) ).

thf(1815,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[412]) ).

thf(1816,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[413]) ).

thf(1817,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[414]) ).

thf(1818,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[415]) ).

thf(1819,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[416]) ).

thf(1820,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[417]) ).

thf(1821,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[418]) ).

thf(1822,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[419]) ).

thf(1823,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[420]) ).

thf(1824,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[421]) ).

thf(1825,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[422]) ).

thf(1826,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[423]) ).

thf(1827,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[424]) ).

thf(1828,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[425]) ).

thf(1829,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[426]) ).

thf(1830,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[427]) ).

thf(1831,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[428]) ).

thf(1832,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[429]) ).

thf(1833,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[430]) ).

thf(1834,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[431]) ).

thf(1835,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[432]) ).

thf(1836,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[433]) ).

thf(1837,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[434]) ).

thf(1838,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[435]) ).

thf(1839,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[436]) ).

thf(1840,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[437]) ).

thf(1841,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[438]) ).

thf(1842,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[439]) ).

thf(1843,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[440]) ).

thf(1844,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[441]) ).

thf(1845,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[442]) ).

thf(1846,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[443]) ).

thf(1847,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[444]) ).

thf(1848,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[445]) ).

thf(1849,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[446]) ).

thf(1850,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[447]) ).

thf(1851,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[448]) ).

thf(1852,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[449]) ).

thf(1853,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[450]) ).

thf(1854,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[451]) ).

thf(1855,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[452]) ).

thf(1856,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[453]) ).

thf(1857,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[454]) ).

thf(1858,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[455]) ).

thf(1859,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[456]) ).

thf(1860,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[457]) ).

thf(1861,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[458]) ).

thf(1862,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[459]) ).

thf(1863,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[460]) ).

thf(1864,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[461]) ).

thf(1865,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[462]) ).

thf(1866,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[463]) ).

thf(1867,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[464]) ).

thf(1868,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[465]) ).

thf(1869,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[466]) ).

thf(1870,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[467]) ).

thf(1871,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[468]) ).

thf(1872,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[469]) ).

thf(1873,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[470]) ).

thf(1874,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[471]) ).

thf(1875,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[472]) ).

thf(1876,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[473]) ).

thf(1877,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[474]) ).

thf(1878,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[475]) ).

thf(1879,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[476]) ).

thf(1880,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[477]) ).

thf(1881,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[478]) ).

thf(1882,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[479]) ).

thf(1883,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[480]) ).

thf(1884,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[481]) ).

thf(1885,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[482]) ).

thf(1886,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[483]) ).

thf(1887,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[484]) ).

thf(1888,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[485]) ).

thf(1889,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[486]) ).

thf(1890,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[487]) ).

thf(1891,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[488]) ).

thf(1892,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[489]) ).

thf(1893,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[490]) ).

thf(1894,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[491]) ).

thf(1895,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[492]) ).

thf(1896,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[493]) ).

thf(1897,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[494]) ).

thf(1898,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[495]) ).

thf(1899,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[496]) ).

thf(1900,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[497]) ).

thf(1901,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[498]) ).

thf(1902,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[499]) ).

thf(1903,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[500]) ).

thf(1904,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[501]) ).

thf(1905,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[502]) ).

thf(1906,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[503]) ).

thf(1907,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[504]) ).

thf(1908,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[505]) ).

thf(1909,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[506]) ).

thf(1910,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[507]) ).

thf(1911,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[508]) ).

thf(1912,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[509]) ).

thf(1913,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[510]) ).

thf(1914,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[511]) ).

thf(1915,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[512]) ).

thf(1916,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[513]) ).

thf(1917,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[514]) ).

thf(1918,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[515]) ).

thf(1919,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[516]) ).

thf(1920,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[517]) ).

thf(1921,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[518]) ).

thf(1922,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[519]) ).

thf(1923,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[520]) ).

thf(1924,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Olordered__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[521]) ).

thf(1925,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[522]) ).

thf(1926,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[523]) ).

thf(1927,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[524]) ).

thf(1928,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[525]) ).

thf(1929,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[526]) ).

thf(1930,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[527]) ).

thf(1931,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[528]) ).

thf(1932,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[529]) ).

thf(1933,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[530]) ).

thf(1934,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[531]) ).

thf(1935,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[532]) ).

thf(1936,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[533]) ).

thf(1937,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[534]) ).

thf(1938,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[535]) ).

thf(1939,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[536]) ).

thf(1940,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[537]) ).

thf(1941,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[538]) ).

thf(1942,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[539]) ).

thf(1943,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[540]) ).

thf(1944,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[541]) ).

thf(1945,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[542]) ).

thf(1946,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[543]) ).

thf(1947,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[544]) ).

thf(1948,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[545]) ).

thf(1949,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[546]) ).

thf(1950,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[547]) ).

thf(1951,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[548]) ).

thf(1952,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[549]) ).

thf(1953,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[550]) ).

thf(1954,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oidom @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[551]) ).

thf(1955,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[552]) ).

thf(1956,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[553]) ).

thf(1957,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[554]) ).

thf(1958,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[555]) ).

thf(1959,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[556]) ).

thf(1960,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[557]) ).

thf(1961,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[558]) ).

thf(1962,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[559]) ).

thf(1963,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[560]) ).

thf(1964,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Olordered__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[561]) ).

thf(1965,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[562]) ).

thf(1966,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[563]) ).

thf(1967,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[564]) ).

thf(1968,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[565]) ).

thf(1969,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[566]) ).

thf(1970,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[567]) ).

thf(1971,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[568]) ).

thf(1972,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[569]) ).

thf(1973,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[570]) ).

thf(1974,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[571]) ).

thf(1975,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[572]) ).

thf(1976,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[573]) ).

thf(1977,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[574]) ).

thf(1978,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[575]) ).

thf(1979,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[576]) ).

thf(1980,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[577]) ).

thf(1981,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[578]) ).

thf(1982,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[579]) ).

thf(1983,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[580]) ).

thf(1984,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[581]) ).

thf(1985,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[582]) ).

thf(1986,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[583]) ).

thf(1987,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[584]) ).

thf(1988,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[585]) ).

thf(1989,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[586]) ).

thf(1990,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[587]) ).

thf(1991,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[588]) ).

thf(1992,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[589]) ).

thf(1993,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[590]) ).

thf(1994,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[591]) ).

thf(1995,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[592]) ).

thf(1996,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[593]) ).

thf(1997,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[594]) ).

thf(1998,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[595]) ).

thf(1999,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[596]) ).

thf(2000,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[597]) ).

thf(2001,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[598]) ).

thf(2002,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[599]) ).

thf(2003,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[600]) ).

thf(2004,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[601]) ).

thf(2005,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[602]) ).

thf(2006,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[603]) ).

thf(2007,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[604]) ).

thf(2008,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[605]) ).

thf(2009,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[606]) ).

thf(2010,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[607]) ).

thf(2011,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[608]) ).

thf(2012,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[609]) ).

thf(2013,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[610]) ).

thf(2014,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[611]) ).

thf(2015,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[612]) ).

thf(2016,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[613]) ).

thf(2017,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[614]) ).

thf(2018,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[615]) ).

thf(2019,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[616]) ).

thf(2020,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[617]) ).

thf(2021,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[618]) ).

thf(2022,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[619]) ).

thf(2023,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[620]) ).

thf(2024,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[621]) ).

thf(2025,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[622]) ).

thf(2026,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[623]) ).

thf(2027,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[624]) ).

thf(2028,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[625]) ).

thf(2029,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[626]) ).

thf(2030,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Olordered__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[627]) ).

thf(2031,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[628]) ).

thf(2032,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[629]) ).

thf(2033,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[630]) ).

thf(2034,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[631]) ).

thf(2035,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[632]) ).

thf(2036,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[633]) ).

thf(2037,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[634]) ).

thf(2038,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[635]) ).

thf(2039,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[636]) ).

thf(2040,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__idom @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[637]) ).

thf(2041,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[638]) ).

thf(2042,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[639]) ).

thf(2043,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[640]) ).

thf(2044,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[641]) ).

thf(2045,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[642]) ).

thf(2046,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[643]) ).

thf(2047,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[644]) ).

thf(2048,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[645]) ).

thf(2049,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[646]) ).

thf(2050,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[647]) ).

thf(2051,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[648]) ).

thf(2052,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[649]) ).

thf(2053,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[650]) ).

thf(2054,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[651]) ).

thf(2055,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[652]) ).

thf(2056,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oidom @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[653]) ).

thf(2057,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[654]) ).

thf(2058,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[655]) ).

thf(2059,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[656]) ).

thf(2060,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[657]) ).

thf(2061,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[658]) ).

thf(2062,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[659]) ).

thf(2063,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[660]) ).

thf(2064,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[661]) ).

thf(2065,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[662]) ).

thf(2066,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[663]) ).

thf(2067,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Oinverse @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[664]) ).

thf(2068,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ofield @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[665]) ).

thf(2069,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[666]) ).

thf(2070,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[667]) ).

thf(2071,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[668]) ).

thf(2072,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[669]) ).

thf(2073,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[670]) ).

thf(2074,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[671]) ).

thf(2075,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[672]) ).

thf(2076,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[673]) ).

thf(2077,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[674]) ).

thf(2078,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[675]) ).

thf(2079,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[676]) ).

thf(2080,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[677]) ).

thf(2081,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[678]) ).

thf(2082,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[679]) ).

thf(2083,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[680]) ).

thf(2084,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[681]) ).

thf(2085,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[682]) ).

thf(2086,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[683]) ).

thf(2087,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[684]) ).

thf(2088,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[685]) ).

thf(2089,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[686]) ).

thf(2090,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[687]) ).

thf(2091,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[688]) ).

thf(2092,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[689]) ).

thf(2093,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[690]) ).

thf(2094,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[691]) ).

thf(2095,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[692]) ).

thf(2096,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[693]) ).

thf(2097,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[694]) ).

thf(2098,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[695]) ).

thf(2099,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[696]) ).

thf(2100,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[697]) ).

thf(2101,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[698]) ).

thf(2102,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[699]) ).

thf(2103,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[700]) ).

thf(2104,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[701]) ).

thf(2105,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[702]) ).

thf(2106,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[703]) ).

thf(2107,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[704]) ).

thf(2108,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[705]) ).

thf(2109,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[706]) ).

thf(2110,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[707]) ).

thf(2111,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[708]) ).

thf(2112,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[709]) ).

thf(2113,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[710]) ).

thf(2114,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[711]) ).

thf(2115,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[712]) ).

thf(2116,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[713]) ).

thf(2117,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[714]) ).

thf(2118,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[715]) ).

thf(2119,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[716]) ).

thf(2120,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[717]) ).

thf(2121,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[718]) ).

thf(2122,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[719]) ).

thf(2123,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[720]) ).

thf(2124,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[721]) ).

thf(2125,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[722]) ).

thf(2126,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[723]) ).

thf(2127,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[724]) ).

thf(2128,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[725]) ).

thf(2129,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[726]) ).

thf(2130,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[727]) ).

thf(2131,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[728]) ).

thf(2132,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[729]) ).

thf(2133,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[730]) ).

thf(2134,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[731]) ).

thf(2135,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[732]) ).

thf(2136,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[733]) ).

thf(2137,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[734]) ).

thf(2138,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[735]) ).

thf(2139,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[736]) ).

thf(2140,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[737]) ).

thf(2141,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[738]) ).

thf(2142,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[739]) ).

thf(2143,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[740]) ).

thf(2144,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[741]) ).

thf(2145,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[742]) ).

thf(2146,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[743]) ).

thf(2147,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[744]) ).

thf(2148,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[745]) ).

thf(2149,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[746]) ).

thf(2150,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[747]) ).

thf(2151,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[748]) ).

thf(2152,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[749]) ).

thf(2153,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[750]) ).

thf(2154,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[751]) ).

thf(2155,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[752]) ).

thf(2156,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[753]) ).

thf(2157,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[754]) ).

thf(2158,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[755]) ).

thf(2159,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[756]) ).

thf(2160,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[757]) ).

thf(2161,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[758]) ).

thf(2162,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[759]) ).

thf(2163,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[760]) ).

thf(2164,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[761]) ).

thf(2165,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[762]) ).

thf(2166,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[763]) ).

thf(2167,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[764]) ).

thf(2168,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oidom @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[765]) ).

thf(2169,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Oinverse @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[766]) ).

thf(2170,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[767]) ).

thf(2171,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[768]) ).

thf(2172,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[769]) ).

thf(2173,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[770]) ).

thf(2174,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[771]) ).

thf(2175,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[772]) ).

thf(2176,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[773]) ).

thf(2177,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[774]) ).

thf(2178,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[775]) ).

thf(2179,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[776]) ).

thf(2180,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[777]) ).

thf(2181,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[778]) ).

thf(2182,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[779]) ).

thf(2183,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[780]) ).

thf(2184,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[781]) ).

thf(2185,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[782]) ).

thf(2186,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[783]) ).

thf(2187,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[784]) ).

thf(2188,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[785]) ).

thf(2189,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[786]) ).

thf(2190,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[787]) ).

thf(2191,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[788]) ).

thf(2192,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[789]) ).

thf(2193,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[790]) ).

thf(2194,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
          | ( class_HOL_Oinverse @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[791]) ).

thf(2195,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[792]) ).

thf(2196,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[793]) ).

thf(2197,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[794]) ).

thf(2198,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[795]) ).

thf(2199,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[796]) ).

thf(2200,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[797]) ).

thf(2201,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[798]) ).

thf(2202,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[799]) ).

thf(2203,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[800]) ).

thf(2204,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[801]) ).

thf(2205,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[802]) ).

thf(2206,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[803]) ).

thf(2207,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[804]) ).

thf(2208,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[805]) ).

thf(2209,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[806]) ).

thf(2210,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[807]) ).

thf(2211,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[808]) ).

thf(2212,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[809]) ).

thf(2213,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[810]) ).

thf(2214,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[811]) ).

thf(2215,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[812]) ).

thf(2216,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[813]) ).

thf(2217,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[814]) ).

thf(2218,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[815]) ).

thf(2219,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[816]) ).

thf(2220,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[817]) ).

thf(2221,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[818]) ).

thf(2222,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[819]) ).

thf(2223,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[820]) ).

thf(2224,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[821]) ).

thf(2225,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[822]) ).

thf(2226,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[823]) ).

thf(2227,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[824]) ).

thf(2228,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[825]) ).

thf(2229,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[826]) ).

thf(2230,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[827]) ).

thf(2231,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[828]) ).

thf(2232,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[829]) ).

thf(2233,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[830]) ).

thf(2234,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[831]) ).

thf(2235,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[832]) ).

thf(2236,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[833]) ).

thf(2237,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[834]) ).

thf(2238,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[835]) ).

thf(2239,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[836]) ).

thf(2240,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[837]) ).

thf(2241,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[838]) ).

thf(2242,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[839]) ).

thf(2243,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[840]) ).

thf(2244,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[841]) ).

thf(2245,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[842]) ).

thf(2246,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[843]) ).

thf(2247,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[844]) ).

thf(2248,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[845]) ).

thf(2249,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[846]) ).

thf(2250,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[847]) ).

thf(2251,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[848]) ).

thf(2252,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[849]) ).

thf(2253,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[850]) ).

thf(2254,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[851]) ).

thf(2255,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[852]) ).

thf(2256,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[853]) ).

thf(2257,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[854]) ).

thf(2258,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[855]) ).

thf(2259,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[856]) ).

thf(2260,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[857]) ).

thf(2261,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[858]) ).

thf(2262,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[859]) ).

thf(2263,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[860]) ).

thf(2264,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[861]) ).

thf(2265,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[862]) ).

thf(2266,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[863]) ).

thf(2267,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[864]) ).

thf(2268,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[865]) ).

thf(2269,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[866]) ).

thf(2270,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[867]) ).

thf(2271,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[868]) ).

thf(2272,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[869]) ).

thf(2273,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[870]) ).

thf(2274,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[871]) ).

thf(2275,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[872]) ).

thf(2276,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[873]) ).

thf(2277,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[874]) ).

thf(2278,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[875]) ).

thf(2279,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[876]) ).

thf(2280,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[877]) ).

thf(2281,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[878]) ).

thf(2282,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[879]) ).

thf(2283,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[880]) ).

thf(2284,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[881]) ).

thf(2285,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[882]) ).

thf(2286,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[883]) ).

thf(2287,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[884]) ).

thf(2288,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[885]) ).

thf(2289,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[886]) ).

thf(2290,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[887]) ).

thf(2291,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[888]) ).

thf(2292,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[889]) ).

thf(2293,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[890]) ).

thf(2294,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[891]) ).

thf(2295,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[892]) ).

thf(2296,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[893]) ).

thf(2297,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[894]) ).

thf(2298,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[895]) ).

thf(2299,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[896]) ).

thf(2300,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[897]) ).

thf(2301,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[898]) ).

thf(2302,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[899]) ).

thf(2303,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[900]) ).

thf(2304,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[901]) ).

thf(2305,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[902]) ).

thf(2306,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[903]) ).

thf(2307,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[904]) ).

thf(2308,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[905]) ).

thf(2309,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[906]) ).

thf(2310,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[907]) ).

thf(2311,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[908]) ).

thf(2312,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[909]) ).

thf(2313,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[910]) ).

thf(2314,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[911]) ).

thf(2315,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[912]) ).

thf(2316,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[913]) ).

thf(2317,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[914]) ).

thf(2318,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[915]) ).

thf(2319,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[916]) ).

thf(2320,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[917]) ).

thf(2321,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[918]) ).

thf(2322,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[919]) ).

thf(2323,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[920]) ).

thf(2324,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[921]) ).

thf(2325,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[922]) ).

thf(2326,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[923]) ).

thf(2327,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[924]) ).

thf(2328,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[925]) ).

thf(2329,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[926]) ).

thf(2330,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[927]) ).

thf(2331,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[928]) ).

thf(2332,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[929]) ).

thf(2333,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[930]) ).

thf(2334,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[931]) ).

thf(2335,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[932]) ).

thf(2336,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[933]) ).

thf(2337,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[934]) ).

thf(2338,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[935]) ).

thf(2339,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[936]) ).

thf(2340,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[937]) ).

thf(2341,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[938]) ).

thf(2342,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[939]) ).

thf(2343,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[940]) ).

thf(2344,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[941]) ).

thf(2345,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[942]) ).

thf(2346,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[943]) ).

thf(2347,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[944]) ).

thf(2348,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Nat_Opower @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[945]) ).

thf(2349,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Oorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[946]) ).

thf(2350,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[947]) ).

thf(2351,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[948]) ).

thf(2352,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[949]) ).

thf(2353,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[950]) ).

thf(2354,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[951]) ).

thf(2355,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Osemigroup__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[952]) ).

thf(2356,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Osemigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[953]) ).

thf(2357,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[954]) ).

thf(2358,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[955]) ).

thf(2359,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[956]) ).

thf(2360,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[957]) ).

thf(2361,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[958]) ).

thf(2362,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[959]) ).

thf(2363,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[960]) ).

thf(2364,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[961]) ).

thf(2365,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[962]) ).

thf(2366,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[963]) ).

thf(2367,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[964]) ).

thf(2368,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[965]) ).

thf(2369,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[966]) ).

thf(2370,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[967]) ).

thf(2371,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[968]) ).

thf(2372,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[969]) ).

thf(2373,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[970]) ).

thf(2374,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[971]) ).

thf(2375,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[972]) ).

thf(2376,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[973]) ).

thf(2377,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[974]) ).

thf(2378,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[975]) ).

thf(2379,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[976]) ).

thf(2380,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[977]) ).

thf(2381,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[978]) ).

thf(2382,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[979]) ).

thf(2383,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[980]) ).

thf(2384,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[981]) ).

thf(2385,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[982]) ).

thf(2386,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[983]) ).

thf(2387,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[984]) ).

thf(2388,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[985]) ).

thf(2389,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[986]) ).

thf(2390,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[987]) ).

thf(2391,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[988]) ).

thf(2392,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[989]) ).

thf(2393,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[990]) ).

thf(2394,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[991]) ).

thf(2395,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[992]) ).

thf(2396,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[993]) ).

thf(2397,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[994]) ).

thf(2398,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[995]) ).

thf(2399,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[996]) ).

thf(2400,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[997]) ).

thf(2401,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[998]) ).

thf(2402,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[999]) ).

thf(2403,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1000]) ).

thf(2404,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1001]) ).

thf(2405,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1002]) ).

thf(2406,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1003]) ).

thf(2407,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1004]) ).

thf(2408,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1005]) ).

thf(2409,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1006]) ).

thf(2410,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1007]) ).

thf(2411,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1008]) ).

thf(2412,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1009]) ).

thf(2413,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1010]) ).

thf(2414,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1011]) ).

thf(2415,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1012]) ).

thf(2416,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1013]) ).

thf(2417,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1014]) ).

thf(2418,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1015]) ).

thf(2419,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1016]) ).

thf(2420,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1017]) ).

thf(2421,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1018]) ).

thf(2422,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1019]) ).

thf(2423,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1020]) ).

thf(2424,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1021]) ).

thf(2425,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1022]) ).

thf(2426,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1023]) ).

thf(2427,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1024]) ).

thf(2428,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1025]) ).

thf(2429,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1026]) ).

thf(2430,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1027]) ).

thf(2431,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1028]) ).

thf(2432,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1029]) ).

thf(2433,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1030]) ).

thf(2434,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1031]) ).

thf(2435,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1032]) ).

thf(2436,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1033]) ).

thf(2437,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1034]) ).

thf(2438,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1035]) ).

thf(2439,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1036]) ).

thf(2440,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1037]) ).

thf(2441,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1038]) ).

thf(2442,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1039]) ).

thf(2443,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1040]) ).

thf(2444,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1041]) ).

thf(2445,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1042]) ).

thf(2446,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1043]) ).

thf(2447,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1044]) ).

thf(2448,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1045]) ).

thf(2449,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1046]) ).

thf(2450,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1047]) ).

thf(2451,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1048]) ).

thf(2452,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1049]) ).

thf(2453,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1050]) ).

thf(2454,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1051]) ).

thf(2455,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1052]) ).

thf(2456,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1053]) ).

thf(2457,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1054]) ).

thf(2458,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1055]) ).

thf(2459,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1056]) ).

thf(2460,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1057]) ).

thf(2461,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1058]) ).

thf(2462,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1059]) ).

thf(2463,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1060]) ).

thf(2464,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1061]) ).

thf(2465,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1062]) ).

thf(2466,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1063]) ).

thf(2467,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1064]) ).

thf(2468,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1065]) ).

thf(2469,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1066]) ).

thf(2470,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1067]) ).

thf(2471,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1068]) ).

thf(2472,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1069]) ).

thf(2473,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1070]) ).

thf(2474,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1071]) ).

thf(2475,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1072]) ).

thf(2476,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1073]) ).

thf(2477,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1074]) ).

thf(2478,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1075]) ).

thf(2479,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1076]) ).

thf(2480,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1077]) ).

thf(2481,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1078]) ).

thf(2482,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1079]) ).

thf(2483,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1080]) ).

thf(2484,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1081]) ).

thf(2485,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1082]) ).

thf(2486,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1083]) ).

thf(2487,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1084]) ).

thf(2488,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1085]) ).

thf(2489,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1086]) ).

thf(2490,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1087]) ).

thf(2491,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1088]) ).

thf(2492,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1089]) ).

thf(2493,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1090]) ).

thf(2494,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1091]) ).

thf(2495,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1092]) ).

thf(2496,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1093]) ).

thf(2497,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1094]) ).

thf(2498,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1095]) ).

thf(2499,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1096]) ).

thf(2500,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1097]) ).

thf(2501,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1098]) ).

thf(2502,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1099]) ).

thf(2503,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1100]) ).

thf(2504,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1101]) ).

thf(2505,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1102]) ).

thf(2506,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1103]) ).

thf(2507,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1104]) ).

thf(2508,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1105]) ).

thf(2509,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1106]) ).

thf(2510,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1107]) ).

thf(2511,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1108]) ).

thf(2512,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1109]) ).

thf(2513,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1110]) ).

thf(2514,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1111]) ).

thf(2515,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1112]) ).

thf(2516,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1113]) ).

thf(2517,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1114]) ).

thf(2518,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Numeral_Onumber @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1115]) ).

thf(2519,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1116]) ).

thf(2520,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1117]) ).

thf(2521,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1118]) ).

thf(2522,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1119]) ).

thf(2523,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1120]) ).

thf(2524,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1121]) ).

thf(2525,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1122]) ).

thf(2526,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1123]) ).

thf(2527,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1124]) ).

thf(2528,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1125]) ).

thf(2529,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1126]) ).

thf(2530,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1127]) ).

thf(2531,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1128]) ).

thf(2532,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1129]) ).

thf(2533,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1130]) ).

thf(2534,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1131]) ).

thf(2535,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1132]) ).

thf(2536,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1133]) ).

thf(2537,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1134]) ).

thf(2538,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1135]) ).

thf(2539,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1136]) ).

thf(2540,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1137]) ).

thf(2541,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1138]) ).

thf(2542,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1139]) ).

thf(2543,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Omeet__semilorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1140]) ).

thf(2544,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Omeet__semilorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1141]) ).

thf(2545,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1142]) ).

thf(2546,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1143]) ).

thf(2547,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1144]) ).

thf(2548,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1145]) ).

thf(2549,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Ojoin__semilorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1146]) ).

thf(2550,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Ojoin__semilorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1147]) ).

thf(2551,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_sum @ T_2 @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 )
          | ~ ( class_Finite__Set_Ofinite @ T_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1148]) ).

thf(2552,plain,
    ( ( ! [T_1: $i] : ( class_Nat_Opower @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1149]) ).

thf(2553,plain,
    ( ( ! [T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_set @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1150]) ).

thf(2554,plain,
    ( ( ! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1151]) ).

thf(2555,plain,
    ( ( ! [T_1: $i] : ( class_Orderings_Oord @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1152]) ).

thf(2556,plain,
    ( ( ! [T_1: $i] : ( class_HOL_Ominus @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1153]) ).

thf(2557,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_prod @ T_2 @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 )
          | ~ ( class_Finite__Set_Ofinite @ T_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1154]) ).

thf(2558,plain,
    ( ( class_HOL_Ominus @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1155]) ).

thf(2559,plain,
    ( ( class_Wellfounded__Recursion_Owellorder @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1156]) ).

thf(2560,plain,
    ( ( class_Orderings_Olinorder @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1157]) ).

thf(2561,plain,
    ( ( class_LOrder_Olorder @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1158]) ).

thf(2562,plain,
    ( ( class_LOrder_Ojoin__semilorder @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1159]) ).

thf(2563,plain,
    ( ( class_Parity_Oeven__odd @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1160]) ).

thf(2564,plain,
    ( ( class_Numeral_Onumber @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1161]) ).

thf(2565,plain,
    ( ( class_Power_Orecpower @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1162]) ).

thf(2566,plain,
    ( ( class_Divides_Odiv @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1163]) ).

thf(2567,plain,
    ( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1164]) ).

thf(2568,plain,
    ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1165]) ).

thf(2569,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1166]) ).

thf(2570,plain,
    ( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1167]) ).

thf(2571,plain,
    ( ( class_LOrder_Omeet__semilorder @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1168]) ).

thf(2572,plain,
    ( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1169]) ).

thf(2573,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1170]) ).

thf(2574,plain,
    ( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1171]) ).

thf(2575,plain,
    ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1172]) ).

thf(2576,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1173]) ).

thf(2577,plain,
    ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1174]) ).

thf(2578,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1175]) ).

thf(2579,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1176]) ).

thf(2580,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1177]) ).

thf(2581,plain,
    ( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1178]) ).

thf(2582,plain,
    ( ( class_Orderings_Oorder @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1179]) ).

thf(2583,plain,
    ( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1180]) ).

thf(2584,plain,
    ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1181]) ).

thf(2585,plain,
    ( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1182]) ).

thf(2586,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1183]) ).

thf(2587,plain,
    ( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1184]) ).

thf(2588,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1185]) ).

thf(2589,plain,
    ( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1186]) ).

thf(2590,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1187]) ).

thf(2591,plain,
    ( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1188]) ).

thf(2592,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1189]) ).

thf(2593,plain,
    ( ( class_Orderings_Oord @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1190]) ).

thf(2594,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1191]) ).

thf(2595,plain,
    ( ( class_Ring__and__Field_Osemiring @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1192]) ).

thf(2596,plain,
    ( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1193]) ).

thf(2597,plain,
    ( ( class_OrderedGroup_Osemigroup__mult @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1194]) ).

thf(2598,plain,
    ( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1195]) ).

thf(2599,plain,
    ( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1196]) ).

thf(2600,plain,
    ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1197]) ).

thf(2601,plain,
    ( ( class_Nat_Opower @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1198]) ).

thf(2602,plain,
    ( ( class_HOL_Otimes @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1199]) ).

thf(2603,plain,
    ( ( class_HOL_Oplus @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1200]) ).

thf(2604,plain,
    ( ( class_HOL_Ozero @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1201]) ).

thf(2605,plain,
    ( ( class_HOL_Oone @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1202]) ).

thf(2606,plain,
    ( ( ! [T_2: $i,T_1: $i] : ( class_Nat_Opower @ ( tc_fun @ T_2 @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1203]) ).

thf(2607,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 )
          | ~ ( class_Finite__Set_Ofinite @ T_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1204]) ).

thf(2608,plain,
    ( ( class_Finite__Set_Ofinite @ tc_bool )
    = $true ),
    inference(unfold_def,[status(thm)],[1205]) ).

thf(2609,plain,
    ( ( class_Finite__Set_Ofinite @ tc_Product__Type_Ounit )
    = $true ),
    inference(unfold_def,[status(thm)],[1206]) ).

thf(2610,plain,
    ( ( class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1207]) ).

thf(2611,plain,
    ( ( class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1208]) ).

thf(2612,plain,
    ( ( class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1209]) ).

thf(2613,plain,
    ( ( class_Parity_Oeven__odd @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1210]) ).

thf(2614,plain,
    ( ( class_Power_Orecpower @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1211]) ).

thf(2615,plain,
    ( ( class_Nat_Opower @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1212]) ).

thf(2616,plain,
    ( ( class_Divides_Odiv @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1213]) ).

thf(2617,plain,
    ( ( class_Numeral_Onumber__ring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1214]) ).

thf(2618,plain,
    ( ( class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1215]) ).

thf(2619,plain,
    ( ( class_Numeral_Onumber @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1216]) ).

thf(2620,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1217]) ).

thf(2621,plain,
    ( ( class_Ring__and__Field_Oidom @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1218]) ).

thf(2622,plain,
    ( ( class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1219]) ).

thf(2623,plain,
    ( ( class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1220]) ).

thf(2624,plain,
    ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1221]) ).

thf(2625,plain,
    ( ( class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1222]) ).

thf(2626,plain,
    ( ( class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1223]) ).

thf(2627,plain,
    ( ( class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1224]) ).

thf(2628,plain,
    ( ( class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1225]) ).

thf(2629,plain,
    ( ( class_Orderings_Oord @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1226]) ).

thf(2630,plain,
    ( ( class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1227]) ).

thf(2631,plain,
    ( ( class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1228]) ).

thf(2632,plain,
    ( ( class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1229]) ).

thf(2633,plain,
    ( ( class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1230]) ).

thf(2634,plain,
    ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1231]) ).

thf(2635,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1232]) ).

thf(2636,plain,
    ( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1233]) ).

thf(2637,plain,
    ( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1234]) ).

thf(2638,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1235]) ).

thf(2639,plain,
    ( ( class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1236]) ).

thf(2640,plain,
    ( ( class_HOL_Ozero @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1237]) ).

thf(2641,plain,
    ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1238]) ).

thf(2642,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1239]) ).

thf(2643,plain,
    ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1240]) ).

thf(2644,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1241]) ).

thf(2645,plain,
    ( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1242]) ).

thf(2646,plain,
    ( ( class_LOrder_Olorder @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1243]) ).

thf(2647,plain,
    ( ( class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1244]) ).

thf(2648,plain,
    ( ( class_LOrder_Omeet__semilorder @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1245]) ).

thf(2649,plain,
    ( ( class_Orderings_Oorder @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1246]) ).

thf(2650,plain,
    ( ( class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1247]) ).

thf(2651,plain,
    ( ( class_HOL_Otimes @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1248]) ).

thf(2652,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1249]) ).

thf(2653,plain,
    ( ( class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1250]) ).

thf(2654,plain,
    ( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1251]) ).

thf(2655,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1252]) ).

thf(2656,plain,
    ( ( class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1253]) ).

thf(2657,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1254]) ).

thf(2658,plain,
    ( ( class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1255]) ).

thf(2659,plain,
    ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1256]) ).

thf(2660,plain,
    ( ( class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1257]) ).

thf(2661,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1258]) ).

thf(2662,plain,
    ( ( class_HOL_Oplus @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1259]) ).

thf(2663,plain,
    ( ( class_Ring__and__Field_Oring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1260]) ).

thf(2664,plain,
    ( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1261]) ).

thf(2665,plain,
    ( ( class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1262]) ).

thf(2666,plain,
    ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1263]) ).

thf(2667,plain,
    ( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1264]) ).

thf(2668,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1265]) ).

thf(2669,plain,
    ( ( class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1266]) ).

thf(2670,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1267]) ).

thf(2671,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1268]) ).

thf(2672,plain,
    ( ( class_Ring__and__Field_Osemiring @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1269]) ).

thf(2673,plain,
    ( ( class_HOL_Oone @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1270]) ).

thf(2674,plain,
    ( ( class_HOL_Ominus @ tc_IntDef_Oint )
    = $true ),
    inference(unfold_def,[status(thm)],[1271]) ).

thf(2675,plain,
    ( ( ! [T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1272]) ).

thf(2676,plain,
    ( ( ! [V_rb: $i,T_b: $i,V_ra: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_rb @ T_b )
          | ~ ( c_Wellfounded__Recursion_Owf @ V_ra @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ V_ra @ V_rb @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1273]) ).

thf(2677,plain,
    ( ( c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1274]) ).

thf(2678,plain,
    ( ( ! [V_R2: $i,T_b: $i,V_R1: $i,T_a: $i] :
          ( ~ ( c_Relation_Otrans @ V_R2 @ T_b )
          | ~ ( c_Relation_Otrans @ V_R1 @ T_a )
          | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ V_R1 @ V_R2 @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1275]) ).

thf(2679,plain,
    ( ( c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1276]) ).

thf(2680,plain,
    ( ( ! [T_a: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1277]) ).

thf(2681,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1278]) ).

thf(2682,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1279]) ).

thf(2683,plain,
    ( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1280]) ).

thf(2684,plain,
    ( ( ! [V_p: $i,V_r: $i,T_a: $i] :
          ( ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1281]) ).

thf(2685,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ T_a )
          | ( c_in @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ V_B @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1282]) ).

thf(2686,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ T_a )
          | ( V_u
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1283]) ).

thf(2687,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ V_B @ T_b )
          | ( V_u
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1284]) ).

thf(2688,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1285]) ).

thf(2689,plain,
    ( ( ! [V_b: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
          ( ~ ( c_in @ V_b @ V_B @ T_a )
          | ( c_in @ ( c_Sum__Type_OInr @ V_b @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_b @ T_a ) @ ( tc_sum @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1286]) ).

thf(2690,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ( c_in @ ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1287]) ).

thf(2691,plain,
    ( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1288]) ).

thf(2692,plain,
    ( ( ! [V_B: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
          | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1289]) ).

thf(2693,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1290]) ).

thf(2694,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1291]) ).

thf(2695,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( c_in @ V_c @ V_B @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1292]) ).

thf(2696,plain,
    ( ( ! [V_a: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ c_emptyset @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1293]) ).

thf(2697,plain,
    ( ( ! [V_a: $i,T_a: $i] : ( c_in @ V_a @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1294]) ).

thf(2698,plain,
    ( ( ! [V_b: $i,V_a: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a )
          | ( V_b = V_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1295]) ).

thf(2699,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1296]) ).

thf(2700,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1297]) ).

thf(2701,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1298]) ).

thf(2702,plain,
    ( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1299]) ).

thf(2703,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a )
          | ( c_in @ V_A @ ( c_Main_OUnionE__1 @ V_A @ V_C @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1300]) ).

thf(2704,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a )
          | ( c_in @ ( c_Main_OUnionE__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1301]) ).

thf(2705,plain,
    ( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ c_UNIV @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1302]) ).

thf(2706,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Main_OInterI__1 @ V_A @ V_C @ T_a ) @ T_a )
          | ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1303]) ).

thf(2707,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a )
          | ( c_in @ ( c_Main_OInterI__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1304]) ).

thf(2708,plain,
    ( ( ! [V_k: $i] : ( c_in @ ( c_SetInterval_OlessThan @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1305]) ).

thf(2709,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1306]) ).

thf(2710,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1307]) ).

thf(2711,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1308]) ).

thf(2712,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1309]) ).

thf(2713,plain,
    ( ( ! [V_k: $i] : ( c_in @ ( c_SetInterval_OatMost @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1310]) ).

thf(2714,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1311]) ).

thf(2715,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1312]) ).

thf(2716,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1313]) ).

thf(2717,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1314]) ).

thf(2718,plain,
    ( ( ! [V_b: $i,V_c: $i,T_b: $i,T_c: $i,V_r: $i,V_a: $i,T_a: $i,V_s: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_r @ ( tc_prod @ T_b @ T_c ) )
          | ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_s @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ ( tc_prod @ T_a @ T_c ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1315]) ).

thf(2719,plain,
    ( ( ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( V_xz
            = ( c_Pair @ ( c_Main_Orel__compE__1 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__3 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1316]) ).

thf(2720,plain,
    ( ( ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__2 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_a @ T_c ) @ V_s @ ( tc_prod @ T_a @ T_c ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1317]) ).

thf(2721,plain,
    ( ( ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__3 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_c @ T_b ) @ V_r @ ( tc_prod @ T_c @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1318]) ).

thf(2722,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1319]) ).

thf(2723,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1320]) ).

thf(2724,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
          | ( V_c
            = ( c_Pair @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1321]) ).

thf(2725,plain,
    ( ( ! [V_yx: $i,V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_yx @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( V_yx
            = ( c_Pair @ ( c_Main_OconverseE__2 @ V_r @ V_yx @ T_b @ T_a ) @ ( c_Main_OconverseE__1 @ V_r @ V_yx @ T_b @ T_a ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1322]) ).

thf(2726,plain,
    ( ( ! [V_yx: $i,V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_yx @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ V_r @ V_yx @ T_b @ T_a ) @ ( c_Main_OconverseE__2 @ V_r @ V_yx @ T_b @ T_a ) @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1323]) ).

thf(2727,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1324]) ).

thf(2728,plain,
    ( ( ! [V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1325]) ).

thf(2729,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1326]) ).

thf(2730,plain,
    ( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1327]) ).

thf(2731,plain,
    ( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Main_OImageE__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1328]) ).

thf(2732,plain,
    ( ( ! [V_p: $i,T_a: $i] :
          ( ~ ( c_in @ V_p @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
          | ( V_p
            = ( c_Pair @ ( c_Main_OIdE__1 @ V_p @ T_a ) @ ( c_Main_OIdE__1 @ V_p @ T_a ) @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1329]) ).

thf(2733,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1330]) ).

thf(2734,plain,
    ( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
          | ( c_in @ ( c_Pair @ V_a @ ( c_Main_ODomainE__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1331]) ).

thf(2735,plain,
    ( ( ! [T_a: $i,V_x: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ( c_lessequals @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1332]) ).

thf(2736,plain,
    ( ( ! [V_n: $i] : ( c_less @ c_0 @ ( c_Suc @ V_n ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1333]) ).

thf(2737,plain,
    ( ( ! [V_n: $i] :
          ~ ( c_less @ V_n @ V_n @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1334]) ).

thf(2738,plain,
    ( ( ! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1335]) ).

thf(2739,plain,
    ( ( ! [V_n: $i] : ( c_lessequals @ c_0 @ V_n @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1336]) ).

thf(2740,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1337]) ).

thf(2741,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1338]) ).

thf(2742,plain,
    ( ( ! [V_A: $i,T_a: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1339]) ).

thf(2743,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_l: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ~ ( c_in @ V_l @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ ( c_List_Olist_OCons @ V_a @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1340]) ).

thf(2744,plain,
    ( ( ! [V_x: $i,V_l: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_x @ V_A @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1341]) ).

thf(2745,plain,
    ( ( ! [V_x: $i,V_l: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_l @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1342]) ).

thf(2746,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_xs @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1343]) ).

thf(2747,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1344]) ).

thf(2748,plain,
    ( ( ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1345]) ).

thf(2749,plain,
    ( ( ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ V_ys @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1346]) ).

thf(2750,plain,
    ( ( ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs
            = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( c_Main_Olistrel__Cons2__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1347]) ).

thf(2751,plain,
    ( ( ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ V_y @ ( c_Main_Olistrel__Cons1__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1348]) ).

thf(2752,plain,
    ( ( ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ V_ys @ ( c_Main_Olistrel__Cons1__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1349]) ).

thf(2753,plain,
    ( ( ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs
            = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( c_Main_Olistrel__Cons1__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1350]) ).

thf(2754,plain,
    ( ( ! [V_xs: $i,T_a: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1351]) ).

thf(2755,plain,
    ( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ V_A @ V_xs @ T_a ) @ V_A @ T_a )
          | ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1352]) ).

thf(2756,plain,
    ( ( ! [V_xs: $i,V_A: $i,T_a: $i] :
          ( ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ ( c_Main_Oin__listsI__1 @ V_A @ V_xs @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1353]) ).

thf(2757,plain,
    ( ( ! [V_xs: $i,V_A: $i,T_a: $i,V_U: $i] :
          ( ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ~ ( c_in @ V_U @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
          | ( c_in @ V_U @ V_A @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1354]) ).

thf(2758,plain,
    ( ( ! [V_xs: $i,T_a: $i] : ( c_in @ ( c_List_Oset @ V_xs @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1355]) ).

thf(2759,plain,
    ( ( ! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1356]) ).

thf(2760,plain,
    ( ( ! [V_m: $i,V_d: $i] :
          ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_IntDef_Oint )
           != c_0 )
          | ( V_m
            = ( c_times @ V_d @ ( c_Main_Ozmod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_IntDef_Oint ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1357]) ).

thf(2761,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_m @ V_k @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1358]) ).

thf(2762,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_k @ V_m @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1359]) ).

thf(2763,plain,
    ( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ c_1 @ V_m @ tc_IntDef_Oint ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1360]) ).

thf(2764,plain,
    ( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_IntDef_Oint ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1361]) ).

thf(2765,plain,
    ( ( ! [V_n: $i,V_m: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ V_n ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ V_m ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1362]) ).

thf(2766,plain,
    ( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ V_n ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ V_m ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1363]) ).

thf(2767,plain,
    ( ( ! [V_S: $i,T_a: $i,V_y: $i,V_x: $i] :
          ( ~ ( c_Infinite__Set_Oatmost__one @ V_S @ T_a )
          | ~ ( c_in @ V_y @ V_S @ T_a )
          | ~ ( c_in @ V_x @ V_S @ T_a )
          | ( V_y = V_x ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1364]) ).

thf(2768,plain,
    ( ( ! [V_m: $i,V_n: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ V_n @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1365]) ).

thf(2769,plain,
    ( ( ! [V_m: $i,V_n: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ V_m @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1366]) ).

thf(2770,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
          | ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_Union @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1367]) ).

thf(2771,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
          | ( c_in @ ( c_Main_Ofinite__Union__1 @ V_A @ T_a ) @ V_A @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_Union @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1368]) ).

thf(2772,plain,
    ( ( ! [V_G: $i,T_a: $i,V_F: $i] :
          ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1369]) ).

thf(2773,plain,
    ( ( ! [V_F: $i,T_a: $i,V_G: $i] :
          ( ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1370]) ).

thf(2774,plain,
    ( ( ! [V_A: $i,T_a: $i,V_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_insert @ V_a @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1371]) ).

thf(2775,plain,
    ( ( ! [T_a: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1372]) ).

thf(2776,plain,
    ( ( ! [V_m: $i,V_d: $i] :
          ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_nat )
           != c_0 )
          | ( V_m
            = ( c_times @ V_d @ ( c_Main_Omod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1373]) ).

thf(2777,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_m @ V_k @ tc_nat ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1374]) ).

thf(2778,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_k @ V_m @ tc_nat ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1375]) ).

thf(2779,plain,
    ( ( ! [V_k: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ V_k @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1376]) ).

thf(2780,plain,
    ( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1377]) ).

thf(2781,plain,
    ( ( ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
          ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1378]) ).

thf(2782,plain,
    ( ( ! [V_M: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
          ( ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1379]) ).

thf(2783,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1380]) ).

thf(2784,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1381]) ).

thf(2785,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1382]) ).

thf(2786,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1383]) ).

thf(2787,plain,
    ( ( ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i,V_M: $i,V_A: $i] :
          ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1384]) ).

thf(2788,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OuprodE__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1385]) ).

thf(2789,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OuprodE__2 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1386]) ).

thf(2790,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_c
            = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ ( c_Main_OuprodE__2 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1387]) ).

thf(2791,plain,
    ( ( ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1388]) ).

thf(2792,plain,
    ( ( ! [V_M: $i,V_M_H: $i,T_a: $i,T_b: $i,V_r: $i,V_s: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ V_M_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1389]) ).

thf(2793,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1390]) ).

thf(2794,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1391]) ).

thf(2795,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1392]) ).

thf(2796,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1393]) ).

thf(2797,plain,
    ( ( ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i,V_M: $i,V_M_H: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1394]) ).

thf(2798,plain,
    ( ( ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__3 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1395]) ).

thf(2799,plain,
    ( ( ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__4 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1396]) ).

thf(2800,plain,
    ( ( ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_c
            = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__2 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__4 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1397]) ).

thf(2801,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Datatype__Universe_ONumb @ V_x @ T_a @ T_b )
           != ( c_Datatype__Universe_ONumb @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1398]) ).

thf(2802,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Datatype__Universe_OLeaf @ V_x @ T_a @ T_b )
           != ( c_Datatype__Universe_OLeaf @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1399]) ).

thf(2803,plain,
    ( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ v_G ) @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1402]) ).

thf(2804,plain,
    ( ( ~ $false ) = $true ),
    inference(polarity_switch,[status(thm)],[1403]) ).

thf(2805,plain,
    ( ( ! [V_H: $i,V_H_H: $i] :
          ( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_H ) @ ( c_Message_Oanalz @ V_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
          | ! [V_G: $i,V_G_H: $i] :
              ( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
              | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ V_G_H @ V_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1405]) ).

thf(2806,plain,
    ( ( ! [V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ V_Y @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ! [V_X: $i] :
              ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1407]) ).

thf(2807,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ! [V_K: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1410]) ).

thf(2808,plain,
    ( ( ! [V_nat: $i,V_msg: $i,V_nat_H: $i,V_msg_H: $i] :
          ( ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
           != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
          | ( V_msg = V_msg_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1415]) ).

thf(2809,plain,
    ( ( ! [V_nat: $i,V_msg: $i,V_nat_H: $i] :
          ( ! [V_msg_H: $i] :
              ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
             != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1416]) ).

thf(2810,plain,
    ( ( ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i,V_msg2_H: $i] :
          ( ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
           != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
          | ( V_msg2 = V_msg2_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1417]) ).

thf(2811,plain,
    ( ( ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i] :
          ( ! [V_msg2_H: $i] :
              ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
             != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
          | ( V_msg1 = V_msg1_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1418]) ).

thf(2812,plain,
    ( ( ! [V_msg: $i,V_msg_H: $i] :
          ( ( ( c_Message_Omsg_OHash @ V_msg )
           != ( c_Message_Omsg_OHash @ V_msg_H ) )
          | ( V_msg = V_msg_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1419]) ).

thf(2813,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_OKey @ V_nat )
           != ( c_Message_Omsg_OKey @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1420]) ).

thf(2814,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_ONonce @ V_nat )
           != ( c_Message_Omsg_ONonce @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1421]) ).

thf(2815,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_ONumber @ V_nat )
           != ( c_Message_Omsg_ONumber @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1422]) ).

thf(2816,plain,
    ( ( ! [V_agent: $i,V_agent_H: $i] :
          ( ( ( c_Message_Omsg_OAgent @ V_agent )
           != ( c_Message_Omsg_OAgent @ V_agent_H ) )
          | ( V_agent = V_agent_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1423]) ).

thf(2817,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Oagent_OFriend @ V_nat )
           != ( c_Message_Oagent_OFriend @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1428]) ).

thf(2818,plain,
    ( ( ! [V_nat: $i] :
          ( c_Message_Oagent_OSpy
         != ( c_Message_Oagent_OFriend @ V_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1429]) ).

thf(2819,plain,
    ( ( ! [V_nat: $i] :
          ( ( c_Message_Oagent_OFriend @ V_nat )
         != c_Message_Oagent_OSpy ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1430]) ).

thf(2820,plain,
    ( ( c_Message_Oagent_OSpy != c_Message_Oagent_OServer )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1431]) ).

thf(2821,plain,
    ( ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1432]) ).

thf(2822,plain,
    ( ( ! [V_nat_H: $i] :
          ( ( c_Message_Oagent_OFriend @ V_nat_H )
         != c_Message_Oagent_OServer ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1433]) ).

thf(2823,plain,
    ( ( ! [V_nat_H: $i] :
          ( c_Message_Oagent_OServer
         != ( c_Message_Oagent_OFriend @ V_nat_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1434]) ).

thf(2824,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
              | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1448]) ).

thf(2825,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
              | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1451]) ).

thf(2826,plain,
    ( ( ! [V_b: $i,T_b: $i,T_a: $i,V_a: $i] :
          ( ( c_Sum__Type_OInr @ V_b @ T_b @ T_a )
         != ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1456]) ).

thf(2827,plain,
    ( ( ! [V_x: $i,T_b: $i,T_a: $i,V_y: $i] :
          ( ( ( c_Sum__Type_OInr @ V_x @ T_b @ T_a )
           != ( c_Sum__Type_OInr @ V_y @ T_b @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1457]) ).

thf(2828,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
          ( ( c_Sum__Type_OInl @ V_a @ T_a @ T_b )
         != ( c_Sum__Type_OInr @ V_b @ T_b @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1458]) ).

thf(2829,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Sum__Type_OInl @ V_x @ T_a @ T_b )
           != ( c_Sum__Type_OInl @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1459]) ).

thf(2830,plain,
    ( ( ! [V_b: $i,T_a: $i,V_a: $i,V_A: $i] :
          ( ( ( c_insert @ V_b @ c_emptyset @ T_a )
           != ( c_insert @ V_a @ V_A @ T_a ) )
          | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1461]) ).

thf(2831,plain,
    ( ( ! [V_b: $i,T_a: $i,V_a: $i] :
          ( ! [V_A: $i] :
              ( ( c_insert @ V_b @ c_emptyset @ T_a )
             != ( c_insert @ V_a @ V_A @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1462]) ).

thf(2832,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ V_A @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1464]) ).

thf(2833,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ V_A @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1465]) ).

thf(2834,plain,
    ( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
          | ( V_a = V_b )
          | ( c_in @ V_a @ V_A @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1467]) ).

thf(2835,plain,
    ( ( ! [V_a: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_B @ T_a )
          | ! [V_b: $i] : ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1469]) ).

thf(2836,plain,
    ( ( ! [V_A: $i,V_X: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ V_X @ T_a )
          | ! [V_C: $i] :
              ( ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
              | ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1471]) ).

thf(2837,plain,
    ( ( ! [V_A: $i,V_B: $i] :
          ( ! [T_a: $i] :
              ( ( c_union @ V_A @ V_B @ T_a )
             != c_emptyset )
          | ( V_B = c_emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1473]) ).

thf(2838,plain,
    ( ( ! [V_A: $i] :
          ( ! [V_B: $i,T_a: $i] :
              ( ( c_union @ V_A @ V_B @ T_a )
             != c_emptyset )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1474]) ).

thf(2839,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1476]) ).

thf(2840,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ! [V_A: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1477]) ).

thf(2841,plain,
    ( ( c_UNIV != c_emptyset )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1478]) ).

thf(2842,plain,
    ( ( ! [V_X: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
          | ! [V_A: $i] :
              ( ~ ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a )
              | ( c_in @ V_A @ V_X @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1481]) ).

thf(2843,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ! [V_A: $i] :
              ( ~ ( c_in @ V_c @ V_A @ T_a )
              | ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1482]) ).

thf(2844,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] :
              ( ( c_in @ V_c @ V_B @ T_a )
              | ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1485]) ).

thf(2845,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ! [V_A: $i] :
              ~ ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1487]) ).

thf(2846,plain,
    ( ( ! [V_A: $i,T_a: $i,V_B: $i] :
          ( ( ( c_uminus @ V_A @ ( tc_set @ T_a ) )
           != ( c_uminus @ V_B @ ( tc_set @ T_a ) ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1490]) ).

thf(2847,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ V_x @ V_y @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1493]) ).

thf(2848,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1494]) ).

thf(2849,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_less @ V_i @ V_k @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1495]) ).

thf(2850,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a )
              | ( c_less @ V_i @ V_k @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1496]) ).

thf(2851,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OlessThan @ V_x @ T_a )
               != ( c_SetInterval_OlessThan @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1497]) ).

thf(2852,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ~ ( c_lessequals @ V_y @ V_x @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1498]) ).

thf(2853,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1499]) ).

thf(2854,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_k: $i,V_i: $i] :
              ( ~ ( c_less @ V_k @ V_i @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1500]) ).

thf(2855,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a )
              | ( c_less @ V_k @ V_i @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1501]) ).

thf(2856,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OgreaterThan @ V_x @ T_a )
               != ( c_SetInterval_OgreaterThan @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1502]) ).

thf(2857,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ V_x @ V_y @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1503]) ).

thf(2858,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1504]) ).

thf(2859,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_lessequals @ V_i @ V_k @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1505]) ).

thf(2860,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a )
              | ( c_lessequals @ V_i @ V_k @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1506]) ).

thf(2861,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OatMost @ V_x @ T_a )
               != ( c_SetInterval_OatMost @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1507]) ).

thf(2862,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ~ ( c_lessequals @ V_y @ V_x @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1508]) ).

thf(2863,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1509]) ).

thf(2864,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_k: $i,V_i: $i] :
              ( ~ ( c_lessequals @ V_k @ V_i @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1510]) ).

thf(2865,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a )
              | ( c_lessequals @ V_k @ V_i @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1511]) ).

thf(2866,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OatLeast @ V_x @ T_a )
               != ( c_SetInterval_OatLeast @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1512]) ).

thf(2867,plain,
    ( ( ! [V_a: $i,V_b: $i] :
          ( ! [T_a: $i] :
              ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1513]) ).

thf(2868,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
          ( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
           != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
          | ( V_b = V_b_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1519]) ).

thf(2869,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i] :
          ( ! [V_b_H: $i] :
              ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
             != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1520]) ).

thf(2870,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] :
              ~ ( c_less @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1521]) ).

thf(2871,plain,
    ( ( c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0 )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1522]) ).

thf(2872,plain,
    ( ( c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1523]) ).

thf(2873,plain,
    ( ( ! [V_n: $i] :
          ( ( V_n = c_0 )
          | ( c_less @ c_0 @ V_n @ tc_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1528]) ).

thf(2874,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_plus @ V_m @ V_n @ tc_nat )
           != c_0 )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1536]) ).

thf(2875,plain,
    ( ( ! [V_m: $i] :
          ( ! [V_n: $i] :
              ( ( c_plus @ V_m @ V_n @ tc_nat )
             != c_0 )
          | ( V_m = c_0 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1537]) ).

thf(2876,plain,
    ( ( ! [V_n: $i] :
          ( ~ ( c_less @ c_0 @ V_n @ tc_nat )
          | ! [V_m: $i] : ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1538]) ).

thf(2877,plain,
    ( ( ! [V_m: $i] :
          ( ~ ( c_less @ c_0 @ V_m @ tc_nat )
          | ! [V_n: $i] : ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1539]) ).

thf(2878,plain,
    ( ( ! [V_m: $i] :
          ( c_0
         != ( c_Suc @ V_m ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1541]) ).

thf(2879,plain,
    ( ( ! [V_m: $i] :
          ( ( c_Suc @ V_m )
         != c_0 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1542]) ).

thf(2880,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_Suc @ V_m )
           != ( c_Suc @ V_n ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1547]) ).

thf(2881,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( ( c_List_Oset @ V_xs @ T_a )
             != c_emptyset )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1549]) ).

thf(2882,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( c_emptyset
             != ( c_List_Oset @ V_xs @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1551]) ).

thf(2883,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( V_xs
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1553]) ).

thf(2884,plain,
    ( ( ! [V_ys: $i,V_xs: $i] :
          ( ! [T_a: $i] :
              ( V_ys
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1555]) ).

thf(2885,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
          ( ( ( c_append @ V_xs @ V_ys @ T_a )
           != ( c_append @ V_xs @ V_zs @ T_a ) )
          | ( V_ys = V_zs ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1556]) ).

thf(2886,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
          ( ( ( c_List_Orev @ V_xs @ T_a )
           != ( c_List_Orev @ V_ys @ T_a ) )
          | ( V_xs = V_ys ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1557]) ).

thf(2887,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( ( c_List_Orev @ V_xs @ T_a )
             != c_List_Olist_ONil )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1559]) ).

thf(2888,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
          ( ( ( c_List_Orev @ V_xs @ T_a )
           != ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
          | ( V_xs
            = ( c_append @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1561]) ).

thf(2889,plain,
    ( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
          ( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
           != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
          | ( V_list = V_list_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1562]) ).

thf(2890,plain,
    ( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i] :
          ( ! [V_list_H: $i] :
              ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
             != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1563]) ).

thf(2891,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
         != c_List_Olist_ONil ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1564]) ).

thf(2892,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( c_List_Olist_ONil
         != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1565]) ).

thf(2893,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_List_Oremdups @ V_xs @ T_a )
           != V_xs )
          | ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
            = ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1566]) ).

thf(2894,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
           != ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
          | ( ( c_List_Oremdups @ V_xs @ T_a )
            = V_xs ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1567]) ).

thf(2895,plain,
    ( ( ! [V_xs: $i] :
          ( ( V_xs = c_List_Olist_ONil )
          | ! [T_a: $i] : ( c_less @ c_0 @ ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1568]) ).

thf(2896,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
             != c_0 )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1571]) ).

thf(2897,plain,
    ( ( ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i,V_nibble2_H: $i] :
          ( ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
           != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
          | ( V_nibble2 = V_nibble2_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1572]) ).

thf(2898,plain,
    ( ( ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i] :
          ( ! [V_nibble2_H: $i] :
              ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
             != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
          | ( V_nibble1 = V_nibble1_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1573]) ).

thf(2899,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != V_xs )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1575]) ).

thf(2900,plain,
    ( ( ! [V_xs: $i] :
          ( ! [V_ys: $i,T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != V_ys )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1577]) ).

thf(2901,plain,
    ( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
          ( ( ( c_append @ V_ys @ V_xs @ T_a )
           != ( c_append @ V_zs @ V_xs @ T_a ) )
          | ( V_ys = V_zs ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1578]) ).

thf(2902,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != c_List_Olist_ONil )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1580]) ).

thf(2903,plain,
    ( ( ! [V_xs: $i] :
          ( ! [V_ys: $i,T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != c_List_Olist_ONil )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1581]) ).

thf(2904,plain,
    ( ( ! [V_ys: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_ys @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ! [V_xs: $i] :
              ( ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
              | ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1582]) ).

thf(2905,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
          ( ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
           != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1585]) ).

thf(2906,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i] :
          ( ! [V_y: $i] :
              ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
             != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
          | ( V_xs = V_ys ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1586]) ).

thf(2907,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( c_List_Olist_ONil
             != ( c_List_Orev @ V_xs @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1589]) ).

thf(2908,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( c_List_Olist_ONil
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1591]) ).

thf(2909,plain,
    ( ( ! [V_xs: $i] :
          ( ! [V_ys: $i,T_a: $i] :
              ( c_List_Olist_ONil
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1592]) ).

thf(2910,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_IntDef_Oint @ V_m )
           != ( c_IntDef_Oint @ V_n ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1600]) ).

thf(2911,plain,
    ( ( ! [V_k: $i,V_n: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_k @ V_n @ tc_nat )
          | ! [V_m: $i] :
              ( ~ ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat )
              | ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1602]) ).

thf(2912,plain,
    ( ( ! [V_k: $i,V_m: $i] :
          ( ! [V_n: $i] :
              ~ ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat )
          | ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1604]) ).

thf(2913,plain,
    ( ( ! [V_G: $i,T_a: $i] :
          ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_F: $i] :
              ( ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
              | ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1607]) ).

thf(2914,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_a: $i] : ( c_in @ ( c_minus @ V_A @ ( c_insert @ V_a @ V_B @ T_a ) @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1612]) ).

thf(2915,plain,
    ( ( c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1614]) ).

thf(2916,plain,
    ( ( c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1615]) ).

thf(2917,plain,
    ( ( ! [V_A: $i] :
          ( ! [V_r: $i,T_a: $i] :
              ( ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a )
             != c_emptyset )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1617]) ).

thf(2918,plain,
    ( ( ! [V_A: $i] :
          ( ! [V_r: $i,T_a: $i] :
              ( c_emptyset
             != ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1619]) ).

thf(2919,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_k: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1622]) ).

thf(2920,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1623]) ).

thf(2921,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1624]) ).

thf(2922,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i,V_N_H: $i] :
          ( ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
           != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
          | ( V_N = V_N_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1625]) ).

thf(2923,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i] :
          ( ! [V_N_H: $i] :
              ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
             != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
          | ( V_M = V_M_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1626]) ).

thf(2924,plain,
    ( ( ! [V_k: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1627]) ).

thf(2925,plain,
    ( ( ! [V_k: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
         != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1628]) ).

thf(2926,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1629]) ).

thf(2927,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_k: $i] :
          ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1630]) ).

thf(2928,plain,
    ( ( ! [V_N: $i,T_a: $i,T_b: $i,V_M: $i] :
          ( ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1631]) ).

thf(2929,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( ( c_Datatype__Universe_OIn1 @ V_M @ T_a @ T_b )
           != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) )
          | ( V_M = V_N ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1632]) ).

thf(2930,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
         != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1633]) ).

thf(2931,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
           != ( c_Datatype__Universe_OIn0 @ V_N @ T_a @ T_b ) )
          | ( V_M = V_N ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1634]) ).

thf(2932,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1635]) ).

thf(2933,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
          ( ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
           != ( c_Datatype__Universe_OAtom @ V_b @ T_a @ T_b ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1636]) ).

thf(2934,plain,
    ( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
          ( ( ( c_Datatype_Ooption_OSome @ V_a @ T_a )
           != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1637]) ).

thf(2935,plain,
    ( ( ! [V_a_H: $i,T_a: $i] :
          ( ( c_Datatype_Ooption_OSome @ V_a_H @ T_a )
         != c_Datatype_Ooption_ONone ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1638]) ).

thf(2936,plain,
    ( ( ! [V_a_H: $i,T_a: $i] :
          ( c_Datatype_Ooption_ONone
         != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1639]) ).

thf(2937,plain,
    ( ( ! [V_x: $i] :
          ( ( V_x = c_Datatype_Ooption_ONone )
          | ! [T_a: $i] :
              ( V_x
              = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1640]) ).

thf(2938,plain,
    ( ( ! [V_x: $i] :
          ( ( V_x = c_Datatype_Ooption_ONone )
          | ! [T_a: $i] :
              ( V_x
              = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1641]) ).

thf(2939,plain,
    ( ( ! [V_rb: $i,T_b: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_rb @ T_b )
          | ! [V_ra: $i,T_a: $i] :
              ( ~ ( c_Wellfounded__Recursion_Owf @ V_ra @ T_a )
              | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ V_ra @ V_rb @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2676]) ).

thf(2940,plain,
    ( ( ! [V_R2: $i,T_b: $i] :
          ( ~ ( c_Relation_Otrans @ V_R2 @ T_b )
          | ! [V_R1: $i,T_a: $i] :
              ( ~ ( c_Relation_Otrans @ V_R1 @ T_a )
              | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ V_R1 @ V_R2 @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2678]) ).

thf(2941,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ T_b @ T_a ) )
          | ( c_in @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2686]) ).

thf(2942,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ V_B @ T_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2687]) ).

thf(2943,plain,
    ( ( ! [V_b: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ V_B @ T_a )
          | ! [T_b: $i,V_A: $i] : ( c_in @ ( c_Sum__Type_OInr @ V_b @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_b @ T_a ) @ ( tc_sum @ T_b @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2689]) ).

thf(2944,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ! [T_b: $i,V_B: $i] : ( c_in @ ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2690]) ).

thf(2945,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] :
              ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
              | ( c_in @ V_c @ V_B @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2695]) ).

thf(2946,plain,
    ( ( ! [V_a: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ c_emptyset @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2696]) ).

thf(2947,plain,
    ( ( ! [V_b: $i,V_a: $i] :
          ( ! [T_a: $i] :
              ~ ( c_in @ V_b @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a )
          | ( V_b = V_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2698]) ).

thf(2948,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( V_A = V_B )
          | ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2699]) ).

thf(2949,plain,
    ( ( ! [V_b: $i,V_c: $i,T_b: $i,T_c: $i,V_r: $i,V_a: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_r @ ( tc_prod @ T_b @ T_c ) )
          | ! [T_a: $i,V_s: $i] :
              ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_s @ ( tc_prod @ T_a @ T_b ) )
              | ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ ( tc_prod @ T_a @ T_c ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2718]) ).

thf(2950,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ! [T_b: $i,V_r: $i] :
              ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
              | ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2729]) ).

thf(2951,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2735]) ).

thf(2952,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ! [V_l: $i] :
              ( ~ ( c_in @ V_l @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
              | ( c_in @ ( c_List_Olist_OCons @ V_a @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2743]) ).

thf(2953,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i,V_r: $i] :
              ~ ( c_in @ ( c_Pair @ V_xs @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2746]) ).

thf(2954,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i,V_r: $i] :
              ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2747]) ).

thf(2955,plain,
    ( ( ! [V_xs: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ! [V_U: $i] :
              ( ~ ( c_in @ V_U @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
              | ( c_in @ V_U @ V_A @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2757]) ).

thf(2956,plain,
    ( ( ! [V_m: $i,V_d: $i] :
          ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_IntDef_Oint )
           != c_0 )
          | ( V_m
            = ( c_times @ V_d @ ( c_Main_Ozmod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_IntDef_Oint ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2760]) ).

thf(2957,plain,
    ( ( ! [V_S: $i,T_a: $i] :
          ( ~ ( c_Infinite__Set_Oatmost__one @ V_S @ T_a )
          | ! [V_y: $i] :
              ( ~ ( c_in @ V_y @ V_S @ T_a )
              | ! [V_x: $i] :
                  ( ~ ( c_in @ V_x @ V_S @ T_a )
                  | ( V_y = V_x ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2767]) ).

thf(2958,plain,
    ( ( ! [V_G: $i,T_a: $i] :
          ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_F: $i] : ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2772]) ).

thf(2959,plain,
    ( ( ! [V_F: $i,T_a: $i] :
          ( ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_G: $i] : ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2773]) ).

thf(2960,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_a: $i] : ( c_in @ ( c_insert @ V_a @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2774]) ).

thf(2961,plain,
    ( ( ! [V_m: $i,V_d: $i] :
          ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_nat )
           != c_0 )
          | ( V_m
            = ( c_times @ V_d @ ( c_Main_Omod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_nat ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2776]) ).

thf(2962,plain,
    ( ( ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ! [V_A: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2781]) ).

thf(2963,plain,
    ( ( ! [V_M: $i,V_A: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ! [V_B: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2782]) ).

thf(2964,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2784]) ).

thf(2965,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2785]) ).

thf(2966,plain,
    ( ( ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ! [V_M: $i,V_A: $i] :
              ( ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
              | ( c_in @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2787]) ).

thf(2967,plain,
    ( ( ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ! [V_r: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2791]) ).

thf(2968,plain,
    ( ( ! [V_M: $i,V_M_H: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ! [V_s: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ V_M_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2792]) ).

thf(2969,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2794]) ).

thf(2970,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2795]) ).

thf(2971,plain,
    ( ( ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i,V_M: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ! [V_M_H: $i,V_r: $i] :
              ( ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
              | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2797]) ).

thf(2972,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Datatype__Universe_ONumb @ V_x @ T_a @ T_b )
           != ( c_Datatype__Universe_ONumb @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2801]) ).

thf(2973,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Datatype__Universe_OLeaf @ V_x @ T_a @ T_b )
           != ( c_Datatype__Universe_OLeaf @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2802]) ).

thf(2974,plain,
    ( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ v_G ) @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[2803]) ).

thf(2975,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Datatype__Universe_OLeaf @ V_x @ T_a @ T_b )
           != ( c_Datatype__Universe_OLeaf @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[2973]) ).

thf(2976,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Datatype__Universe_ONumb @ V_x @ T_a @ T_b )
           != ( c_Datatype__Universe_ONumb @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[2972]) ).

thf(2977,plain,
    ( ( ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_c
            = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__2 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__4 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2800]) ).

thf(2978,plain,
    ( ( ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__4 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2799]) ).

thf(2979,plain,
    ( ( ! [V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( c_Main_OdprodE__3 @ V_c @ V_r @ V_s @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2798]) ).

thf(2980,plain,
    ( ( ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i,V_M: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ! [V_M_H: $i,V_r: $i] :
              ( ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
              | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odprod @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2971]) ).

thf(2981,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2796]) ).

thf(2982,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2970]) ).

thf(2983,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( V_w
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2969]) ).

thf(2984,plain,
    ( ( ! [V_w: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_w @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ V_r @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__2 @ V_r @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ V_s @ V_w @ T_a @ T_b ) @ ( c_Main_OdsumE__4 @ V_s @ V_w @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2793]) ).

thf(2985,plain,
    ( ( ! [V_M: $i,V_M_H: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_M @ V_M_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_r @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ! [V_s: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn0 @ V_M_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2968]) ).

thf(2986,plain,
    ( ( ! [V_N: $i,V_N_H: $i,T_a: $i,T_b: $i,V_s: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_N @ V_N_H @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ V_s @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) )
          | ! [V_r: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_OIn1 @ V_N_H @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) @ ( c_Datatype__Universe_Odsum @ V_r @ V_s @ T_a @ T_b ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2967]) ).

thf(2987,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_c
            = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ ( c_Main_OuprodE__2 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2790]) ).

thf(2988,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OuprodE__2 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2789]) ).

thf(2989,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_c @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OuprodE__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2788]) ).

thf(2990,plain,
    ( ( ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ! [V_M: $i,V_A: $i] :
              ( ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
              | ( c_in @ ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ouprod @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2966]) ).

thf(2991,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2786]) ).

thf(2992,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2965]) ).

thf(2993,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( V_u
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2964]) ).

thf(2994,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OusumE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ( c_in @ ( c_Main_OusumE__2 @ V_B @ V_u @ T_a @ T_b ) @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2783]) ).

thf(2995,plain,
    ( ( ! [V_M: $i,V_A: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_M @ V_A @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ! [V_B: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2963]) ).

thf(2996,plain,
    ( ( ! [V_N: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_N @ V_B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) )
          | ! [V_A: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) @ ( c_Datatype__Universe_Ousum @ V_A @ V_B @ T_a @ T_b ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2962]) ).

thf(2997,plain,
    ( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2780]) ).

thf(2998,plain,
    ( ( ! [V_k: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ V_k @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2779]) ).

thf(2999,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_k @ V_m @ tc_nat ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2778]) ).

thf(3000,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_m @ V_k @ tc_nat ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2777]) ).

thf(3001,plain,
    ( ( ! [V_m: $i,V_d: $i] :
          ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_nat )
           != c_0 )
          | ( V_m
            = ( c_times @ V_d @ ( c_Main_Omod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2961]) ).

thf(3002,plain,
    ( ( ! [T_a: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2775]) ).

thf(3003,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_a: $i] : ( c_in @ ( c_insert @ V_a @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2960]) ).

thf(3004,plain,
    ( ( ! [V_F: $i,T_a: $i] :
          ( ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_G: $i] : ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2959]) ).

thf(3005,plain,
    ( ( ! [V_G: $i,T_a: $i] :
          ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_F: $i] : ( c_in @ ( c_inter @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2958]) ).

thf(3006,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
          | ( c_in @ ( c_Main_Ofinite__Union__1 @ V_A @ T_a ) @ V_A @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_Union @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2771]) ).

thf(3007,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
          | ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_Union @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2770]) ).

thf(3008,plain,
    ( ( ! [V_m: $i,V_n: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ V_m @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2769]) ).

thf(3009,plain,
    ( ( ! [V_m: $i,V_n: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ V_n @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2768]) ).

thf(3010,plain,
    ( ( ! [V_S: $i,T_a: $i] :
          ( ~ ( c_Infinite__Set_Oatmost__one @ V_S @ T_a )
          | ! [V_y: $i] :
              ( ~ ( c_in @ V_y @ V_S @ T_a )
              | ! [V_x: $i] :
                  ( ~ ( c_in @ V_x @ V_S @ T_a )
                  | ( V_y = V_x ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2957]) ).

thf(3011,plain,
    ( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ V_n ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ V_m ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(copy,[status(thm)],[2766]) ).

thf(3012,plain,
    ( ( ! [V_n: $i,V_m: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ V_n ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ V_m ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(copy,[status(thm)],[2765]) ).

thf(3013,plain,
    ( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_IntDef_Oint ) )
    = $true ),
    inference(copy,[status(thm)],[2764]) ).

thf(3014,plain,
    ( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ c_1 @ V_m @ tc_IntDef_Oint ) )
    = $true ),
    inference(copy,[status(thm)],[2763]) ).

thf(3015,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_k @ V_m @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(copy,[status(thm)],[2762]) ).

thf(3016,plain,
    ( ( ! [V_k: $i,V_m: $i] : ( c_Divides_Oop_Advd @ V_k @ ( c_times @ V_m @ V_k @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
    = $true ),
    inference(copy,[status(thm)],[2761]) ).

thf(3017,plain,
    ( ( ! [V_m: $i,V_d: $i] :
          ( ( ( c_Divides_Oop_Amod @ V_m @ V_d @ tc_IntDef_Oint )
           != c_0 )
          | ( V_m
            = ( c_times @ V_d @ ( c_Main_Ozmod__eq__0D__dest__1 @ V_d @ V_m ) @ tc_IntDef_Oint ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2956]) ).

thf(3018,plain,
    ( ( ! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[2759]) ).

thf(3019,plain,
    ( ( ! [V_xs: $i,T_a: $i] : ( c_in @ ( c_List_Oset @ V_xs @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2758]) ).

thf(3020,plain,
    ( ( ! [V_xs: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ! [V_U: $i] :
              ( ~ ( c_in @ V_U @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
              | ( c_in @ V_U @ V_A @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2955]) ).

thf(3021,plain,
    ( ( ! [V_xs: $i,V_A: $i,T_a: $i] :
          ( ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ ( c_Main_Oin__listsI__1 @ V_A @ V_xs @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2756]) ).

thf(3022,plain,
    ( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ V_A @ V_xs @ T_a ) @ V_A @ T_a )
          | ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2755]) ).

thf(3023,plain,
    ( ( ! [V_xs: $i,T_a: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2754]) ).

thf(3024,plain,
    ( ( ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs
            = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( c_Main_Olistrel__Cons1__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2753]) ).

thf(3025,plain,
    ( ( ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ V_ys @ ( c_Main_Olistrel__Cons1__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2752]) ).

thf(3026,plain,
    ( ( ! [V_y: $i,V_ys: $i,T_a: $i,V_xs: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ V_y @ ( c_Main_Olistrel__Cons1__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2751]) ).

thf(3027,plain,
    ( ( ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs
            = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ ( c_Main_Olistrel__Cons2__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2750]) ).

thf(3028,plain,
    ( ( ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ V_ys @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2749]) ).

thf(3029,plain,
    ( ( ! [V_xs: $i,V_y: $i,V_ys: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ V_r @ V_xs @ V_y @ V_ys @ T_a ) @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2748]) ).

thf(3030,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i,V_r: $i] :
              ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ V_xs @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2954]) ).

thf(3031,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i,V_r: $i] :
              ~ ( c_in @ ( c_Pair @ V_xs @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olistrel @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2953]) ).

thf(3032,plain,
    ( ( ! [V_x: $i,V_l: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_l @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2745]) ).

thf(3033,plain,
    ( ( ! [V_x: $i,V_l: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_x @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2744]) ).

thf(3034,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ! [V_l: $i] :
              ( ~ ( c_in @ V_l @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
              | ( c_in @ ( c_List_Olist_OCons @ V_a @ V_l @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2952]) ).

thf(3035,plain,
    ( ( ! [V_A: $i,T_a: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2742]) ).

thf(3036,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2741]) ).

thf(3037,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2740]) ).

thf(3038,plain,
    ( ( ! [V_n: $i] : ( c_lessequals @ c_0 @ V_n @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2739]) ).

thf(3039,plain,
    ( ( ! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2738]) ).

thf(3040,plain,
    ( ( ! [V_n: $i] :
          ~ ( c_less @ V_n @ V_n @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2737]) ).

thf(3041,plain,
    ( ( ! [V_n: $i] : ( c_less @ c_0 @ ( c_Suc @ V_n ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[2736]) ).

thf(3042,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2951]) ).

thf(3043,plain,
    ( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
          | ( c_in @ ( c_Pair @ V_a @ ( c_Main_ODomainE__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2734]) ).

thf(3044,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2733]) ).

thf(3045,plain,
    ( ( ! [V_p: $i,T_a: $i] :
          ( ~ ( c_in @ V_p @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
          | ( V_p
            = ( c_Pair @ ( c_Main_OIdE__1 @ V_p @ T_a ) @ ( c_Main_OIdE__1 @ V_p @ T_a ) @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2732]) ).

thf(3046,plain,
    ( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Main_OImageE__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2731]) ).

thf(3047,plain,
    ( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2730]) ).

thf(3048,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ! [T_b: $i,V_r: $i] :
              ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
              | ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2950]) ).

thf(3049,plain,
    ( ( ! [V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2728]) ).

thf(3050,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2727]) ).

thf(3051,plain,
    ( ( ! [V_yx: $i,V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_yx @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ V_r @ V_yx @ T_b @ T_a ) @ ( c_Main_OconverseE__2 @ V_r @ V_yx @ T_b @ T_a ) @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2726]) ).

thf(3052,plain,
    ( ( ! [V_yx: $i,V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_yx @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( V_yx
            = ( c_Pair @ ( c_Main_OconverseE__2 @ V_r @ V_yx @ T_b @ T_a ) @ ( c_Main_OconverseE__1 @ V_r @ V_yx @ T_b @ T_a ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2725]) ).

thf(3053,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
          | ( V_c
            = ( c_Pair @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2724]) ).

thf(3054,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ ( c_Main_OdiagE__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2723]) ).

thf(3055,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_Odiag @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2722]) ).

thf(3056,plain,
    ( ( ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__3 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_c @ T_b ) @ V_r @ ( tc_prod @ T_c @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2721]) ).

thf(3057,plain,
    ( ( ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__2 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_a @ T_c ) @ V_s @ ( tc_prod @ T_a @ T_c ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2720]) ).

thf(3058,plain,
    ( ( ! [V_xz: $i,V_r: $i,V_s: $i,T_c: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_xz @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_c @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( V_xz
            = ( c_Pair @ ( c_Main_Orel__compE__1 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ ( c_Main_Orel__compE__3 @ V_r @ V_s @ V_xz @ T_c @ T_b @ T_a ) @ T_a @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2719]) ).

thf(3059,plain,
    ( ( ! [V_b: $i,V_c: $i,T_b: $i,T_c: $i,V_r: $i,V_a: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_r @ ( tc_prod @ T_b @ T_c ) )
          | ! [T_a: $i,V_s: $i] :
              ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_s @ ( tc_prod @ T_a @ T_b ) )
              | ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ ( tc_prod @ T_a @ T_c ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2949]) ).

thf(3060,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2717]) ).

thf(3061,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[2716]) ).

thf(3062,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2715]) ).

thf(3063,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[2714]) ).

thf(3064,plain,
    ( ( ! [V_k: $i] : ( c_in @ ( c_SetInterval_OatMost @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2713]) ).

thf(3065,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2712]) ).

thf(3066,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[2711]) ).

thf(3067,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ V_l @ V_u @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2710]) ).

thf(3068,plain,
    ( ( ! [V_l: $i,V_u: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ V_l @ V_u @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[2709]) ).

thf(3069,plain,
    ( ( ! [V_k: $i] : ( c_in @ ( c_SetInterval_OlessThan @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2708]) ).

thf(3070,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a )
          | ( c_in @ ( c_Main_OInterI__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2707]) ).

thf(3071,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Main_OInterI__1 @ V_A @ V_C @ T_a ) @ T_a )
          | ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2706]) ).

thf(3072,plain,
    ( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ c_UNIV @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[2705]) ).

thf(3073,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a )
          | ( c_in @ ( c_Main_OUnionE__1 @ V_A @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2704]) ).

thf(3074,plain,
    ( ( ! [V_A: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a )
          | ( c_in @ V_A @ ( c_Main_OUnionE__1 @ V_A @ V_C @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2703]) ).

thf(3075,plain,
    ( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2702]) ).

thf(3076,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2701]) ).

thf(3077,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2700]) ).

thf(3078,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( V_A = V_B )
          | ( c_less @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2948]) ).

thf(3079,plain,
    ( ( ! [V_b: $i,V_a: $i] :
          ( ! [T_a: $i] :
              ~ ( c_in @ V_b @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a )
          | ( V_b = V_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2947]) ).

thf(3080,plain,
    ( ( ! [V_a: $i,T_a: $i] : ( c_in @ V_a @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[2697]) ).

thf(3081,plain,
    ( ( ! [V_a: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ c_emptyset @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2946]) ).

thf(3082,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] :
              ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
              | ( c_in @ V_c @ V_B @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2945]) ).

thf(3083,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2694]) ).

thf(3084,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2693]) ).

thf(3085,plain,
    ( ( ! [V_B: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
          | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(copy,[status(thm)],[2692]) ).

thf(3086,plain,
    ( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2691]) ).

thf(3087,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_A @ T_a )
          | ! [T_b: $i,V_B: $i] : ( c_in @ ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2944]) ).

thf(3088,plain,
    ( ( ! [V_b: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ V_B @ T_a )
          | ! [T_b: $i,V_A: $i] : ( c_in @ ( c_Sum__Type_OInr @ V_b @ T_a @ T_b ) @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_b @ T_a ) @ ( tc_sum @ T_b @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2943]) ).

thf(3089,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ T_b @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2688]) ).

thf(3090,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ V_B @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2942]) ).

thf(3091,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( V_u
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ T_b @ T_a ) )
          | ( c_in @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2941]) ).

thf(3092,plain,
    ( ( ! [V_u: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
          ( ~ ( c_in @ V_u @ ( c_Sum__Type_OPlus @ V_A @ V_B @ T_a @ T_b ) @ ( tc_sum @ T_a @ T_b ) )
          | ( c_in @ ( c_Main_OPlusE__1 @ V_A @ V_u @ T_a @ T_b ) @ V_A @ T_a )
          | ( c_in @ ( c_Main_OPlusE__2 @ V_B @ V_u @ T_b @ T_a ) @ V_B @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2685]) ).

thf(3093,plain,
    ( ( ! [V_p: $i,V_r: $i,T_a: $i] :
          ( ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2684]) ).

thf(3094,plain,
    ( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2683]) ).

thf(3095,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2682]) ).

thf(3096,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2681]) ).

thf(3097,plain,
    ( ( ! [T_a: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[2680]) ).

thf(3098,plain,
    ( ( c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2679]) ).

thf(3099,plain,
    ( ( ! [V_R2: $i,T_b: $i] :
          ( ~ ( c_Relation_Otrans @ V_R2 @ T_b )
          | ! [V_R1: $i,T_a: $i] :
              ( ~ ( c_Relation_Otrans @ V_R1 @ T_a )
              | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ V_R1 @ V_R2 @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2940]) ).

thf(3100,plain,
    ( ( c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2677]) ).

thf(3101,plain,
    ( ( ! [V_rb: $i,T_b: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_rb @ T_b )
          | ! [V_ra: $i,T_a: $i] :
              ( ~ ( c_Wellfounded__Recursion_Owf @ V_ra @ T_a )
              | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ V_ra @ V_rb @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2939]) ).

thf(3102,plain,
    ( ( ! [T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2675]) ).

thf(3103,plain,
    ( ( class_HOL_Ominus @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2674]) ).

thf(3104,plain,
    ( ( class_HOL_Oone @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2673]) ).

thf(3105,plain,
    ( ( class_Ring__and__Field_Osemiring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2672]) ).

thf(3106,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2671]) ).

thf(3107,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2670]) ).

thf(3108,plain,
    ( ( class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2669]) ).

thf(3109,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2668]) ).

thf(3110,plain,
    ( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2667]) ).

thf(3111,plain,
    ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2666]) ).

thf(3112,plain,
    ( ( class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2665]) ).

thf(3113,plain,
    ( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2664]) ).

thf(3114,plain,
    ( ( class_Ring__and__Field_Oring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2663]) ).

thf(3115,plain,
    ( ( class_HOL_Oplus @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2662]) ).

thf(3116,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2661]) ).

thf(3117,plain,
    ( ( class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2660]) ).

thf(3118,plain,
    ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2659]) ).

thf(3119,plain,
    ( ( class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2658]) ).

thf(3120,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2657]) ).

thf(3121,plain,
    ( ( class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2656]) ).

thf(3122,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2655]) ).

thf(3123,plain,
    ( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2654]) ).

thf(3124,plain,
    ( ( class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2653]) ).

thf(3125,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2652]) ).

thf(3126,plain,
    ( ( class_HOL_Otimes @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2651]) ).

thf(3127,plain,
    ( ( class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2650]) ).

thf(3128,plain,
    ( ( class_Orderings_Oorder @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2649]) ).

thf(3129,plain,
    ( ( class_LOrder_Omeet__semilorder @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2648]) ).

thf(3130,plain,
    ( ( class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2647]) ).

thf(3131,plain,
    ( ( class_LOrder_Olorder @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2646]) ).

thf(3132,plain,
    ( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2645]) ).

thf(3133,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2644]) ).

thf(3134,plain,
    ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2643]) ).

thf(3135,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2642]) ).

thf(3136,plain,
    ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2641]) ).

thf(3137,plain,
    ( ( class_HOL_Ozero @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2640]) ).

thf(3138,plain,
    ( ( class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2639]) ).

thf(3139,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2638]) ).

thf(3140,plain,
    ( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2637]) ).

thf(3141,plain,
    ( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2636]) ).

thf(3142,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2635]) ).

thf(3143,plain,
    ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2634]) ).

thf(3144,plain,
    ( ( class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2633]) ).

thf(3145,plain,
    ( ( class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2632]) ).

thf(3146,plain,
    ( ( class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2631]) ).

thf(3147,plain,
    ( ( class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2630]) ).

thf(3148,plain,
    ( ( class_Orderings_Oord @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2629]) ).

thf(3149,plain,
    ( ( class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2628]) ).

thf(3150,plain,
    ( ( class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2627]) ).

thf(3151,plain,
    ( ( class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2626]) ).

thf(3152,plain,
    ( ( class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2625]) ).

thf(3153,plain,
    ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2624]) ).

thf(3154,plain,
    ( ( class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2623]) ).

thf(3155,plain,
    ( ( class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2622]) ).

thf(3156,plain,
    ( ( class_Ring__and__Field_Oidom @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2621]) ).

thf(3157,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2620]) ).

thf(3158,plain,
    ( ( class_Numeral_Onumber @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2619]) ).

thf(3159,plain,
    ( ( class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2618]) ).

thf(3160,plain,
    ( ( class_Numeral_Onumber__ring @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2617]) ).

thf(3161,plain,
    ( ( class_Divides_Odiv @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2616]) ).

thf(3162,plain,
    ( ( class_Nat_Opower @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2615]) ).

thf(3163,plain,
    ( ( class_Power_Orecpower @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2614]) ).

thf(3164,plain,
    ( ( class_Parity_Oeven__odd @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2613]) ).

thf(3165,plain,
    ( ( class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2612]) ).

thf(3166,plain,
    ( ( class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2611]) ).

thf(3167,plain,
    ( ( class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[2610]) ).

thf(3168,plain,
    ( ( class_Finite__Set_Ofinite @ tc_Product__Type_Ounit )
    = $true ),
    inference(copy,[status(thm)],[2609]) ).

thf(3169,plain,
    ( ( class_Finite__Set_Ofinite @ tc_bool )
    = $true ),
    inference(copy,[status(thm)],[2608]) ).

thf(3170,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 )
          | ~ ( class_Finite__Set_Ofinite @ T_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2607]) ).

thf(3171,plain,
    ( ( ! [T_2: $i,T_1: $i] : ( class_Nat_Opower @ ( tc_fun @ T_2 @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2606]) ).

thf(3172,plain,
    ( ( class_HOL_Oone @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2605]) ).

thf(3173,plain,
    ( ( class_HOL_Ozero @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2604]) ).

thf(3174,plain,
    ( ( class_HOL_Oplus @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2603]) ).

thf(3175,plain,
    ( ( class_HOL_Otimes @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2602]) ).

thf(3176,plain,
    ( ( class_Nat_Opower @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2601]) ).

thf(3177,plain,
    ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2600]) ).

thf(3178,plain,
    ( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2599]) ).

thf(3179,plain,
    ( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2598]) ).

thf(3180,plain,
    ( ( class_OrderedGroup_Osemigroup__mult @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2597]) ).

thf(3181,plain,
    ( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2596]) ).

thf(3182,plain,
    ( ( class_Ring__and__Field_Osemiring @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2595]) ).

thf(3183,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2594]) ).

thf(3184,plain,
    ( ( class_Orderings_Oord @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2593]) ).

thf(3185,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2592]) ).

thf(3186,plain,
    ( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2591]) ).

thf(3187,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2590]) ).

thf(3188,plain,
    ( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2589]) ).

thf(3189,plain,
    ( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2588]) ).

thf(3190,plain,
    ( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2587]) ).

thf(3191,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2586]) ).

thf(3192,plain,
    ( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2585]) ).

thf(3193,plain,
    ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2584]) ).

thf(3194,plain,
    ( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2583]) ).

thf(3195,plain,
    ( ( class_Orderings_Oorder @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2582]) ).

thf(3196,plain,
    ( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2581]) ).

thf(3197,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2580]) ).

thf(3198,plain,
    ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2579]) ).

thf(3199,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2578]) ).

thf(3200,plain,
    ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2577]) ).

thf(3201,plain,
    ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2576]) ).

thf(3202,plain,
    ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2575]) ).

thf(3203,plain,
    ( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2574]) ).

thf(3204,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2573]) ).

thf(3205,plain,
    ( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2572]) ).

thf(3206,plain,
    ( ( class_LOrder_Omeet__semilorder @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2571]) ).

thf(3207,plain,
    ( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2570]) ).

thf(3208,plain,
    ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2569]) ).

thf(3209,plain,
    ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2568]) ).

thf(3210,plain,
    ( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2567]) ).

thf(3211,plain,
    ( ( class_Divides_Odiv @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2566]) ).

thf(3212,plain,
    ( ( class_Power_Orecpower @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2565]) ).

thf(3213,plain,
    ( ( class_Numeral_Onumber @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2564]) ).

thf(3214,plain,
    ( ( class_Parity_Oeven__odd @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2563]) ).

thf(3215,plain,
    ( ( class_LOrder_Ojoin__semilorder @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2562]) ).

thf(3216,plain,
    ( ( class_LOrder_Olorder @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2561]) ).

thf(3217,plain,
    ( ( class_Orderings_Olinorder @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2560]) ).

thf(3218,plain,
    ( ( class_Wellfounded__Recursion_Owellorder @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2559]) ).

thf(3219,plain,
    ( ( class_HOL_Ominus @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[2558]) ).

thf(3220,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_prod @ T_2 @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 )
          | ~ ( class_Finite__Set_Ofinite @ T_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2557]) ).

thf(3221,plain,
    ( ( ! [T_1: $i] : ( class_HOL_Ominus @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2556]) ).

thf(3222,plain,
    ( ( ! [T_1: $i] : ( class_Orderings_Oord @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2555]) ).

thf(3223,plain,
    ( ( ! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2554]) ).

thf(3224,plain,
    ( ( ! [T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_set @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2553]) ).

thf(3225,plain,
    ( ( ! [T_1: $i] : ( class_Nat_Opower @ ( tc_set @ T_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2552]) ).

thf(3226,plain,
    ( ( ! [T_2: $i,T_1: $i] :
          ( ( class_Finite__Set_Ofinite @ ( tc_sum @ T_2 @ T_1 ) )
          | ~ ( class_Finite__Set_Ofinite @ T_1 )
          | ~ ( class_Finite__Set_Ofinite @ T_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2551]) ).

thf(3227,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Ojoin__semilorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2550]) ).

thf(3228,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Ojoin__semilorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2549]) ).

thf(3229,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2548]) ).

thf(3230,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2547]) ).

thf(3231,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2546]) ).

thf(3232,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Olorder @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2545]) ).

thf(3233,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Omeet__semilorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2544]) ).

thf(3234,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_LOrder_Omeet__semilorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2543]) ).

thf(3235,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2542]) ).

thf(3236,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2541]) ).

thf(3237,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2540]) ).

thf(3238,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2539]) ).

thf(3239,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2538]) ).

thf(3240,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2537]) ).

thf(3241,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2536]) ).

thf(3242,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2535]) ).

thf(3243,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2534]) ).

thf(3244,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2533]) ).

thf(3245,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2532]) ).

thf(3246,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2531]) ).

thf(3247,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2530]) ).

thf(3248,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2529]) ).

thf(3249,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2528]) ).

thf(3250,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2527]) ).

thf(3251,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2526]) ).

thf(3252,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2525]) ).

thf(3253,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2524]) ).

thf(3254,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2523]) ).

thf(3255,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2522]) ).

thf(3256,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2521]) ).

thf(3257,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2520]) ).

thf(3258,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2519]) ).

thf(3259,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Numeral_Onumber @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2518]) ).

thf(3260,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2517]) ).

thf(3261,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2516]) ).

thf(3262,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2515]) ).

thf(3263,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2514]) ).

thf(3264,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2513]) ).

thf(3265,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Numeral_Onumber__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2512]) ).

thf(3266,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2511]) ).

thf(3267,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2510]) ).

thf(3268,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2509]) ).

thf(3269,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2508]) ).

thf(3270,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2507]) ).

thf(3271,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2506]) ).

thf(3272,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2505]) ).

thf(3273,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2504]) ).

thf(3274,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2503]) ).

thf(3275,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2502]) ).

thf(3276,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2501]) ).

thf(3277,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2500]) ).

thf(3278,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2499]) ).

thf(3279,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2498]) ).

thf(3280,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2497]) ).

thf(3281,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2496]) ).

thf(3282,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2495]) ).

thf(3283,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2494]) ).

thf(3284,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2493]) ).

thf(3285,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2492]) ).

thf(3286,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2491]) ).

thf(3287,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2490]) ).

thf(3288,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2489]) ).

thf(3289,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2488]) ).

thf(3290,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2487]) ).

thf(3291,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2486]) ).

thf(3292,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2485]) ).

thf(3293,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2484]) ).

thf(3294,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2483]) ).

thf(3295,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2482]) ).

thf(3296,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2481]) ).

thf(3297,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2480]) ).

thf(3298,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2479]) ).

thf(3299,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2478]) ).

thf(3300,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2477]) ).

thf(3301,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2476]) ).

thf(3302,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2475]) ).

thf(3303,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2474]) ).

thf(3304,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2473]) ).

thf(3305,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2472]) ).

thf(3306,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2471]) ).

thf(3307,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2470]) ).

thf(3308,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2469]) ).

thf(3309,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2468]) ).

thf(3310,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2467]) ).

thf(3311,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2466]) ).

thf(3312,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2465]) ).

thf(3313,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2464]) ).

thf(3314,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2463]) ).

thf(3315,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2462]) ).

thf(3316,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2461]) ).

thf(3317,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2460]) ).

thf(3318,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2459]) ).

thf(3319,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2458]) ).

thf(3320,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2457]) ).

thf(3321,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2456]) ).

thf(3322,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2455]) ).

thf(3323,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2454]) ).

thf(3324,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2453]) ).

thf(3325,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2452]) ).

thf(3326,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2451]) ).

thf(3327,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2450]) ).

thf(3328,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2449]) ).

thf(3329,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2448]) ).

thf(3330,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2447]) ).

thf(3331,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2446]) ).

thf(3332,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2445]) ).

thf(3333,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2444]) ).

thf(3334,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2443]) ).

thf(3335,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2442]) ).

thf(3336,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2441]) ).

thf(3337,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2440]) ).

thf(3338,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2439]) ).

thf(3339,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2438]) ).

thf(3340,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2437]) ).

thf(3341,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2436]) ).

thf(3342,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2435]) ).

thf(3343,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2434]) ).

thf(3344,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2433]) ).

thf(3345,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2432]) ).

thf(3346,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2431]) ).

thf(3347,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2430]) ).

thf(3348,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2429]) ).

thf(3349,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2428]) ).

thf(3350,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2427]) ).

thf(3351,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2426]) ).

thf(3352,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2425]) ).

thf(3353,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2424]) ).

thf(3354,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2423]) ).

thf(3355,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2422]) ).

thf(3356,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2421]) ).

thf(3357,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2420]) ).

thf(3358,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2419]) ).

thf(3359,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2418]) ).

thf(3360,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2417]) ).

thf(3361,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2416]) ).

thf(3362,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2415]) ).

thf(3363,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2414]) ).

thf(3364,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2413]) ).

thf(3365,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2412]) ).

thf(3366,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2411]) ).

thf(3367,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2410]) ).

thf(3368,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2409]) ).

thf(3369,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2408]) ).

thf(3370,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Omonoid__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2407]) ).

thf(3371,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2406]) ).

thf(3372,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2405]) ).

thf(3373,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2404]) ).

thf(3374,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2403]) ).

thf(3375,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2402]) ).

thf(3376,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2401]) ).

thf(3377,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2400]) ).

thf(3378,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2399]) ).

thf(3379,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2398]) ).

thf(3380,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2397]) ).

thf(3381,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2396]) ).

thf(3382,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2395]) ).

thf(3383,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2394]) ).

thf(3384,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2393]) ).

thf(3385,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2392]) ).

thf(3386,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2391]) ).

thf(3387,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2390]) ).

thf(3388,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2389]) ).

thf(3389,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2388]) ).

thf(3390,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2387]) ).

thf(3391,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2386]) ).

thf(3392,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2385]) ).

thf(3393,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2384]) ).

thf(3394,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2383]) ).

thf(3395,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2382]) ).

thf(3396,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2381]) ).

thf(3397,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2380]) ).

thf(3398,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2379]) ).

thf(3399,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2378]) ).

thf(3400,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2377]) ).

thf(3401,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2376]) ).

thf(3402,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2375]) ).

thf(3403,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2374]) ).

thf(3404,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2373]) ).

thf(3405,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2372]) ).

thf(3406,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2371]) ).

thf(3407,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2370]) ).

thf(3408,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2369]) ).

thf(3409,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2368]) ).

thf(3410,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2367]) ).

thf(3411,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2366]) ).

thf(3412,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2365]) ).

thf(3413,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2364]) ).

thf(3414,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2363]) ).

thf(3415,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2362]) ).

thf(3416,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2361]) ).

thf(3417,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2360]) ).

thf(3418,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2359]) ).

thf(3419,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2358]) ).

thf(3420,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2357]) ).

thf(3421,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Osemigroup__add @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2356]) ).

thf(3422,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_OrderedGroup_Osemigroup__mult @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2355]) ).

thf(3423,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2354]) ).

thf(3424,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2353]) ).

thf(3425,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2352]) ).

thf(3426,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2351]) ).

thf(3427,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Olinorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2350]) ).

thf(3428,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Orderings_Oorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2349]) ).

thf(3429,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Nat_Opower @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2348]) ).

thf(3430,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2347]) ).

thf(3431,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2346]) ).

thf(3432,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2345]) ).

thf(3433,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2344]) ).

thf(3434,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2343]) ).

thf(3435,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2342]) ).

thf(3436,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2341]) ).

thf(3437,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2340]) ).

thf(3438,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2339]) ).

thf(3439,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2338]) ).

thf(3440,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2337]) ).

thf(3441,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2336]) ).

thf(3442,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2335]) ).

thf(3443,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2334]) ).

thf(3444,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2333]) ).

thf(3445,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2332]) ).

thf(3446,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2331]) ).

thf(3447,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2330]) ).

thf(3448,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2329]) ).

thf(3449,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2328]) ).

thf(3450,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2327]) ).

thf(3451,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2326]) ).

thf(3452,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2325]) ).

thf(3453,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Power_Orecpower @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2324]) ).

thf(3454,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2323]) ).

thf(3455,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2322]) ).

thf(3456,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2321]) ).

thf(3457,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2320]) ).

thf(3458,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2319]) ).

thf(3459,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2318]) ).

thf(3460,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2317]) ).

thf(3461,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2316]) ).

thf(3462,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2315]) ).

thf(3463,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2314]) ).

thf(3464,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2313]) ).

thf(3465,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2312]) ).

thf(3466,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2311]) ).

thf(3467,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2310]) ).

thf(3468,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2309]) ).

thf(3469,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2308]) ).

thf(3470,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2307]) ).

thf(3471,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2306]) ).

thf(3472,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2305]) ).

thf(3473,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2304]) ).

thf(3474,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2303]) ).

thf(3475,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2302]) ).

thf(3476,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2301]) ).

thf(3477,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2300]) ).

thf(3478,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2299]) ).

thf(3479,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2298]) ).

thf(3480,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2297]) ).

thf(3481,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2296]) ).

thf(3482,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2295]) ).

thf(3483,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2294]) ).

thf(3484,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2293]) ).

thf(3485,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2292]) ).

thf(3486,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2291]) ).

thf(3487,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2290]) ).

thf(3488,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2289]) ).

thf(3489,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2288]) ).

thf(3490,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2287]) ).

thf(3491,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2286]) ).

thf(3492,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2285]) ).

thf(3493,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2284]) ).

thf(3494,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2283]) ).

thf(3495,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2282]) ).

thf(3496,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2281]) ).

thf(3497,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2280]) ).

thf(3498,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2279]) ).

thf(3499,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2278]) ).

thf(3500,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2277]) ).

thf(3501,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2276]) ).

thf(3502,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2275]) ).

thf(3503,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2274]) ).

thf(3504,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2273]) ).

thf(3505,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2272]) ).

thf(3506,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2271]) ).

thf(3507,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2270]) ).

thf(3508,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2269]) ).

thf(3509,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2268]) ).

thf(3510,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2267]) ).

thf(3511,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2266]) ).

thf(3512,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2265]) ).

thf(3513,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2264]) ).

thf(3514,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2263]) ).

thf(3515,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2262]) ).

thf(3516,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2261]) ).

thf(3517,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2260]) ).

thf(3518,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2259]) ).

thf(3519,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2258]) ).

thf(3520,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2257]) ).

thf(3521,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2256]) ).

thf(3522,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2255]) ).

thf(3523,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2254]) ).

thf(3524,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2253]) ).

thf(3525,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2252]) ).

thf(3526,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2251]) ).

thf(3527,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2250]) ).

thf(3528,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2249]) ).

thf(3529,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2248]) ).

thf(3530,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2247]) ).

thf(3531,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2246]) ).

thf(3532,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2245]) ).

thf(3533,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2244]) ).

thf(3534,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2243]) ).

thf(3535,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2242]) ).

thf(3536,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2241]) ).

thf(3537,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2240]) ).

thf(3538,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2239]) ).

thf(3539,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2238]) ).

thf(3540,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2237]) ).

thf(3541,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2236]) ).

thf(3542,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2235]) ).

thf(3543,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2234]) ).

thf(3544,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2233]) ).

thf(3545,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2232]) ).

thf(3546,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2231]) ).

thf(3547,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2230]) ).

thf(3548,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2229]) ).

thf(3549,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2228]) ).

thf(3550,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2227]) ).

thf(3551,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2226]) ).

thf(3552,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2225]) ).

thf(3553,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2224]) ).

thf(3554,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2223]) ).

thf(3555,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2222]) ).

thf(3556,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2221]) ).

thf(3557,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2220]) ).

thf(3558,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2219]) ).

thf(3559,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2218]) ).

thf(3560,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2217]) ).

thf(3561,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2216]) ).

thf(3562,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2215]) ).

thf(3563,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2214]) ).

thf(3564,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2213]) ).

thf(3565,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2212]) ).

thf(3566,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2211]) ).

thf(3567,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2210]) ).

thf(3568,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2209]) ).

thf(3569,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2208]) ).

thf(3570,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2207]) ).

thf(3571,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2206]) ).

thf(3572,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2205]) ).

thf(3573,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2204]) ).

thf(3574,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2203]) ).

thf(3575,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2202]) ).

thf(3576,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2201]) ).

thf(3577,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2200]) ).

thf(3578,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2199]) ).

thf(3579,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2198]) ).

thf(3580,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2197]) ).

thf(3581,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2196]) ).

thf(3582,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2195]) ).

thf(3583,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
          | ( class_HOL_Oinverse @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2194]) ).

thf(3584,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2193]) ).

thf(3585,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2192]) ).

thf(3586,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2191]) ).

thf(3587,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2190]) ).

thf(3588,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2189]) ).

thf(3589,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2188]) ).

thf(3590,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2187]) ).

thf(3591,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2186]) ).

thf(3592,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2185]) ).

thf(3593,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2184]) ).

thf(3594,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2183]) ).

thf(3595,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2182]) ).

thf(3596,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2181]) ).

thf(3597,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2180]) ).

thf(3598,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2179]) ).

thf(3599,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2178]) ).

thf(3600,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2177]) ).

thf(3601,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2176]) ).

thf(3602,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2175]) ).

thf(3603,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2174]) ).

thf(3604,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2173]) ).

thf(3605,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2172]) ).

thf(3606,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2171]) ).

thf(3607,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2170]) ).

thf(3608,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Oinverse @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2169]) ).

thf(3609,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oidom @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2168]) ).

thf(3610,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2167]) ).

thf(3611,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2166]) ).

thf(3612,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2165]) ).

thf(3613,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2164]) ).

thf(3614,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2163]) ).

thf(3615,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2162]) ).

thf(3616,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Ofield @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2161]) ).

thf(3617,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2160]) ).

thf(3618,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2159]) ).

thf(3619,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2158]) ).

thf(3620,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2157]) ).

thf(3621,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2156]) ).

thf(3622,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2155]) ).

thf(3623,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2154]) ).

thf(3624,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2153]) ).

thf(3625,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2152]) ).

thf(3626,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2151]) ).

thf(3627,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2150]) ).

thf(3628,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2149]) ).

thf(3629,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2148]) ).

thf(3630,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2147]) ).

thf(3631,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2146]) ).

thf(3632,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2145]) ).

thf(3633,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2144]) ).

thf(3634,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2143]) ).

thf(3635,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2142]) ).

thf(3636,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2141]) ).

thf(3637,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2140]) ).

thf(3638,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2139]) ).

thf(3639,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2138]) ).

thf(3640,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2137]) ).

thf(3641,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2136]) ).

thf(3642,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2135]) ).

thf(3643,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2134]) ).

thf(3644,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2133]) ).

thf(3645,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2132]) ).

thf(3646,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2131]) ).

thf(3647,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oidom @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2130]) ).

thf(3648,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2129]) ).

thf(3649,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2128]) ).

thf(3650,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2127]) ).

thf(3651,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2126]) ).

thf(3652,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2125]) ).

thf(3653,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2124]) ).

thf(3654,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2123]) ).

thf(3655,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2122]) ).

thf(3656,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2121]) ).

thf(3657,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2120]) ).

thf(3658,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2119]) ).

thf(3659,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2118]) ).

thf(3660,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2117]) ).

thf(3661,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2116]) ).

thf(3662,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2115]) ).

thf(3663,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2114]) ).

thf(3664,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2113]) ).

thf(3665,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2112]) ).

thf(3666,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2111]) ).

thf(3667,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2110]) ).

thf(3668,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2109]) ).

thf(3669,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2108]) ).

thf(3670,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2107]) ).

thf(3671,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2106]) ).

thf(3672,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2105]) ).

thf(3673,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2104]) ).

thf(3674,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2103]) ).

thf(3675,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2102]) ).

thf(3676,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2101]) ).

thf(3677,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2100]) ).

thf(3678,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Olordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2099]) ).

thf(3679,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2098]) ).

thf(3680,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2097]) ).

thf(3681,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2096]) ).

thf(3682,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2095]) ).

thf(3683,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2094]) ).

thf(3684,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2093]) ).

thf(3685,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2092]) ).

thf(3686,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2091]) ).

thf(3687,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2090]) ).

thf(3688,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2089]) ).

thf(3689,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2088]) ).

thf(3690,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2087]) ).

thf(3691,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2086]) ).

thf(3692,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2085]) ).

thf(3693,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2084]) ).

thf(3694,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2083]) ).

thf(3695,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2082]) ).

thf(3696,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2081]) ).

thf(3697,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2080]) ).

thf(3698,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2079]) ).

thf(3699,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2078]) ).

thf(3700,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2077]) ).

thf(3701,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2076]) ).

thf(3702,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2075]) ).

thf(3703,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2074]) ).

thf(3704,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2073]) ).

thf(3705,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2072]) ).

thf(3706,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2071]) ).

thf(3707,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2070]) ).

thf(3708,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2069]) ).

thf(3709,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ofield @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2068]) ).

thf(3710,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Oinverse @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2067]) ).

thf(3711,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2066]) ).

thf(3712,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2065]) ).

thf(3713,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2064]) ).

thf(3714,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2063]) ).

thf(3715,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2062]) ).

thf(3716,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2061]) ).

thf(3717,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2060]) ).

thf(3718,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2059]) ).

thf(3719,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2058]) ).

thf(3720,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2057]) ).

thf(3721,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oidom @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2056]) ).

thf(3722,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2055]) ).

thf(3723,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2054]) ).

thf(3724,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2053]) ).

thf(3725,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2052]) ).

thf(3726,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2051]) ).

thf(3727,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2050]) ).

thf(3728,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2049]) ).

thf(3729,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2048]) ).

thf(3730,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2047]) ).

thf(3731,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2046]) ).

thf(3732,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2045]) ).

thf(3733,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2044]) ).

thf(3734,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2043]) ).

thf(3735,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2042]) ).

thf(3736,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2041]) ).

thf(3737,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__idom @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2040]) ).

thf(3738,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2039]) ).

thf(3739,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2038]) ).

thf(3740,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2037]) ).

thf(3741,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2036]) ).

thf(3742,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2035]) ).

thf(3743,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2034]) ).

thf(3744,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2033]) ).

thf(3745,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2032]) ).

thf(3746,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2031]) ).

thf(3747,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Olordered__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2030]) ).

thf(3748,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2029]) ).

thf(3749,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2028]) ).

thf(3750,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2027]) ).

thf(3751,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2026]) ).

thf(3752,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2025]) ).

thf(3753,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2024]) ).

thf(3754,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2023]) ).

thf(3755,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2022]) ).

thf(3756,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2021]) ).

thf(3757,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2020]) ).

thf(3758,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2019]) ).

thf(3759,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2018]) ).

thf(3760,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2017]) ).

thf(3761,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2016]) ).

thf(3762,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2015]) ).

thf(3763,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2014]) ).

thf(3764,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2013]) ).

thf(3765,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2012]) ).

thf(3766,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2011]) ).

thf(3767,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2010]) ).

thf(3768,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2009]) ).

thf(3769,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__field @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2008]) ).

thf(3770,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2007]) ).

thf(3771,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2006]) ).

thf(3772,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2005]) ).

thf(3773,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2004]) ).

thf(3774,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2003]) ).

thf(3775,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2002]) ).

thf(3776,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2001]) ).

thf(3777,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[2000]) ).

thf(3778,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1999]) ).

thf(3779,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1998]) ).

thf(3780,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1997]) ).

thf(3781,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1996]) ).

thf(3782,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1995]) ).

thf(3783,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1994]) ).

thf(3784,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1993]) ).

thf(3785,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1992]) ).

thf(3786,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1991]) ).

thf(3787,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1990]) ).

thf(3788,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1989]) ).

thf(3789,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1988]) ).

thf(3790,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1987]) ).

thf(3791,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1986]) ).

thf(3792,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1985]) ).

thf(3793,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1984]) ).

thf(3794,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1983]) ).

thf(3795,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1982]) ).

thf(3796,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1981]) ).

thf(3797,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1980]) ).

thf(3798,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1979]) ).

thf(3799,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1978]) ).

thf(3800,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1977]) ).

thf(3801,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1976]) ).

thf(3802,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1975]) ).

thf(3803,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1974]) ).

thf(3804,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1973]) ).

thf(3805,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1972]) ).

thf(3806,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1971]) ).

thf(3807,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1970]) ).

thf(3808,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1969]) ).

thf(3809,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1968]) ).

thf(3810,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1967]) ).

thf(3811,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1966]) ).

thf(3812,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1965]) ).

thf(3813,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Olordered__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1964]) ).

thf(3814,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1963]) ).

thf(3815,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1962]) ).

thf(3816,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1961]) ).

thf(3817,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1960]) ).

thf(3818,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1959]) ).

thf(3819,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1958]) ).

thf(3820,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1957]) ).

thf(3821,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1956]) ).

thf(3822,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1955]) ).

thf(3823,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Oidom @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1954]) ).

thf(3824,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1953]) ).

thf(3825,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1952]) ).

thf(3826,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1951]) ).

thf(3827,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__idom @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1950]) ).

thf(3828,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1949]) ).

thf(3829,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1948]) ).

thf(3830,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1947]) ).

thf(3831,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1946]) ).

thf(3832,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1945]) ).

thf(3833,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1944]) ).

thf(3834,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1943]) ).

thf(3835,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1942]) ).

thf(3836,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1941]) ).

thf(3837,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1940]) ).

thf(3838,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1939]) ).

thf(3839,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1938]) ).

thf(3840,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1937]) ).

thf(3841,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1936]) ).

thf(3842,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1935]) ).

thf(3843,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1934]) ).

thf(3844,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1933]) ).

thf(3845,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1932]) ).

thf(3846,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1931]) ).

thf(3847,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1930]) ).

thf(3848,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1929]) ).

thf(3849,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1928]) ).

thf(3850,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1927]) ).

thf(3851,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1926]) ).

thf(3852,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1925]) ).

thf(3853,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Olordered__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1924]) ).

thf(3854,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Opordered__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1923]) ).

thf(3855,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1922]) ).

thf(3856,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1921]) ).

thf(3857,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1920]) ).

thf(3858,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1919]) ).

thf(3859,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1918]) ).

thf(3860,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1917]) ).

thf(3861,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1916]) ).

thf(3862,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1915]) ).

thf(3863,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1914]) ).

thf(3864,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1913]) ).

thf(3865,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1912]) ).

thf(3866,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1911]) ).

thf(3867,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1910]) ).

thf(3868,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1909]) ).

thf(3869,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1908]) ).

thf(3870,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1907]) ).

thf(3871,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1906]) ).

thf(3872,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1905]) ).

thf(3873,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1904]) ).

thf(3874,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1903]) ).

thf(3875,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1902]) ).

thf(3876,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1901]) ).

thf(3877,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1900]) ).

thf(3878,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1899]) ).

thf(3879,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1898]) ).

thf(3880,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1897]) ).

thf(3881,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1896]) ).

thf(3882,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1895]) ).

thf(3883,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1894]) ).

thf(3884,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1893]) ).

thf(3885,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1892]) ).

thf(3886,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1891]) ).

thf(3887,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1890]) ).

thf(3888,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1889]) ).

thf(3889,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1888]) ).

thf(3890,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1887]) ).

thf(3891,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1886]) ).

thf(3892,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1885]) ).

thf(3893,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1884]) ).

thf(3894,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1883]) ).

thf(3895,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1882]) ).

thf(3896,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1881]) ).

thf(3897,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1880]) ).

thf(3898,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1879]) ).

thf(3899,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1878]) ).

thf(3900,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1877]) ).

thf(3901,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1876]) ).

thf(3902,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1875]) ).

thf(3903,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1874]) ).

thf(3904,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1873]) ).

thf(3905,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1872]) ).

thf(3906,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1871]) ).

thf(3907,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1870]) ).

thf(3908,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1869]) ).

thf(3909,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1868]) ).

thf(3910,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1867]) ).

thf(3911,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1866]) ).

thf(3912,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1865]) ).

thf(3913,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1864]) ).

thf(3914,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1863]) ).

thf(3915,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1862]) ).

thf(3916,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1861]) ).

thf(3917,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1860]) ).

thf(3918,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1859]) ).

thf(3919,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1858]) ).

thf(3920,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1857]) ).

thf(3921,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1856]) ).

thf(3922,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1855]) ).

thf(3923,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1854]) ).

thf(3924,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1853]) ).

thf(3925,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1852]) ).

thf(3926,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1851]) ).

thf(3927,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1850]) ).

thf(3928,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
          | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1849]) ).

thf(3929,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1848]) ).

thf(3930,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1847]) ).

thf(3931,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1846]) ).

thf(3932,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1845]) ).

thf(3933,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1844]) ).

thf(3934,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1843]) ).

thf(3935,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1842]) ).

thf(3936,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1841]) ).

thf(3937,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1840]) ).

thf(3938,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1839]) ).

thf(3939,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1838]) ).

thf(3940,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1837]) ).

thf(3941,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1836]) ).

thf(3942,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1835]) ).

thf(3943,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1834]) ).

thf(3944,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1833]) ).

thf(3945,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1832]) ).

thf(3946,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1831]) ).

thf(3947,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1830]) ).

thf(3948,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1829]) ).

thf(3949,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1828]) ).

thf(3950,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1827]) ).

thf(3951,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1826]) ).

thf(3952,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1825]) ).

thf(3953,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1824]) ).

thf(3954,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1823]) ).

thf(3955,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1822]) ).

thf(3956,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1821]) ).

thf(3957,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1820]) ).

thf(3958,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1819]) ).

thf(3959,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1818]) ).

thf(3960,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1817]) ).

thf(3961,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1816]) ).

thf(3962,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1815]) ).

thf(3963,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1814]) ).

thf(3964,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1813]) ).

thf(3965,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1812]) ).

thf(3966,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1811]) ).

thf(3967,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1810]) ).

thf(3968,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1809]) ).

thf(3969,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1808]) ).

thf(3970,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1807]) ).

thf(3971,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1806]) ).

thf(3972,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1805]) ).

thf(3973,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1804]) ).

thf(3974,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1803]) ).

thf(3975,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1802]) ).

thf(3976,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1801]) ).

thf(3977,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1800]) ).

thf(3978,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1799]) ).

thf(3979,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1798]) ).

thf(3980,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1797]) ).

thf(3981,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1796]) ).

thf(3982,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1795]) ).

thf(3983,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1794]) ).

thf(3984,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1793]) ).

thf(3985,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1792]) ).

thf(3986,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1791]) ).

thf(3987,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1790]) ).

thf(3988,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1789]) ).

thf(3989,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1788]) ).

thf(3990,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1787]) ).

thf(3991,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1786]) ).

thf(3992,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1785]) ).

thf(3993,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1784]) ).

thf(3994,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1783]) ).

thf(3995,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1782]) ).

thf(3996,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1781]) ).

thf(3997,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1780]) ).

thf(3998,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1779]) ).

thf(3999,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1778]) ).

thf(4000,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1777]) ).

thf(4001,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1776]) ).

thf(4002,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1775]) ).

thf(4003,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1774]) ).

thf(4004,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1773]) ).

thf(4005,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1772]) ).

thf(4006,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1771]) ).

thf(4007,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1770]) ).

thf(4008,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1769]) ).

thf(4009,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1768]) ).

thf(4010,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1767]) ).

thf(4011,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1766]) ).

thf(4012,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1765]) ).

thf(4013,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1764]) ).

thf(4014,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1763]) ).

thf(4015,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1762]) ).

thf(4016,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1761]) ).

thf(4017,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1760]) ).

thf(4018,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1759]) ).

thf(4019,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1758]) ).

thf(4020,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1757]) ).

thf(4021,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1756]) ).

thf(4022,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1755]) ).

thf(4023,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1754]) ).

thf(4024,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1753]) ).

thf(4025,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1752]) ).

thf(4026,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1751]) ).

thf(4027,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1750]) ).

thf(4028,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1749]) ).

thf(4029,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__ring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1748]) ).

thf(4030,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1747]) ).

thf(4031,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1746]) ).

thf(4032,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1745]) ).

thf(4033,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1744]) ).

thf(4034,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1743]) ).

thf(4035,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1742]) ).

thf(4036,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1741]) ).

thf(4037,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1740]) ).

thf(4038,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1739]) ).

thf(4039,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1738]) ).

thf(4040,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1737]) ).

thf(4041,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
          | ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1736]) ).

thf(4042,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1735]) ).

thf(4043,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1734]) ).

thf(4044,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1733]) ).

thf(4045,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1732]) ).

thf(4046,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1731]) ).

thf(4047,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1730]) ).

thf(4048,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1729]) ).

thf(4049,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1728]) ).

thf(4050,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1727]) ).

thf(4051,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1726]) ).

thf(4052,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1725]) ).

thf(4053,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1724]) ).

thf(4054,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1723]) ).

thf(4055,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1722]) ).

thf(4056,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Oring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1721]) ).

thf(4057,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Oab__group__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1720]) ).

thf(4058,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1719]) ).

thf(4059,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1718]) ).

thf(4060,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1717]) ).

thf(4061,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1716]) ).

thf(4062,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1715]) ).

thf(4063,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1714]) ).

thf(4064,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1713]) ).

thf(4065,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1712]) ).

thf(4066,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1711]) ).

thf(4067,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1710]) ).

thf(4068,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Ominus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1709]) ).

thf(4069,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1708]) ).

thf(4070,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1707]) ).

thf(4071,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1706]) ).

thf(4072,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1705]) ).

thf(4073,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1704]) ).

thf(4074,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1703]) ).

thf(4075,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Oring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1702]) ).

thf(4076,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1701]) ).

thf(4077,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1700]) ).

thf(4078,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1699]) ).

thf(4079,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1698]) ).

thf(4080,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1697]) ).

thf(4081,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1696]) ).

thf(4082,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1695]) ).

thf(4083,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1694]) ).

thf(4084,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1693]) ).

thf(4085,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1692]) ).

thf(4086,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1691]) ).

thf(4087,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1690]) ).

thf(4088,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1689]) ).

thf(4089,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1688]) ).

thf(4090,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1687]) ).

thf(4091,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1686]) ).

thf(4092,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1685]) ).

thf(4093,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1684]) ).

thf(4094,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1683]) ).

thf(4095,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1682]) ).

thf(4096,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1681]) ).

thf(4097,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1680]) ).

thf(4098,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1679]) ).

thf(4099,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1678]) ).

thf(4100,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1677]) ).

thf(4101,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1676]) ).

thf(4102,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1675]) ).

thf(4103,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1674]) ).

thf(4104,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1673]) ).

thf(4105,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1672]) ).

thf(4106,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1671]) ).

thf(4107,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1670]) ).

thf(4108,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1669]) ).

thf(4109,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1668]) ).

thf(4110,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1667]) ).

thf(4111,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1666]) ).

thf(4112,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1665]) ).

thf(4113,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1664]) ).

thf(4114,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Oone @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1663]) ).

thf(4115,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1662]) ).

thf(4116,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Otimes @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1661]) ).

thf(4117,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1660]) ).

thf(4118,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1659]) ).

thf(4119,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1658]) ).

thf(4120,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1657]) ).

thf(4121,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_Ring__and__Field_Osemiring @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1656]) ).

thf(4122,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1655]) ).

thf(4123,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Ozero @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1654]) ).

thf(4124,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1653]) ).

thf(4125,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Osemigroup__add @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1652]) ).

thf(4126,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_HOL_Oplus @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1651]) ).

thf(4127,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
          | ( class_OrderedGroup_Omonoid__mult @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1650]) ).

thf(4128,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_Orderings_Oord @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1649]) ).

thf(4129,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_Orderings_Oorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1648]) ).

thf(4130,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_LOrder_Omeet__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1647]) ).

thf(4131,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_LOrder_Ojoin__semilorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1646]) ).

thf(4132,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_LOrder_Olorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1645]) ).

thf(4133,plain,
    ( ( ! [T: $i] :
          ( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
          | ( class_Orderings_Olinorder @ T ) ) )
    = $true ),
    inference(copy,[status(thm)],[1644]) ).

thf(4134,plain,
    ( ( ! [V_x: $i,V_xo: $i,T_a: $i] :
          ( ~ ( c_in @ V_x @ ( c_Datatype_Oo2s @ V_xo @ T_a ) @ T_a )
          | ( V_xo
            = ( c_Datatype_Ooption_OSome @ V_x @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1643]) ).

thf(4135,plain,
    ( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ V_x @ T_a ) @ T_a ) @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[1642]) ).

thf(4136,plain,
    ( ( ! [V_x: $i] :
          ( ( V_x = c_Datatype_Ooption_ONone )
          | ! [T_a: $i] :
              ( V_x
              = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2938]) ).

thf(4137,plain,
    ( ( ! [V_x: $i] :
          ( ( V_x = c_Datatype_Ooption_ONone )
          | ! [T_a: $i] :
              ( V_x
              = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ V_x @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2937]) ).

thf(4138,plain,
    ( ( ! [V_a_H: $i,T_a: $i] :
          ( c_Datatype_Ooption_ONone
         != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2936]) ).

thf(4139,plain,
    ( ( ! [V_a_H: $i,T_a: $i] :
          ( ( c_Datatype_Ooption_OSome @ V_a_H @ T_a )
         != c_Datatype_Ooption_ONone ) )
    = $true ),
    inference(copy,[status(thm)],[2935]) ).

thf(4140,plain,
    ( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
          ( ( ( c_Datatype_Ooption_OSome @ V_a @ T_a )
           != ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2934]) ).

thf(4141,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
          ( ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
           != ( c_Datatype__Universe_OAtom @ V_b @ T_a @ T_b ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2933]) ).

thf(4142,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2932]) ).

thf(4143,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
           != ( c_Datatype__Universe_OIn0 @ V_N @ T_a @ T_b ) )
          | ( V_M = V_N ) ) )
    = $true ),
    inference(copy,[status(thm)],[2931]) ).

thf(4144,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b )
         != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2930]) ).

thf(4145,plain,
    ( ( ! [V_M: $i,T_a: $i,T_b: $i,V_N: $i] :
          ( ( ( c_Datatype__Universe_OIn1 @ V_M @ T_a @ T_b )
           != ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b ) )
          | ( V_M = V_N ) ) )
    = $true ),
    inference(copy,[status(thm)],[2929]) ).

thf(4146,plain,
    ( ( ! [V_N: $i,T_a: $i,T_b: $i,V_M: $i] :
          ( ( c_Datatype__Universe_OIn1 @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OIn0 @ V_M @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2928]) ).

thf(4147,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_k: $i] :
          ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2927]) ).

thf(4148,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2926]) ).

thf(4149,plain,
    ( ( ! [V_k: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
         != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2925]) ).

thf(4150,plain,
    ( ( ! [V_k: $i,T_a: $i,T_b: $i,V_M: $i,V_N: $i] :
          ( ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b )
         != ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2924]) ).

thf(4151,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i] :
          ( ! [V_N_H: $i] :
              ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
             != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
          | ( V_M = V_M_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2923]) ).

thf(4152,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_M_H: $i,V_N_H: $i] :
          ( ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
           != ( c_Datatype__Universe_OScons @ V_M_H @ V_N_H @ T_a @ T_b ) )
          | ( V_N = V_N_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2922]) ).

thf(4153,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OAtom @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2921]) ).

thf(4154,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_a: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_OLeaf @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2920]) ).

thf(4155,plain,
    ( ( ! [V_M: $i,V_N: $i,T_a: $i,T_b: $i,V_k: $i] :
          ( ( c_Datatype__Universe_OScons @ V_M @ V_N @ T_a @ T_b )
         != ( c_Datatype__Universe_ONumb @ V_k @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2919]) ).

thf(4156,plain,
    ( ( ! [V_m: $i] :
          ( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_nat )
          | ( V_m = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1621]) ).

thf(4157,plain,
    ( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[1620]) ).

thf(4158,plain,
    ( ( ! [V_A: $i] :
          ( ! [V_r: $i,T_a: $i] :
              ( c_emptyset
             != ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a ) )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[2918]) ).

thf(4159,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( c_emptyset
          = ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1618]) ).

thf(4160,plain,
    ( ( ! [V_A: $i] :
          ( ! [V_r: $i,T_a: $i] :
              ( ( c_Equiv__Relations_Oquotient @ V_A @ V_r @ T_a )
             != c_emptyset )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[2917]) ).

thf(4161,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a )
          = c_emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[1616]) ).

thf(4162,plain,
    ( ( c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight )
    = $true ),
    inference(copy,[status(thm)],[2916]) ).

thf(4163,plain,
    ( ( c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft )
    = $true ),
    inference(copy,[status(thm)],[2915]) ).

thf(4164,plain,
    ( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_minus @ V_A @ ( c_insert @ V_a @ V_B @ T_a ) @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1613]) ).

thf(4165,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_a: $i] : ( c_in @ ( c_minus @ V_A @ ( c_insert @ V_a @ V_B @ T_a ) @ ( tc_set @ T_a ) ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2914]) ).

thf(4166,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Pow @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) )
          | ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1611]) ).

thf(4167,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_Pow @ V_A @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1610]) ).

thf(4168,plain,
    ( ( ! [V_F: $i,V_G: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1609]) ).

thf(4169,plain,
    ( ( ! [V_F: $i,V_G: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1608]) ).

thf(4170,plain,
    ( ( ! [V_G: $i,T_a: $i] :
          ( ~ ( c_in @ V_G @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
          | ! [V_F: $i] :
              ( ~ ( c_in @ V_F @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) )
              | ( c_in @ ( c_union @ V_F @ V_G @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2913]) ).

thf(4171,plain,
    ( ( ! [V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_a @ T_b ) ) )
          | ( c_in @ V_r @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_b @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1606]) ).

thf(4172,plain,
    ( ( ! [V_r: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_r @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_b @ T_a ) ) )
          | ( c_in @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ T_a @ T_b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1605]) ).

thf(4173,plain,
    ( ( ! [V_k: $i,V_m: $i] :
          ( ! [V_n: $i] :
              ~ ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat )
          | ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2912]) ).

thf(4174,plain,
    ( ( ! [V_k: $i,V_m: $i,V_n: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat )
          | ( c_Divides_Oop_Advd @ V_k @ V_n @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1603]) ).

thf(4175,plain,
    ( ( ! [V_k: $i,V_n: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_k @ V_n @ tc_nat )
          | ! [V_m: $i] :
              ( ~ ( c_Divides_Oop_Advd @ V_k @ V_m @ tc_nat )
              | ( c_Divides_Oop_Advd @ V_k @ ( c_GCD_Ogcd @ ( c_Pair @ V_m @ V_n @ tc_nat @ tc_nat ) ) @ tc_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2911]) ).

thf(4176,plain,
    ( ( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1601]) ).

thf(4177,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_IntDef_Oint @ V_m )
           != ( c_IntDef_Oint @ V_n ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(copy,[status(thm)],[2910]) ).

thf(4178,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_z @ ( c_uminus @ V_w @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[1599]) ).

thf(4179,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ V_z @ ( c_uminus @ V_w @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[1598]) ).

thf(4180,plain,
    ( ( ! [V_m: $i] :
          ( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_IntDef_Oint )
          | ( V_m = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1597]) ).

thf(4181,plain,
    ( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint )
    = $true ),
    inference(copy,[status(thm)],[1596]) ).

thf(4182,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ V_z @ tc_IntDef_Oint ) @ V_w @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[1595]) ).

thf(4183,plain,
    ( ( ! [V_z: $i,V_w: $i] :
          ( ~ ( c_Divides_Oop_Advd @ V_z @ V_w @ tc_IntDef_Oint )
          | ( c_Divides_Oop_Advd @ ( c_uminus @ V_z @ tc_IntDef_Oint ) @ V_w @ tc_IntDef_Oint ) ) )
    = $true ),
    inference(copy,[status(thm)],[1594]) ).

thf(4184,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_r: $i] :
          ~ ( c_in @ ( c_Pair @ V_xs @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1593]) ).

thf(4185,plain,
    ( ( ! [V_xs: $i] :
          ( ! [V_ys: $i,T_a: $i] :
              ( c_List_Olist_ONil
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2909]) ).

thf(4186,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( c_List_Olist_ONil
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2908]) ).

thf(4187,plain,
    ( ( ! [T_a: $i] :
          ( c_List_Olist_ONil
          = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1590]) ).

thf(4188,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( c_List_Olist_ONil
             != ( c_List_Orev @ V_xs @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2907]) ).

thf(4189,plain,
    ( ( ! [T_a: $i] :
          ( c_List_Olist_ONil
          = ( c_List_Orev @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1588]) ).

thf(4190,plain,
    ( ( ! [V_ys: $i,T_a: $i,V_r: $i] :
          ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ V_ys @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olex @ V_r @ T_a ) @ ( tc_prod @ ( tc_List_Olist @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1587]) ).

thf(4191,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i] :
          ( ! [V_y: $i] :
              ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
             != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
          | ( V_xs = V_ys ) ) )
    = $true ),
    inference(copy,[status(thm)],[2906]) ).

thf(4192,plain,
    ( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
          ( ( ( c_append @ V_xs @ ( c_List_Olist_OCons @ V_x @ c_List_Olist_ONil @ T_a ) @ T_a )
           != ( c_append @ V_ys @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[2905]) ).

thf(4193,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1584]) ).

thf(4194,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_A: $i] :
          ( ~ ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ( c_in @ V_ys @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1583]) ).

thf(4195,plain,
    ( ( ! [V_ys: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_ys @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
          | ! [V_xs: $i] :
              ( ~ ( c_in @ V_xs @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) )
              | ( c_in @ ( c_append @ V_xs @ V_ys @ T_a ) @ ( c_List_Olists @ V_A @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2904]) ).

thf(4196,plain,
    ( ( ! [V_xs: $i] :
          ( ! [V_ys: $i,T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != c_List_Olist_ONil )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2903]) ).

thf(4197,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != c_List_Olist_ONil )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2902]) ).

thf(4198,plain,
    ( ( ! [T_a: $i] :
          ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a )
          = c_List_Olist_ONil ) )
    = $true ),
    inference(copy,[status(thm)],[1579]) ).

thf(4199,plain,
    ( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
          ( ( ( c_append @ V_ys @ V_xs @ T_a )
           != ( c_append @ V_zs @ V_xs @ T_a ) )
          | ( V_ys = V_zs ) ) )
    = $true ),
    inference(copy,[status(thm)],[2901]) ).

thf(4200,plain,
    ( ( ! [V_xs: $i] :
          ( ! [V_ys: $i,T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != V_ys )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2900]) ).

thf(4201,plain,
    ( ( ! [V_ys: $i,T_a: $i] :
          ( ( c_append @ c_List_Olist_ONil @ V_ys @ T_a )
          = V_ys ) )
    = $true ),
    inference(copy,[status(thm)],[1576]) ).

thf(4202,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( ( c_append @ V_xs @ V_ys @ T_a )
             != V_xs )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2899]) ).

thf(4203,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( c_append @ V_xs @ c_List_Olist_ONil @ T_a )
          = V_xs ) )
    = $true ),
    inference(copy,[status(thm)],[1574]) ).

thf(4204,plain,
    ( ( ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i] :
          ( ! [V_nibble2_H: $i] :
              ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
             != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
          | ( V_nibble1 = V_nibble1_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2898]) ).

thf(4205,plain,
    ( ( ! [V_nibble1: $i,V_nibble2: $i,V_nibble1_H: $i,V_nibble2_H: $i] :
          ( ( ( c_List_Ochar_OChar @ V_nibble1 @ V_nibble2 )
           != ( c_List_Ochar_OChar @ V_nibble1_H @ V_nibble2_H ) )
          | ( V_nibble2 = V_nibble2_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2897]) ).

thf(4206,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
             != c_0 )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2896]) ).

thf(4207,plain,
    ( ( ! [T_a: $i] :
          ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) )
          = c_0 ) )
    = $true ),
    inference(copy,[status(thm)],[1570]) ).

thf(4208,plain,
    ( ( ! [T_a: $i] :
          ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[1569]) ).

thf(4209,plain,
    ( ( ! [V_xs: $i] :
          ( ( V_xs = c_List_Olist_ONil )
          | ! [T_a: $i] : ( c_less @ c_0 @ ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2895]) ).

thf(4210,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
           != ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
          | ( ( c_List_Oremdups @ V_xs @ T_a )
            = V_xs ) ) )
    = $true ),
    inference(copy,[status(thm)],[2894]) ).

thf(4211,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( ( ( c_List_Oremdups @ V_xs @ T_a )
           != V_xs )
          | ( ( c_Nat_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
            = ( c_Nat_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2893]) ).

thf(4212,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( c_List_Olist_ONil
         != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2892]) ).

thf(4213,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
         != c_List_Olist_ONil ) )
    = $true ),
    inference(copy,[status(thm)],[2891]) ).

thf(4214,plain,
    ( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i] :
          ( ! [V_list_H: $i] :
              ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
             != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2890]) ).

thf(4215,plain,
    ( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
          ( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
           != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
          | ( V_list = V_list_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2889]) ).

thf(4216,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
          ( ( ( c_List_Orev @ V_xs @ T_a )
           != ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
          | ( V_xs
            = ( c_append @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2888]) ).

thf(4217,plain,
    ( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
          ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
          = ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1560]) ).

thf(4218,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( ( c_List_Orev @ V_xs @ T_a )
             != c_List_Olist_ONil )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2887]) ).

thf(4219,plain,
    ( ( ! [T_a: $i] :
          ( ( c_List_Orev @ c_List_Olist_ONil @ T_a )
          = c_List_Olist_ONil ) )
    = $true ),
    inference(copy,[status(thm)],[1558]) ).

thf(4220,plain,
    ( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
          ( ( ( c_List_Orev @ V_xs @ T_a )
           != ( c_List_Orev @ V_ys @ T_a ) )
          | ( V_xs = V_ys ) ) )
    = $true ),
    inference(copy,[status(thm)],[2886]) ).

thf(4221,plain,
    ( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
          ( ( ( c_append @ V_xs @ V_ys @ T_a )
           != ( c_append @ V_xs @ V_zs @ T_a ) )
          | ( V_ys = V_zs ) ) )
    = $true ),
    inference(copy,[status(thm)],[2885]) ).

thf(4222,plain,
    ( ( ! [V_ys: $i,V_xs: $i] :
          ( ! [T_a: $i] :
              ( V_ys
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2884]) ).

thf(4223,plain,
    ( ( ! [V_ys: $i,T_a: $i] :
          ( V_ys
          = ( c_append @ c_List_Olist_ONil @ V_ys @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1554]) ).

thf(4224,plain,
    ( ( ! [V_xs: $i,V_ys: $i] :
          ( ! [T_a: $i] :
              ( V_xs
             != ( c_append @ V_xs @ V_ys @ T_a ) )
          | ( V_ys = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2883]) ).

thf(4225,plain,
    ( ( ! [V_xs: $i,T_a: $i] :
          ( V_xs
          = ( c_append @ V_xs @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1552]) ).

thf(4226,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( c_emptyset
             != ( c_List_Oset @ V_xs @ T_a ) )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2882]) ).

thf(4227,plain,
    ( ( ! [T_a: $i] :
          ( c_emptyset
          = ( c_List_Oset @ c_List_Olist_ONil @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1550]) ).

thf(4228,plain,
    ( ( ! [V_xs: $i] :
          ( ! [T_a: $i] :
              ( ( c_List_Oset @ V_xs @ T_a )
             != c_emptyset )
          | ( V_xs = c_List_Olist_ONil ) ) )
    = $true ),
    inference(copy,[status(thm)],[2881]) ).

thf(4229,plain,
    ( ( ! [T_a: $i] :
          ( ( c_List_Oset @ c_List_Olist_ONil @ T_a )
          = c_emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[1548]) ).

thf(4230,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_Suc @ V_m )
           != ( c_Suc @ V_n ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(copy,[status(thm)],[2880]) ).

thf(4231,plain,
    ( ( ! [V_n: $i,V_m: $i] :
          ( ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
          | ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1546]) ).

thf(4232,plain,
    ( ( ! [V_n: $i,V_m: $i] :
          ( ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
          | ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1545]) ).

thf(4233,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ~ ( c_less @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
          | ( c_less @ V_m @ V_n @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1544]) ).

thf(4234,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ~ ( c_less @ V_m @ V_n @ tc_nat )
          | ( c_less @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1543]) ).

thf(4235,plain,
    ( ( ! [V_m: $i] :
          ( ( c_Suc @ V_m )
         != c_0 ) )
    = $true ),
    inference(copy,[status(thm)],[2879]) ).

thf(4236,plain,
    ( ( ! [V_m: $i] :
          ( c_0
         != ( c_Suc @ V_m ) ) )
    = $true ),
    inference(copy,[status(thm)],[2878]) ).

thf(4237,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ~ ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat )
          | ( c_less @ c_0 @ V_n @ tc_nat )
          | ( c_less @ c_0 @ V_m @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1540]) ).

thf(4238,plain,
    ( ( ! [V_m: $i] :
          ( ~ ( c_less @ c_0 @ V_m @ tc_nat )
          | ! [V_n: $i] : ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2877]) ).

thf(4239,plain,
    ( ( ! [V_n: $i] :
          ( ~ ( c_less @ c_0 @ V_n @ tc_nat )
          | ! [V_m: $i] : ( c_less @ c_0 @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2876]) ).

thf(4240,plain,
    ( ( ! [V_m: $i] :
          ( ! [V_n: $i] :
              ( ( c_plus @ V_m @ V_n @ tc_nat )
             != c_0 )
          | ( V_m = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2875]) ).

thf(4241,plain,
    ( ( ! [V_m: $i,V_n: $i] :
          ( ( ( c_plus @ V_m @ V_n @ tc_nat )
           != c_0 )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2874]) ).

thf(4242,plain,
    ( ( ( c_plus @ c_0 @ c_0 @ tc_nat )
      = c_0 )
    = $true ),
    inference(copy,[status(thm)],[1535]) ).

thf(4243,plain,
    ( ( ! [V_i: $i] :
          ( ~ ( c_lessequals @ V_i @ c_0 @ tc_nat )
          | ( V_i = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1534]) ).

thf(4244,plain,
    ( ( c_lessequals @ c_0 @ c_0 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[1533]) ).

thf(4245,plain,
    ( ( ! [V_n: $i] :
          ( ~ ( c_less @ V_n @ ( c_Suc @ c_0 ) @ tc_nat )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1532]) ).

thf(4246,plain,
    ( ( c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[1531]) ).

thf(4247,plain,
    ( ( ! [V_n: $i] :
          ( ~ ( c_less @ V_n @ c_1 @ tc_nat )
          | ( V_n = c_0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1530]) ).

thf(4248,plain,
    ( ( c_less @ c_0 @ c_1 @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[1529]) ).

thf(4249,plain,
    ( ( ! [V_n: $i] :
          ( ( V_n = c_0 )
          | ( c_less @ c_0 @ V_n @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2873]) ).

thf(4250,plain,
    ( ( ~ ( c_less @ c_0 @ c_0 @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[1527]) ).

thf(4251,plain,
    ( ( ! [V_i: $i,V_j: $i] :
          ~ ( c_less @ ( c_plus @ V_i @ V_j @ tc_nat ) @ V_i @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[1526]) ).

thf(4252,plain,
    ( ( ! [V_j: $i,V_i: $i] :
          ~ ( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[1525]) ).

thf(4253,plain,
    ( ( ! [V_n: $i] :
          ~ ( c_less @ V_n @ c_0 @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[1524]) ).

thf(4254,plain,
    ( ( c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 )
    = $true ),
    inference(copy,[status(thm)],[2872]) ).

thf(4255,plain,
    ( ( c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0 )
    = $true ),
    inference(copy,[status(thm)],[2871]) ).

thf(4256,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i] :
              ~ ( c_less @ V_x @ V_x @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2870]) ).

thf(4257,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i] :
          ( ! [V_b_H: $i] :
              ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
             != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
          | ( V_a = V_a_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2869]) ).

thf(4258,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
          ( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
           != ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
          | ( V_b = V_b_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2868]) ).

thf(4259,plain,
    ( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1518]) ).

thf(4260,plain,
    ( ( ! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
          ( ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_insert @ V_a @ c_emptyset @ T_b ) @ T_b @ T_a ) @ T_a )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1517]) ).

thf(4261,plain,
    ( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
          | ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_insert @ V_a @ c_emptyset @ T_b ) @ T_b @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1516]) ).

thf(4262,plain,
    ( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
          | ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1515]) ).

thf(4263,plain,
    ( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
          | ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1514]) ).

thf(4264,plain,
    ( ( ! [V_a: $i,V_b: $i] :
          ( ! [T_a: $i] :
              ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ c_Relation_OId @ ( tc_prod @ T_a @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2867]) ).

thf(4265,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OatLeast @ V_x @ T_a )
               != ( c_SetInterval_OatLeast @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2866]) ).

thf(4266,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a )
              | ( c_lessequals @ V_k @ V_i @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2865]) ).

thf(4267,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_k: $i,V_i: $i] :
              ( ~ ( c_lessequals @ V_k @ V_i @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OatLeast @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2864]) ).

thf(4268,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2863]) ).

thf(4269,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ~ ( c_lessequals @ V_y @ V_x @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OatLeast @ V_x @ T_a ) @ ( c_SetInterval_OatLeast @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2862]) ).

thf(4270,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OatMost @ V_x @ T_a )
               != ( c_SetInterval_OatMost @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2861]) ).

thf(4271,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a )
              | ( c_lessequals @ V_i @ V_k @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2860]) ).

thf(4272,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_lessequals @ V_i @ V_k @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OatMost @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2859]) ).

thf(4273,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2858]) ).

thf(4274,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ V_x @ V_y @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OatMost @ V_x @ T_a ) @ ( c_SetInterval_OatMost @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2857]) ).

thf(4275,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OgreaterThan @ V_x @ T_a )
               != ( c_SetInterval_OgreaterThan @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2856]) ).

thf(4276,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a )
              | ( c_less @ V_k @ V_i @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2855]) ).

thf(4277,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_k: $i,V_i: $i] :
              ( ~ ( c_less @ V_k @ V_i @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OgreaterThan @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2854]) ).

thf(4278,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2853]) ).

thf(4279,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ~ ( c_lessequals @ V_y @ V_x @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ V_x @ T_a ) @ ( c_SetInterval_OgreaterThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2852]) ).

thf(4280,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ( ( c_SetInterval_OlessThan @ V_x @ T_a )
               != ( c_SetInterval_OlessThan @ V_y @ T_a ) )
              | ( V_x = V_y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2851]) ).

thf(4281,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a )
              | ( c_less @ V_i @ V_k @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2850]) ).

thf(4282,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oord @ T_a )
          | ! [V_i: $i,V_k: $i] :
              ( ~ ( c_less @ V_i @ V_k @ T_a )
              | ( c_in @ V_i @ ( c_SetInterval_OlessThan @ V_k @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2849]) ).

thf(4283,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2848]) ).

thf(4284,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Olinorder @ T_a )
          | ! [V_x: $i,V_y: $i] :
              ( ~ ( c_lessequals @ V_x @ V_y @ T_a )
              | ( c_lessequals @ ( c_SetInterval_OlessThan @ V_x @ T_a ) @ ( c_SetInterval_OlessThan @ V_y @ T_a ) @ ( tc_set @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2847]) ).

thf(4285,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ~ ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1492]) ).

thf(4286,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ( c_in @ V_c @ V_A @ T_a )
          | ( c_in @ V_c @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1491]) ).

thf(4287,plain,
    ( ( ! [V_A: $i,T_a: $i,V_B: $i] :
          ( ( ( c_uminus @ V_A @ ( tc_set @ T_a ) )
           != ( c_uminus @ V_B @ ( tc_set @ T_a ) ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(copy,[status(thm)],[2846]) ).

thf(4288,plain,
    ( ( ! [V_A: $i,T_a: $i,V_B: $i] :
          ( ~ ( c_lessequals @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1489]) ).

thf(4289,plain,
    ( ( ! [V_B: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
          | ( c_lessequals @ ( c_uminus @ V_A @ ( tc_set @ T_a ) ) @ ( c_uminus @ V_B @ ( tc_set @ T_a ) ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1488]) ).

thf(4290,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ! [V_A: $i] :
              ~ ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2845]) ).

thf(4291,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a )
          | ( c_in @ V_c @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1486]) ).

thf(4292,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] :
              ( ( c_in @ V_c @ V_B @ T_a )
              | ( c_in @ V_c @ ( c_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2844]) ).

thf(4293,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
          | ( c_in @ V_c @ V_B @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1484]) ).

thf(4294,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a )
          | ( c_in @ V_c @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1483]) ).

thf(4295,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ! [V_A: $i] :
              ( ~ ( c_in @ V_c @ V_A @ T_a )
              | ( c_in @ V_c @ ( c_inter @ V_A @ V_B @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2843]) ).

thf(4296,plain,
    ( ( ! [V_X: $i,V_C: $i,T_a: $i] :
          ( ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
          | ! [V_A: $i] :
              ( ~ ( c_in @ V_A @ ( c_Inter @ V_C @ T_a ) @ T_a )
              | ( c_in @ V_A @ V_X @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2842]) ).

thf(4297,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ ( c_Pow @ V_B @ T_a ) @ ( tc_set @ T_a ) )
          | ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1480]) ).

thf(4298,plain,
    ( ( ! [V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( c_in @ V_A @ ( c_Pow @ V_B @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1479]) ).

thf(4299,plain,
    ( ( c_UNIV != c_emptyset )
    = $true ),
    inference(copy,[status(thm)],[2841]) ).

thf(4300,plain,
    ( ( ! [V_c: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_B @ T_a )
          | ! [V_A: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2840]) ).

thf(4301,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2839]) ).

thf(4302,plain,
    ( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
          | ( c_in @ V_c @ V_B @ T_a )
          | ( c_in @ V_c @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1475]) ).

thf(4303,plain,
    ( ( ! [V_A: $i] :
          ( ! [V_B: $i,T_a: $i] :
              ( ( c_union @ V_A @ V_B @ T_a )
             != c_emptyset )
          | ( V_A = c_emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[2838]) ).

thf(4304,plain,
    ( ( ! [V_A: $i,V_B: $i] :
          ( ! [T_a: $i] :
              ( ( c_union @ V_A @ V_B @ T_a )
             != c_emptyset )
          | ( V_B = c_emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[2837]) ).

thf(4305,plain,
    ( ( ! [T_a: $i] :
          ( ( c_union @ c_emptyset @ c_emptyset @ T_a )
          = c_emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[1472]) ).

thf(4306,plain,
    ( ( ! [V_A: $i,V_X: $i,T_a: $i] :
          ( ~ ( c_in @ V_A @ V_X @ T_a )
          | ! [V_C: $i] :
              ( ~ ( c_in @ V_X @ V_C @ ( tc_set @ T_a ) )
              | ( c_in @ V_A @ ( c_Union @ V_C @ T_a ) @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2836]) ).

thf(4307,plain,
    ( ( ! [V_a: $i,T_a: $i] :
          ~ ( c_in @ V_a @ c_emptyset @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[1470]) ).

thf(4308,plain,
    ( ( ! [V_a: $i,V_B: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ V_B @ T_a )
          | ! [V_b: $i] : ( c_in @ V_a @ ( c_insert @ V_b @ V_B @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2835]) ).

thf(4309,plain,
    ( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
    = $true ),
    inference(copy,[status(thm)],[1468]) ).

thf(4310,plain,
    ( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_a @ ( c_insert @ V_b @ V_A @ T_a ) @ T_a )
          | ( V_a = V_b )
          | ( c_in @ V_a @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2834]) ).

thf(4311,plain,
    ( ( ! [V_A: $i,T_a: $i] :
          ~ ( c_less @ V_A @ c_emptyset @ ( tc_set @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1466]) ).

thf(4312,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ V_A @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2833]) ).

thf(4313,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
          ( ( ( c_insert @ V_a @ V_A @ T_a )
           != ( c_insert @ V_b @ c_emptyset @ T_a ) )
          | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2832]) ).

thf(4314,plain,
    ( ( ! [V_A: $i,V_x: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ ( c_insert @ V_x @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) )
          | ( ( c_insert @ V_x @ V_A @ T_a )
            = ( c_insert @ V_x @ c_emptyset @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1463]) ).

thf(4315,plain,
    ( ( ! [V_b: $i,T_a: $i,V_a: $i] :
          ( ! [V_A: $i] :
              ( ( c_insert @ V_b @ c_emptyset @ T_a )
             != ( c_insert @ V_a @ V_A @ T_a ) )
          | ( V_a = V_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2831]) ).

thf(4316,plain,
    ( ( ! [V_b: $i,T_a: $i,V_a: $i,V_A: $i] :
          ( ( ( c_insert @ V_b @ c_emptyset @ T_a )
           != ( c_insert @ V_a @ V_A @ T_a ) )
          | ( c_lessequals @ V_A @ ( c_insert @ V_b @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2830]) ).

thf(4317,plain,
    ( ( ! [V_A: $i,V_x: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_A @ ( c_insert @ V_x @ c_emptyset @ T_a ) @ ( tc_set @ T_a ) )
          | ( ( c_insert @ V_x @ c_emptyset @ T_a )
            = ( c_insert @ V_x @ V_A @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1460]) ).

thf(4318,plain,
    ( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
          ( ( ( c_Sum__Type_OInl @ V_x @ T_a @ T_b )
           != ( c_Sum__Type_OInl @ V_y @ T_a @ T_b ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[2829]) ).

thf(4319,plain,
    ( ( ! [V_a: $i,T_a: $i,T_b: $i,V_b: $i] :
          ( ( c_Sum__Type_OInl @ V_a @ T_a @ T_b )
         != ( c_Sum__Type_OInr @ V_b @ T_b @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[2828]) ).

thf(4320,plain,
    ( ( ! [V_x: $i,T_b: $i,T_a: $i,V_y: $i] :
          ( ( ( c_Sum__Type_OInr @ V_x @ T_b @ T_a )
           != ( c_Sum__Type_OInr @ V_y @ T_b @ T_a ) )
          | ( V_x = V_y ) ) )
    = $true ),
    inference(copy,[status(thm)],[2827]) ).

thf(4321,plain,
    ( ( ! [V_b: $i,T_b: $i,T_a: $i,V_a: $i] :
          ( ( c_Sum__Type_OInr @ V_b @ T_b @ T_a )
         != ( c_Sum__Type_OInl @ V_a @ T_a @ T_b ) ) )
    = $true ),
    inference(copy,[status(thm)],[2826]) ).

thf(4322,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
          | ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1455]) ).

thf(4323,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a )
          | ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1454]) ).

thf(4324,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1453]) ).

thf(4325,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1452]) ).

thf(4326,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Oacyclic @ V_r @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
              | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2825]) ).

thf(4327,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ( c_Wellfounded__Recursion_Owf @ V_r @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[1450]) ).

thf(4328,plain,
    ( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
          | ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1449]) ).

thf(4329,plain,
    ( ( ! [V_r: $i,T_a: $i] :
          ( ~ ( c_Wellfounded__Recursion_Owf @ V_r @ T_a )
          | ! [V_y: $i,V_x: $i] :
              ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
              | ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2824]) ).

thf(4330,plain,
    ( ( ! [V_x: $i,V_y: $i] :
          ( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
          | ( c_less @ V_x @ V_y @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[1447]) ).

thf(4331,plain,
    ( ( ! [V_x: $i,V_y: $i] :
          ( ~ ( c_less @ V_x @ V_y @ tc_nat )
          | ( c_in @ ( c_Pair @ V_x @ V_y @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1446]) ).

thf(4332,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1445]) ).

thf(4333,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1444]) ).

thf(4334,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1443]) ).

thf(4335,plain,
    ( ( ! [V_K: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1442]) ).

thf(4336,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1441]) ).

thf(4337,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1440]) ).

thf(4338,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1439]) ).

thf(4339,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1438]) ).

thf(4340,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_Y @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1437]) ).

thf(4341,plain,
    ( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1436]) ).

thf(4342,plain,
    ( ( ! [V_n: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_n ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_ONonce @ V_n ) @ V_H @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1435]) ).

thf(4343,plain,
    ( ( ! [V_nat_H: $i] :
          ( c_Message_Oagent_OServer
         != ( c_Message_Oagent_OFriend @ V_nat_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2823]) ).

thf(4344,plain,
    ( ( ! [V_nat_H: $i] :
          ( ( c_Message_Oagent_OFriend @ V_nat_H )
         != c_Message_Oagent_OServer ) )
    = $true ),
    inference(copy,[status(thm)],[2822]) ).

thf(4345,plain,
    ( ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )
    = $true ),
    inference(copy,[status(thm)],[2821]) ).

thf(4346,plain,
    ( ( c_Message_Oagent_OSpy != c_Message_Oagent_OServer )
    = $true ),
    inference(copy,[status(thm)],[2820]) ).

thf(4347,plain,
    ( ( ! [V_nat: $i] :
          ( ( c_Message_Oagent_OFriend @ V_nat )
         != c_Message_Oagent_OSpy ) )
    = $true ),
    inference(copy,[status(thm)],[2819]) ).

thf(4348,plain,
    ( ( ! [V_nat: $i] :
          ( c_Message_Oagent_OSpy
         != ( c_Message_Oagent_OFriend @ V_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[2818]) ).

thf(4349,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Oagent_OFriend @ V_nat )
           != ( c_Message_Oagent_OFriend @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2817]) ).

thf(4350,plain,
    ( ( ! [V_K: $i,V_X: $i,V_H: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ V_K ) ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1427]) ).

thf(4351,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1426]) ).

thf(4352,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1425]) ).

thf(4353,plain,
    ( ( ! [V_c: $i,V_G: $i,V_H: $i] :
          ( ~ ( c_in @ V_c @ ( c_Message_Oparts @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
          | ( c_in @ V_c @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ V_c @ ( c_Message_Oparts @ V_G ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1424]) ).

thf(4354,plain,
    ( ( ! [V_agent: $i,V_agent_H: $i] :
          ( ( ( c_Message_Omsg_OAgent @ V_agent )
           != ( c_Message_Omsg_OAgent @ V_agent_H ) )
          | ( V_agent = V_agent_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2816]) ).

thf(4355,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_ONumber @ V_nat )
           != ( c_Message_Omsg_ONumber @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2815]) ).

thf(4356,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_ONonce @ V_nat )
           != ( c_Message_Omsg_ONonce @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2814]) ).

thf(4357,plain,
    ( ( ! [V_nat: $i,V_nat_H: $i] :
          ( ( ( c_Message_Omsg_OKey @ V_nat )
           != ( c_Message_Omsg_OKey @ V_nat_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2813]) ).

thf(4358,plain,
    ( ( ! [V_msg: $i,V_msg_H: $i] :
          ( ( ( c_Message_Omsg_OHash @ V_msg )
           != ( c_Message_Omsg_OHash @ V_msg_H ) )
          | ( V_msg = V_msg_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2812]) ).

thf(4359,plain,
    ( ( ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i] :
          ( ! [V_msg2_H: $i] :
              ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
             != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
          | ( V_msg1 = V_msg1_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2811]) ).

thf(4360,plain,
    ( ( ! [V_msg1: $i,V_msg2: $i,V_msg1_H: $i,V_msg2_H: $i] :
          ( ( ( c_Message_Omsg_OMPair @ V_msg1 @ V_msg2 )
           != ( c_Message_Omsg_OMPair @ V_msg1_H @ V_msg2_H ) )
          | ( V_msg2 = V_msg2_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2810]) ).

thf(4361,plain,
    ( ( ! [V_nat: $i,V_msg: $i,V_nat_H: $i] :
          ( ! [V_msg_H: $i] :
              ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
             != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
          | ( V_nat = V_nat_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2809]) ).

thf(4362,plain,
    ( ( ! [V_nat: $i,V_msg: $i,V_nat_H: $i,V_msg_H: $i] :
          ( ( ( c_Message_Omsg_OCrypt @ V_nat @ V_msg )
           != ( c_Message_Omsg_OCrypt @ V_nat_H @ V_msg_H ) )
          | ( V_msg = V_msg_H ) ) )
    = $true ),
    inference(copy,[status(thm)],[2808]) ).

thf(4363,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1414]) ).

thf(4364,plain,
    ( ( ! [V_X: $i] :
          ~ ( c_in @ V_X @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ) )
    = $true ),
    inference(copy,[status(thm)],[1413]) ).

thf(4365,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Oparts @ ( c_Message_Oparts @ V_H ) ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1412]) ).

thf(4366,plain,
    ( ( ! [V_agt: $i,V_H: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ V_agt ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) )
    = $true ),
    inference(copy,[status(thm)],[1411]) ).

thf(4367,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ! [V_K: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2807]) ).

thf(4368,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OHash @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1409]) ).

thf(4369,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1408]) ).

thf(4370,plain,
    ( ( ! [V_Y: $i,V_H: $i] :
          ( ~ ( c_in @ V_Y @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
          | ! [V_X: $i] :
              ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2806]) ).

thf(4371,plain,
    ( ( ! [V_n: $i,V_H: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ V_n ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) )
    = $true ),
    inference(copy,[status(thm)],[1406]) ).

thf(4372,plain,
    ( ( ! [V_H: $i,V_H_H: $i] :
          ( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_H ) @ ( c_Message_Oanalz @ V_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
          | ! [V_G: $i,V_G_H: $i] :
              ( ~ ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
              | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ V_G_H @ V_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2805]) ).

thf(4373,plain,
    ( ( ! [V_X: $i,V_H: $i] :
          ( ~ ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Osynth @ V_H ) ) @ tc_Message_Omsg )
          | ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[1404]) ).

thf(4374,plain,
    ( ( ~ $false ) = $true ),
    inference(copy,[status(thm)],[2804]) ).

thf(4375,plain,
    ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ v_G ) @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2974]) ).

thf(4376,plain,
    ! [SV1: $i] :
      ( ( ! [SY2005: $i,SY2006: $i,SY2007: $i] :
            ( ( ( c_Datatype__Universe_OLeaf @ SV1 @ SY2005 @ SY2006 )
             != ( c_Datatype__Universe_OLeaf @ SY2007 @ SY2005 @ SY2006 ) )
            | ( SV1 = SY2007 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2975]) ).

thf(4377,plain,
    ! [SV2: $i] :
      ( ( ! [SY2008: $i,SY2009: $i,SY2010: $i] :
            ( ( ( c_Datatype__Universe_ONumb @ SV2 @ SY2008 @ SY2009 )
             != ( c_Datatype__Universe_ONumb @ SY2010 @ SY2008 @ SY2009 ) )
            | ( SV2 = SY2010 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2976]) ).

thf(4378,plain,
    ! [SV3: $i] :
      ( ( ! [SY2011: $i,SY2012: $i,SY2013: $i,SY2014: $i] :
            ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SY2011 @ SY2012 @ SY2013 @ SY2014 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2013 @ SY2014 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2013 @ SY2014 ) ) ) )
            | ( SV3
              = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV3 @ SY2011 @ SY2012 @ SY2013 @ SY2014 ) @ ( c_Main_OdprodE__2 @ SV3 @ SY2011 @ SY2012 @ SY2013 @ SY2014 ) @ SY2013 @ SY2014 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV3 @ SY2011 @ SY2012 @ SY2013 @ SY2014 ) @ ( c_Main_OdprodE__4 @ SV3 @ SY2011 @ SY2012 @ SY2013 @ SY2014 ) @ SY2013 @ SY2014 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2013 @ SY2014 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2013 @ SY2014 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2977]) ).

thf(4379,plain,
    ! [SV4: $i] :
      ( ( ! [SY2015: $i,SY2016: $i,SY2017: $i,SY2018: $i] :
            ( ~ ( c_in @ SV4 @ ( c_Datatype__Universe_Odprod @ SY2015 @ SY2016 @ SY2017 @ SY2018 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2017 @ SY2018 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2017 @ SY2018 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV4 @ SY2015 @ SY2016 @ SY2017 @ SY2018 ) @ ( c_Main_OdprodE__4 @ SV4 @ SY2015 @ SY2016 @ SY2017 @ SY2018 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2017 @ SY2018 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2017 @ SY2018 ) ) ) @ SY2016 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2017 @ SY2018 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2017 @ SY2018 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2978]) ).

thf(4380,plain,
    ! [SV5: $i] :
      ( ( ! [SY2019: $i,SY2020: $i,SY2021: $i,SY2022: $i] :
            ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odprod @ SY2019 @ SY2020 @ SY2021 @ SY2022 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2021 @ SY2022 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2021 @ SY2022 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV5 @ SY2019 @ SY2020 @ SY2021 @ SY2022 ) @ ( c_Main_OdprodE__3 @ SV5 @ SY2019 @ SY2020 @ SY2021 @ SY2022 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2021 @ SY2022 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2021 @ SY2022 ) ) ) @ SY2019 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2021 @ SY2022 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2021 @ SY2022 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2979]) ).

thf(4381,plain,
    ! [SV6: $i] :
      ( ( ! [SY2023: $i,SY2024: $i,SY2025: $i,SY2026: $i,SY2027: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV6 @ SY2023 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) ) @ SY2026 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) ) )
            | ! [SY2028: $i,SY2029: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY2027 @ SY2028 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) ) @ SY2029 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) ) )
                | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY2027 @ SV6 @ SY2024 @ SY2025 ) @ ( c_Datatype__Universe_OScons @ SY2028 @ SY2023 @ SY2024 @ SY2025 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY2029 @ SY2026 @ SY2024 @ SY2025 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2024 @ SY2025 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2980]) ).

thf(4382,plain,
    ! [SV7: $i] :
      ( ( ! [SY2030: $i,SY2031: $i,SY2032: $i,SY2033: $i] :
            ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SY2030 @ SY2031 @ SY2032 @ SY2033 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2032 @ SY2033 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2032 @ SY2033 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SY2030 @ SV7 @ SY2032 @ SY2033 ) @ SY2032 @ SY2033 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SY2030 @ SV7 @ SY2032 @ SY2033 ) @ SY2032 @ SY2033 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2032 @ SY2033 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2032 @ SY2033 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2031 @ SV7 @ SY2032 @ SY2033 ) @ SY2032 @ SY2033 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2031 @ SV7 @ SY2032 @ SY2033 ) @ SY2032 @ SY2033 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2032 @ SY2033 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2032 @ SY2033 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2981]) ).

thf(4383,plain,
    ! [SV8: $i] :
      ( ( ! [SY2034: $i,SY2035: $i,SY2036: $i,SY2037: $i] :
            ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SY2034 @ SY2035 @ SY2036 @ SY2037 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) ) )
            | ( SV8
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SY2034 @ SV8 @ SY2036 @ SY2037 ) @ SY2036 @ SY2037 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SY2034 @ SV8 @ SY2036 @ SY2037 ) @ SY2036 @ SY2037 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2035 @ SV8 @ SY2036 @ SY2037 ) @ ( c_Main_OdsumE__4 @ SY2035 @ SV8 @ SY2036 @ SY2037 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) ) @ SY2035 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2036 @ SY2037 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2982]) ).

thf(4384,plain,
    ! [SV9: $i] :
      ( ( ! [SY2038: $i,SY2039: $i,SY2040: $i,SY2041: $i] :
            ( ~ ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SY2038 @ SY2039 @ SY2040 @ SY2041 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) ) )
            | ( SV9
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2039 @ SV9 @ SY2040 @ SY2041 ) @ SY2040 @ SY2041 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2039 @ SV9 @ SY2040 @ SY2041 ) @ SY2040 @ SY2041 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SY2038 @ SV9 @ SY2040 @ SY2041 ) @ ( c_Main_OdsumE__2 @ SY2038 @ SV9 @ SY2040 @ SY2041 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) ) @ SY2038 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2983]) ).

thf(4385,plain,
    ! [SV10: $i] :
      ( ( ! [SY2042: $i,SY2043: $i,SY2044: $i,SY2045: $i] :
            ( ~ ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SY2042 @ SY2043 @ SY2044 @ SY2045 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SY2042 @ SV10 @ SY2044 @ SY2045 ) @ ( c_Main_OdsumE__2 @ SY2042 @ SV10 @ SY2044 @ SY2045 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) ) @ SY2042 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2043 @ SV10 @ SY2044 @ SY2045 ) @ ( c_Main_OdsumE__4 @ SY2043 @ SV10 @ SY2044 @ SY2045 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) ) @ SY2043 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2044 @ SY2045 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2984]) ).

thf(4386,plain,
    ! [SV11: $i] :
      ( ( ! [SY2046: $i,SY2047: $i,SY2048: $i,SY2049: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV11 @ SY2046 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) ) @ SY2049 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) ) )
            | ! [SY2050: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SY2047 @ SY2048 ) @ ( c_Datatype__Universe_OIn0 @ SY2046 @ SY2047 @ SY2048 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2049 @ SY2050 @ SY2047 @ SY2048 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2047 @ SY2048 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2985]) ).

thf(4387,plain,
    ! [SV12: $i] :
      ( ( ! [SY2051: $i,SY2052: $i,SY2053: $i,SY2054: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV12 @ SY2051 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) ) @ SY2054 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) ) )
            | ! [SY2055: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SY2052 @ SY2053 ) @ ( c_Datatype__Universe_OIn1 @ SY2051 @ SY2052 @ SY2053 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2055 @ SY2054 @ SY2052 @ SY2053 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2052 @ SY2053 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2986]) ).

thf(4388,plain,
    ! [SV13: $i] :
      ( ( ! [SY2056: $i,SY2057: $i,SY2058: $i,SY2059: $i] :
            ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SY2056 @ SY2057 @ SY2058 @ SY2059 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2058 @ SY2059 ) ) )
            | ( SV13
              = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SY2056 @ SY2057 @ SV13 @ SY2058 @ SY2059 ) @ ( c_Main_OuprodE__2 @ SY2056 @ SY2057 @ SV13 @ SY2058 @ SY2059 ) @ SY2058 @ SY2059 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2987]) ).

thf(4389,plain,
    ! [SV14: $i] :
      ( ( ! [SY2060: $i,SY2061: $i,SY2062: $i,SY2063: $i] :
            ( ~ ( c_in @ SV14 @ ( c_Datatype__Universe_Ouprod @ SY2060 @ SY2061 @ SY2062 @ SY2063 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2062 @ SY2063 ) ) )
            | ( c_in @ ( c_Main_OuprodE__2 @ SY2060 @ SY2061 @ SV14 @ SY2062 @ SY2063 ) @ SY2061 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2062 @ SY2063 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2988]) ).

thf(4390,plain,
    ! [SV15: $i] :
      ( ( ! [SY2064: $i,SY2065: $i,SY2066: $i,SY2067: $i] :
            ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ouprod @ SY2064 @ SY2065 @ SY2066 @ SY2067 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2066 @ SY2067 ) ) )
            | ( c_in @ ( c_Main_OuprodE__1 @ SY2064 @ SY2065 @ SV15 @ SY2066 @ SY2067 ) @ SY2064 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2066 @ SY2067 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2989]) ).

thf(4391,plain,
    ! [SV16: $i] :
      ( ( ! [SY2068: $i,SY2069: $i,SY2070: $i] :
            ( ~ ( c_in @ SV16 @ SY2068 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2069 @ SY2070 ) ) )
            | ! [SY2071: $i,SY2072: $i] :
                ( ~ ( c_in @ SY2071 @ SY2072 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2069 @ SY2070 ) ) )
                | ( c_in @ ( c_Datatype__Universe_OScons @ SY2071 @ SV16 @ SY2069 @ SY2070 ) @ ( c_Datatype__Universe_Ouprod @ SY2072 @ SY2068 @ SY2069 @ SY2070 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2069 @ SY2070 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2990]) ).

thf(4392,plain,
    ! [SV17: $i] :
      ( ( ! [SY2073: $i,SY2074: $i,SY2075: $i,SY2076: $i] :
            ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SY2073 @ SY2074 @ SY2075 @ SY2076 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2075 @ SY2076 ) ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SY2073 @ SV17 @ SY2075 @ SY2076 ) @ SY2075 @ SY2076 ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2074 @ SV17 @ SY2075 @ SY2076 ) @ SY2075 @ SY2076 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2991]) ).

thf(4393,plain,
    ! [SV18: $i] :
      ( ( ! [SY2077: $i,SY2078: $i,SY2079: $i,SY2080: $i] :
            ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SY2077 @ SY2078 @ SY2079 @ SY2080 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2079 @ SY2080 ) ) )
            | ( SV18
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SY2077 @ SV18 @ SY2079 @ SY2080 ) @ SY2079 @ SY2080 ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SY2078 @ SV18 @ SY2079 @ SY2080 ) @ SY2078 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2079 @ SY2080 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2992]) ).

thf(4394,plain,
    ! [SV19: $i] :
      ( ( ! [SY2081: $i,SY2082: $i,SY2083: $i,SY2084: $i] :
            ( ~ ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SY2081 @ SY2082 @ SY2083 @ SY2084 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2083 @ SY2084 ) ) )
            | ( SV19
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2082 @ SV19 @ SY2083 @ SY2084 ) @ SY2083 @ SY2084 ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SY2081 @ SV19 @ SY2083 @ SY2084 ) @ SY2081 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2083 @ SY2084 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2993]) ).

thf(4395,plain,
    ! [SV20: $i] :
      ( ( ! [SY2085: $i,SY2086: $i,SY2087: $i,SY2088: $i] :
            ( ~ ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SY2085 @ SY2086 @ SY2087 @ SY2088 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2087 @ SY2088 ) ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SY2085 @ SV20 @ SY2087 @ SY2088 ) @ SY2085 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2087 @ SY2088 ) ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SY2086 @ SV20 @ SY2087 @ SY2088 ) @ SY2086 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2087 @ SY2088 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2994]) ).

thf(4396,plain,
    ! [SV21: $i] :
      ( ( ! [SY2089: $i,SY2090: $i,SY2091: $i] :
            ( ~ ( c_in @ SV21 @ SY2089 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2090 @ SY2091 ) ) )
            | ! [SY2092: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ SV21 @ SY2090 @ SY2091 ) @ ( c_Datatype__Universe_Ousum @ SY2089 @ SY2092 @ SY2090 @ SY2091 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2090 @ SY2091 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2995]) ).

thf(4397,plain,
    ! [SV22: $i] :
      ( ( ! [SY2093: $i,SY2094: $i,SY2095: $i] :
            ( ~ ( c_in @ SV22 @ SY2093 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2094 @ SY2095 ) ) )
            | ! [SY2096: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ SV22 @ SY2094 @ SY2095 ) @ ( c_Datatype__Universe_Ousum @ SY2096 @ SY2093 @ SY2094 @ SY2095 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2094 @ SY2095 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2996]) ).

thf(4398,plain,
    ! [SV23: $i] :
      ( ( c_Divides_Oop_Advd @ SV23 @ c_0 @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2997]) ).

thf(4399,plain,
    ! [SV24: $i] :
      ( ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ SV24 @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2998]) ).

thf(4400,plain,
    ! [SV25: $i] :
      ( ( ! [SY2097: $i] : ( c_Divides_Oop_Advd @ SV25 @ ( c_times @ SV25 @ SY2097 @ tc_nat ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2999]) ).

thf(4401,plain,
    ! [SV26: $i] :
      ( ( ! [SY2098: $i] : ( c_Divides_Oop_Advd @ SV26 @ ( c_times @ SY2098 @ SV26 @ tc_nat ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3000]) ).

thf(4402,plain,
    ! [SV27: $i] :
      ( ( ! [SY2099: $i] :
            ( ( ( c_Divides_Oop_Amod @ SV27 @ SY2099 @ tc_nat )
             != c_0 )
            | ( SV27
              = ( c_times @ SY2099 @ ( c_Main_Omod__eq__0D__dest__1 @ SY2099 @ SV27 ) @ tc_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3001]) ).

thf(4403,plain,
    ! [SV28: $i] :
      ( ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3002]) ).

thf(4404,plain,
    ! [SV29: $i] :
      ( ( ! [SY2100: $i] :
            ( ~ ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ SY2100 ) )
            | ! [SY2101: $i] : ( c_in @ ( c_insert @ SY2101 @ SV29 @ SY2100 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2100 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3003]) ).

thf(4405,plain,
    ! [SV30: $i] :
      ( ( ! [SY2102: $i] :
            ( ~ ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ SY2102 ) )
            | ! [SY2103: $i] : ( c_in @ ( c_inter @ SV30 @ SY2103 @ SY2102 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2102 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3004]) ).

thf(4406,plain,
    ! [SV31: $i] :
      ( ( ! [SY2104: $i] :
            ( ~ ( c_in @ SV31 @ c_Finite__Set_OFinites @ ( tc_set @ SY2104 ) )
            | ! [SY2105: $i] : ( c_in @ ( c_inter @ SY2105 @ SV31 @ SY2104 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2104 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3005]) ).

thf(4407,plain,
    ! [SV32: $i] :
      ( ( ! [SY2106: $i] :
            ( ~ ( c_in @ SV32 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2106 ) ) )
            | ( c_in @ ( c_Main_Ofinite__Union__1 @ SV32 @ SY2106 ) @ SV32 @ ( tc_set @ SY2106 ) )
            | ( c_in @ ( c_Union @ SV32 @ SY2106 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2106 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3006]) ).

thf(4408,plain,
    ! [SV33: $i] :
      ( ( ! [SY2107: $i] :
            ( ~ ( c_in @ SV33 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2107 ) ) )
            | ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV33 @ SY2107 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2107 ) )
            | ( c_in @ ( c_Union @ SV33 @ SY2107 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2107 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3007]) ).

thf(4409,plain,
    ! [SV34: $i] :
      ( ( ! [SY2108: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV34 @ SY2108 @ tc_nat @ tc_nat ) ) @ SV34 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3008]) ).

thf(4410,plain,
    ! [SV35: $i] :
      ( ( ! [SY2109: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV35 @ SY2109 @ tc_nat @ tc_nat ) ) @ SY2109 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3009]) ).

thf(4411,plain,
    ! [SV36: $i] :
      ( ( ! [SY2110: $i] :
            ( ~ ( c_Infinite__Set_Oatmost__one @ SV36 @ SY2110 )
            | ! [SY2111: $i] :
                ( ~ ( c_in @ SY2111 @ SV36 @ SY2110 )
                | ! [SY2112: $i] :
                    ( ~ ( c_in @ SY2112 @ SV36 @ SY2110 )
                    | ( SY2111 = SY2112 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3010]) ).

thf(4412,plain,
    ! [SV37: $i] :
      ( ( ! [SY2113: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ SV37 ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SY2113 ) @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3011]) ).

thf(4413,plain,
    ! [SV38: $i] :
      ( ( ! [SY2114: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ SV38 ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SY2114 ) @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3012]) ).

thf(4414,plain,
    ! [SV39: $i] :
      ( ( c_Divides_Oop_Advd @ SV39 @ c_0 @ tc_IntDef_Oint )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3013]) ).

thf(4415,plain,
    ! [SV40: $i] :
      ( ( c_Divides_Oop_Advd @ c_1 @ SV40 @ tc_IntDef_Oint )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3014]) ).

thf(4416,plain,
    ! [SV41: $i] :
      ( ( ! [SY2115: $i] : ( c_Divides_Oop_Advd @ SV41 @ ( c_times @ SV41 @ SY2115 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3015]) ).

thf(4417,plain,
    ! [SV42: $i] :
      ( ( ! [SY2116: $i] : ( c_Divides_Oop_Advd @ SV42 @ ( c_times @ SY2116 @ SV42 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3016]) ).

thf(4418,plain,
    ! [SV43: $i] :
      ( ( ! [SY2117: $i] :
            ( ( ( c_Divides_Oop_Amod @ SV43 @ SY2117 @ tc_IntDef_Oint )
             != c_0 )
            | ( SV43
              = ( c_times @ SY2117 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SY2117 @ SV43 ) @ tc_IntDef_Oint ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3017]) ).

thf(4419,plain,
    ! [SV44: $i] :
      ( ( ! [SY2118: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ SV44 @ SY2118 ) @ SY2118 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3018]) ).

thf(4420,plain,
    ! [SV45: $i] :
      ( ( ! [SY2119: $i] : ( c_in @ ( c_List_Oset @ SV45 @ SY2119 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3019]) ).

thf(4421,plain,
    ! [SV46: $i] :
      ( ( ! [SY2120: $i,SY2121: $i] :
            ( ~ ( c_in @ SV46 @ ( c_List_Olists @ SY2120 @ SY2121 ) @ ( tc_List_Olist @ SY2121 ) )
            | ! [SY2122: $i] :
                ( ~ ( c_in @ SY2122 @ ( c_List_Oset @ SV46 @ SY2121 ) @ SY2121 )
                | ( c_in @ SY2122 @ SY2120 @ SY2121 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3020]) ).

thf(4422,plain,
    ! [SV47: $i] :
      ( ( ! [SY2123: $i,SY2124: $i] :
            ( ( c_in @ SV47 @ ( c_List_Olists @ SY2123 @ SY2124 ) @ ( tc_List_Olist @ SY2124 ) )
            | ( c_in @ ( c_Main_Oin__listsI__1 @ SY2123 @ SV47 @ SY2124 ) @ ( c_List_Oset @ SV47 @ SY2124 ) @ SY2124 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3021]) ).

thf(4423,plain,
    ! [SV48: $i] :
      ( ( ! [SY2125: $i,SY2126: $i] :
            ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV48 @ SY2125 @ SY2126 ) @ SV48 @ SY2126 )
            | ( c_in @ SY2125 @ ( c_List_Olists @ SV48 @ SY2126 ) @ ( tc_List_Olist @ SY2126 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3022]) ).

thf(4424,plain,
    ! [SV49: $i] :
      ( ( ! [SY2127: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ SV49 @ SY2127 ) @ ( tc_List_Olist @ SY2127 ) ) @ ( c_Nat_Osize @ SV49 @ ( tc_List_Olist @ SY2127 ) ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3023]) ).

thf(4425,plain,
    ! [SV50: $i] :
      ( ( ! [SY2128: $i,SY2129: $i,SY2130: $i,SY2131: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV50 @ SY2128 @ SY2129 ) @ SY2130 @ ( tc_List_Olist @ SY2129 ) @ ( tc_List_Olist @ SY2129 ) ) @ ( c_List_Olistrel @ SY2131 @ SY2129 ) @ ( tc_prod @ ( tc_List_Olist @ SY2129 ) @ ( tc_List_Olist @ SY2129 ) ) )
            | ( SY2130
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY2131 @ SY2130 @ SV50 @ SY2128 @ SY2129 ) @ ( c_Main_Olistrel__Cons1__2 @ SY2131 @ SY2130 @ SV50 @ SY2128 @ SY2129 ) @ SY2129 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3024]) ).

thf(4426,plain,
    ! [SV51: $i] :
      ( ( ! [SY2132: $i,SY2133: $i,SY2134: $i,SY2135: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV51 @ SY2132 @ SY2133 ) @ SY2134 @ ( tc_List_Olist @ SY2133 ) @ ( tc_List_Olist @ SY2133 ) ) @ ( c_List_Olistrel @ SY2135 @ SY2133 ) @ ( tc_prod @ ( tc_List_Olist @ SY2133 ) @ ( tc_List_Olist @ SY2133 ) ) )
            | ( c_in @ ( c_Pair @ SY2132 @ ( c_Main_Olistrel__Cons1__2 @ SY2135 @ SY2134 @ SV51 @ SY2132 @ SY2133 ) @ ( tc_List_Olist @ SY2133 ) @ ( tc_List_Olist @ SY2133 ) ) @ ( c_List_Olistrel @ SY2135 @ SY2133 ) @ ( tc_prod @ ( tc_List_Olist @ SY2133 ) @ ( tc_List_Olist @ SY2133 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3025]) ).

thf(4427,plain,
    ! [SV52: $i] :
      ( ( ! [SY2136: $i,SY2137: $i,SY2138: $i,SY2139: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV52 @ SY2136 @ SY2137 ) @ SY2138 @ ( tc_List_Olist @ SY2137 ) @ ( tc_List_Olist @ SY2137 ) ) @ ( c_List_Olistrel @ SY2139 @ SY2137 ) @ ( tc_prod @ ( tc_List_Olist @ SY2137 ) @ ( tc_List_Olist @ SY2137 ) ) )
            | ( c_in @ ( c_Pair @ SV52 @ ( c_Main_Olistrel__Cons1__1 @ SY2139 @ SY2138 @ SV52 @ SY2136 @ SY2137 ) @ SY2137 @ SY2137 ) @ SY2139 @ ( tc_prod @ SY2137 @ SY2137 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3026]) ).

thf(4428,plain,
    ! [SV53: $i] :
      ( ( ! [SY2140: $i,SY2141: $i,SY2142: $i,SY2143: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV53 @ ( c_List_Olist_OCons @ SY2140 @ SY2141 @ SY2142 ) @ ( tc_List_Olist @ SY2142 ) @ ( tc_List_Olist @ SY2142 ) ) @ ( c_List_Olistrel @ SY2143 @ SY2142 ) @ ( tc_prod @ ( tc_List_Olist @ SY2142 ) @ ( tc_List_Olist @ SY2142 ) ) )
            | ( SV53
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY2143 @ SV53 @ SY2140 @ SY2141 @ SY2142 ) @ ( c_Main_Olistrel__Cons2__2 @ SY2143 @ SV53 @ SY2140 @ SY2141 @ SY2142 ) @ SY2142 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3027]) ).

thf(4429,plain,
    ! [SV54: $i] :
      ( ( ! [SY2144: $i,SY2145: $i,SY2146: $i,SY2147: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV54 @ ( c_List_Olist_OCons @ SY2144 @ SY2145 @ SY2146 ) @ ( tc_List_Olist @ SY2146 ) @ ( tc_List_Olist @ SY2146 ) ) @ ( c_List_Olistrel @ SY2147 @ SY2146 ) @ ( tc_prod @ ( tc_List_Olist @ SY2146 ) @ ( tc_List_Olist @ SY2146 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY2147 @ SV54 @ SY2144 @ SY2145 @ SY2146 ) @ SY2145 @ ( tc_List_Olist @ SY2146 ) @ ( tc_List_Olist @ SY2146 ) ) @ ( c_List_Olistrel @ SY2147 @ SY2146 ) @ ( tc_prod @ ( tc_List_Olist @ SY2146 ) @ ( tc_List_Olist @ SY2146 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3028]) ).

thf(4430,plain,
    ! [SV55: $i] :
      ( ( ! [SY2148: $i,SY2149: $i,SY2150: $i,SY2151: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV55 @ ( c_List_Olist_OCons @ SY2148 @ SY2149 @ SY2150 ) @ ( tc_List_Olist @ SY2150 ) @ ( tc_List_Olist @ SY2150 ) ) @ ( c_List_Olistrel @ SY2151 @ SY2150 ) @ ( tc_prod @ ( tc_List_Olist @ SY2150 ) @ ( tc_List_Olist @ SY2150 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY2151 @ SV55 @ SY2148 @ SY2149 @ SY2150 ) @ SY2148 @ SY2150 @ SY2150 ) @ SY2151 @ ( tc_prod @ SY2150 @ SY2150 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3029]) ).

thf(4431,plain,
    ! [SV56: $i] :
      ( ( ! [SY2152: $i,SY2153: $i] :
            ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV56 @ ( tc_List_Olist @ SY2152 ) @ ( tc_List_Olist @ SY2152 ) ) @ ( c_List_Olistrel @ SY2153 @ SY2152 ) @ ( tc_prod @ ( tc_List_Olist @ SY2152 ) @ ( tc_List_Olist @ SY2152 ) ) )
        | ( SV56 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3030]) ).

thf(4432,plain,
    ! [SV57: $i] :
      ( ( ! [SY2154: $i,SY2155: $i] :
            ~ ( c_in @ ( c_Pair @ SV57 @ c_List_Olist_ONil @ ( tc_List_Olist @ SY2154 ) @ ( tc_List_Olist @ SY2154 ) ) @ ( c_List_Olistrel @ SY2155 @ SY2154 ) @ ( tc_prod @ ( tc_List_Olist @ SY2154 ) @ ( tc_List_Olist @ SY2154 ) ) )
        | ( SV57 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3031]) ).

thf(4433,plain,
    ! [SV58: $i] :
      ( ( ! [SY2156: $i,SY2157: $i,SY2158: $i] :
            ( ~ ( c_in @ ( c_List_Olist_OCons @ SV58 @ SY2156 @ SY2157 ) @ ( c_List_Olists @ SY2158 @ SY2157 ) @ ( tc_List_Olist @ SY2157 ) )
            | ( c_in @ SY2156 @ ( c_List_Olists @ SY2158 @ SY2157 ) @ ( tc_List_Olist @ SY2157 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3032]) ).

thf(4434,plain,
    ! [SV59: $i] :
      ( ( ! [SY2159: $i,SY2160: $i,SY2161: $i] :
            ( ~ ( c_in @ ( c_List_Olist_OCons @ SV59 @ SY2159 @ SY2160 ) @ ( c_List_Olists @ SY2161 @ SY2160 ) @ ( tc_List_Olist @ SY2160 ) )
            | ( c_in @ SV59 @ SY2161 @ SY2160 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3033]) ).

thf(4435,plain,
    ! [SV60: $i] :
      ( ( ! [SY2162: $i,SY2163: $i] :
            ( ~ ( c_in @ SV60 @ SY2162 @ SY2163 )
            | ! [SY2164: $i] :
                ( ~ ( c_in @ SY2164 @ ( c_List_Olists @ SY2162 @ SY2163 ) @ ( tc_List_Olist @ SY2163 ) )
                | ( c_in @ ( c_List_Olist_OCons @ SV60 @ SY2164 @ SY2163 ) @ ( c_List_Olists @ SY2162 @ SY2163 ) @ ( tc_List_Olist @ SY2163 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3034]) ).

thf(4436,plain,
    ! [SV61: $i] :
      ( ( ! [SY2165: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ SV61 @ SY2165 ) @ ( tc_List_Olist @ SY2165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3035]) ).

thf(4437,plain,
    ! [SV62: $i] :
      ( ( ! [SY2166: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ SV62 @ SY2166 )
            | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV62 @ SY2166 ) @ ( tc_List_Olist @ SY2166 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3036]) ).

thf(4438,plain,
    ! [SV63: $i] :
      ( ( ! [SY2167: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ SV63 @ SY2167 )
            | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV63 @ SY2167 ) @ ( tc_List_Olist @ SY2167 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3037]) ).

thf(4439,plain,
    ! [SV64: $i] :
      ( ( c_lessequals @ c_0 @ SV64 @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3038]) ).

thf(4440,plain,
    ! [SV65: $i] :
      ( ( c_less @ SV65 @ ( c_Suc @ SV65 ) @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3039]) ).

thf(4441,plain,
    ! [SV66: $i] :
      ( ( ~ ( c_less @ SV66 @ SV66 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3040]) ).

thf(4442,plain,
    ! [SV67: $i] :
      ( ( c_less @ c_0 @ ( c_Suc @ SV67 ) @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3041]) ).

thf(4443,plain,
    ! [SV68: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV68 )
        | ! [SY2168: $i] : ( c_lessequals @ SY2168 @ SY2168 @ SV68 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3042]) ).

thf(4444,plain,
    ! [SV69: $i] :
      ( ( ! [SY2169: $i,SY2170: $i,SY2171: $i] :
            ( ~ ( c_in @ SV69 @ ( c_Relation_ODomain @ SY2169 @ SY2170 @ SY2171 ) @ SY2170 )
            | ( c_in @ ( c_Pair @ SV69 @ ( c_Main_ODomainE__1 @ SV69 @ SY2169 @ SY2170 @ SY2171 ) @ SY2170 @ SY2171 ) @ SY2169 @ ( tc_prod @ SY2170 @ SY2171 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3043]) ).

thf(4445,plain,
    ! [SV70: $i] :
      ( ( ! [SY2172: $i,SY2173: $i,SY2174: $i,SY2175: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV70 @ SY2172 @ SY2173 @ SY2174 ) @ SY2175 @ ( tc_prod @ SY2173 @ SY2174 ) )
            | ( c_in @ SV70 @ ( c_Relation_ODomain @ SY2175 @ SY2173 @ SY2174 ) @ SY2173 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3044]) ).

thf(4446,plain,
    ! [SV71: $i] :
      ( ( ! [SY2176: $i] :
            ( ~ ( c_in @ SV71 @ c_Relation_OId @ ( tc_prod @ SY2176 @ SY2176 ) )
            | ( SV71
              = ( c_Pair @ ( c_Main_OIdE__1 @ SV71 @ SY2176 ) @ ( c_Main_OIdE__1 @ SV71 @ SY2176 ) @ SY2176 @ SY2176 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3045]) ).

thf(4447,plain,
    ! [SV72: $i] :
      ( ( ! [SY2177: $i,SY2178: $i,SY2179: $i,SY2180: $i] :
            ( ~ ( c_in @ SV72 @ ( c_Relation_OImage @ SY2177 @ SY2178 @ SY2179 @ SY2180 ) @ SY2180 )
            | ( c_in @ ( c_Main_OImageE__1 @ SY2178 @ SV72 @ SY2177 @ SY2179 @ SY2180 ) @ SY2178 @ SY2179 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3046]) ).

thf(4448,plain,
    ! [SV73: $i] :
      ( ( ! [SY2181: $i,SY2182: $i,SY2183: $i,SY2184: $i] :
            ( ~ ( c_in @ SV73 @ ( c_Relation_OImage @ SY2181 @ SY2182 @ SY2183 @ SY2184 ) @ SY2184 )
            | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SY2182 @ SV73 @ SY2181 @ SY2183 @ SY2184 ) @ SV73 @ SY2183 @ SY2184 ) @ SY2181 @ ( tc_prod @ SY2183 @ SY2184 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3047]) ).

thf(4449,plain,
    ! [SV74: $i] :
      ( ( ! [SY2185: $i,SY2186: $i,SY2187: $i] :
            ( ~ ( c_in @ SV74 @ SY2185 @ SY2186 )
            | ! [SY2188: $i,SY2189: $i] :
                ( ~ ( c_in @ ( c_Pair @ SV74 @ SY2187 @ SY2186 @ SY2188 ) @ SY2189 @ ( tc_prod @ SY2186 @ SY2188 ) )
                | ( c_in @ SY2187 @ ( c_Relation_OImage @ SY2189 @ SY2185 @ SY2186 @ SY2188 ) @ SY2188 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3048]) ).

thf(4450,plain,
    ! [SV75: $i] :
      ( ( ! [SY2190: $i,SY2191: $i,SY2192: $i] :
            ( ~ ( c_in @ SV75 @ ( c_Relation_ORange @ SY2190 @ SY2191 @ SY2192 ) @ SY2192 )
            | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV75 @ SY2190 @ SY2192 @ SY2191 ) @ SV75 @ SY2191 @ SY2192 ) @ SY2190 @ ( tc_prod @ SY2191 @ SY2192 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3049]) ).

thf(4451,plain,
    ! [SV76: $i] :
      ( ( ! [SY2193: $i,SY2194: $i,SY2195: $i,SY2196: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV76 @ SY2193 @ SY2194 @ SY2195 ) @ SY2196 @ ( tc_prod @ SY2194 @ SY2195 ) )
            | ( c_in @ SY2193 @ ( c_Relation_ORange @ SY2196 @ SY2194 @ SY2195 ) @ SY2195 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3050]) ).

thf(4452,plain,
    ! [SV77: $i] :
      ( ( ! [SY2197: $i,SY2198: $i,SY2199: $i] :
            ( ~ ( c_in @ SV77 @ ( c_Relation_Oconverse @ SY2197 @ SY2198 @ SY2199 ) @ ( tc_prod @ SY2199 @ SY2198 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SY2197 @ SV77 @ SY2198 @ SY2199 ) @ ( c_Main_OconverseE__2 @ SY2197 @ SV77 @ SY2198 @ SY2199 ) @ SY2198 @ SY2199 ) @ SY2197 @ ( tc_prod @ SY2198 @ SY2199 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3051]) ).

thf(4453,plain,
    ! [SV78: $i] :
      ( ( ! [SY2200: $i,SY2201: $i,SY2202: $i] :
            ( ~ ( c_in @ SV78 @ ( c_Relation_Oconverse @ SY2200 @ SY2201 @ SY2202 ) @ ( tc_prod @ SY2202 @ SY2201 ) )
            | ( SV78
              = ( c_Pair @ ( c_Main_OconverseE__2 @ SY2200 @ SV78 @ SY2201 @ SY2202 ) @ ( c_Main_OconverseE__1 @ SY2200 @ SV78 @ SY2201 @ SY2202 ) @ SY2202 @ SY2201 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3052]) ).

thf(4454,plain,
    ! [SV79: $i] :
      ( ( ! [SY2203: $i,SY2204: $i] :
            ( ~ ( c_in @ SV79 @ ( c_Relation_Odiag @ SY2203 @ SY2204 ) @ ( tc_prod @ SY2204 @ SY2204 ) )
            | ( SV79
              = ( c_Pair @ ( c_Main_OdiagE__1 @ SY2203 @ SV79 @ SY2204 ) @ ( c_Main_OdiagE__1 @ SY2203 @ SV79 @ SY2204 ) @ SY2204 @ SY2204 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3053]) ).

thf(4455,plain,
    ! [SV80: $i] :
      ( ( ! [SY2205: $i,SY2206: $i] :
            ( ~ ( c_in @ SV80 @ ( c_Relation_Odiag @ SY2205 @ SY2206 ) @ ( tc_prod @ SY2206 @ SY2206 ) )
            | ( c_in @ ( c_Main_OdiagE__1 @ SY2205 @ SV80 @ SY2206 ) @ SY2205 @ SY2206 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3054]) ).

thf(4456,plain,
    ! [SV81: $i] :
      ( ( ! [SY2207: $i,SY2208: $i] :
            ( ~ ( c_in @ SV81 @ SY2207 @ SY2208 )
            | ( c_in @ ( c_Pair @ SV81 @ SV81 @ SY2208 @ SY2208 ) @ ( c_Relation_Odiag @ SY2207 @ SY2208 ) @ ( tc_prod @ SY2208 @ SY2208 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3055]) ).

thf(4457,plain,
    ! [SV82: $i] :
      ( ( ! [SY2209: $i,SY2210: $i,SY2211: $i,SY2212: $i,SY2213: $i] :
            ( ~ ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SY2209 @ SY2210 @ SY2211 @ SY2212 @ SY2213 ) @ ( tc_prod @ SY2213 @ SY2212 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SY2209 @ SY2210 @ SV82 @ SY2211 @ SY2212 @ SY2213 ) @ ( c_Main_Orel__compE__3 @ SY2209 @ SY2210 @ SV82 @ SY2211 @ SY2212 @ SY2213 ) @ SY2211 @ SY2212 ) @ SY2209 @ ( tc_prod @ SY2211 @ SY2212 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3056]) ).

thf(4458,plain,
    ! [SV83: $i] :
      ( ( ! [SY2214: $i,SY2215: $i,SY2216: $i,SY2217: $i,SY2218: $i] :
            ( ~ ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SY2214 @ SY2215 @ SY2216 @ SY2217 @ SY2218 ) @ ( tc_prod @ SY2218 @ SY2217 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SY2214 @ SY2215 @ SV83 @ SY2216 @ SY2217 @ SY2218 ) @ ( c_Main_Orel__compE__2 @ SY2214 @ SY2215 @ SV83 @ SY2216 @ SY2217 @ SY2218 ) @ SY2218 @ SY2216 ) @ SY2215 @ ( tc_prod @ SY2218 @ SY2216 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3057]) ).

thf(4459,plain,
    ! [SV84: $i] :
      ( ( ! [SY2219: $i,SY2220: $i,SY2221: $i,SY2222: $i,SY2223: $i] :
            ( ~ ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SY2219 @ SY2220 @ SY2221 @ SY2222 @ SY2223 ) @ ( tc_prod @ SY2223 @ SY2222 ) )
            | ( SV84
              = ( c_Pair @ ( c_Main_Orel__compE__1 @ SY2219 @ SY2220 @ SV84 @ SY2221 @ SY2222 @ SY2223 ) @ ( c_Main_Orel__compE__3 @ SY2219 @ SY2220 @ SV84 @ SY2221 @ SY2222 @ SY2223 ) @ SY2223 @ SY2222 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3058]) ).

thf(4460,plain,
    ! [SV85: $i] :
      ( ( ! [SY2224: $i,SY2225: $i,SY2226: $i,SY2227: $i,SY2228: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV85 @ SY2224 @ SY2225 @ SY2226 ) @ SY2227 @ ( tc_prod @ SY2225 @ SY2226 ) )
            | ! [SY2229: $i,SY2230: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY2228 @ SV85 @ SY2229 @ SY2225 ) @ SY2230 @ ( tc_prod @ SY2229 @ SY2225 ) )
                | ( c_in @ ( c_Pair @ SY2228 @ SY2224 @ SY2229 @ SY2226 ) @ ( c_Relation_Orel__comp @ SY2227 @ SY2230 @ SY2225 @ SY2226 @ SY2229 ) @ ( tc_prod @ SY2229 @ SY2226 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3059]) ).

thf(4461,plain,
    ! [SV86: $i] :
      ( ( ! [SY2231: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV86 @ SY2231 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3060]) ).

thf(4462,plain,
    ! [SV87: $i] :
      ( ( ! [SY2232: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV87 @ SY2232 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3061]) ).

thf(4463,plain,
    ! [SV88: $i] :
      ( ( ! [SY2233: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV88 @ SY2233 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3062]) ).

thf(4464,plain,
    ! [SV89: $i] :
      ( ( ! [SY2234: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV89 @ SY2234 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3063]) ).

thf(4465,plain,
    ! [SV90: $i] :
      ( ( c_in @ ( c_SetInterval_OatMost @ SV90 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3064]) ).

thf(4466,plain,
    ! [SV91: $i] :
      ( ( ! [SY2235: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV91 @ SY2235 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3065]) ).

thf(4467,plain,
    ! [SV92: $i] :
      ( ( ! [SY2236: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV92 @ SY2236 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3066]) ).

thf(4468,plain,
    ! [SV93: $i] :
      ( ( ! [SY2237: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV93 @ SY2237 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3067]) ).

thf(4469,plain,
    ! [SV94: $i] :
      ( ( ! [SY2238: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV94 @ SY2238 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3068]) ).

thf(4470,plain,
    ! [SV95: $i] :
      ( ( c_in @ ( c_SetInterval_OlessThan @ SV95 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3069]) ).

thf(4471,plain,
    ! [SV96: $i] :
      ( ( ! [SY2239: $i,SY2240: $i] :
            ( ( c_in @ SV96 @ ( c_Inter @ SY2239 @ SY2240 ) @ SY2240 )
            | ( c_in @ ( c_Main_OInterI__1 @ SV96 @ SY2239 @ SY2240 ) @ SY2239 @ ( tc_set @ SY2240 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3070]) ).

thf(4472,plain,
    ! [SV97: $i] :
      ( ( ! [SY2241: $i,SY2242: $i] :
            ( ~ ( c_in @ SV97 @ ( c_Main_OInterI__1 @ SV97 @ SY2241 @ SY2242 ) @ SY2242 )
            | ( c_in @ SV97 @ ( c_Inter @ SY2241 @ SY2242 ) @ SY2242 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3071]) ).

thf(4473,plain,
    ! [SV98: $i] :
      ( ( ! [SY2243: $i] : ( c_in @ SV98 @ c_UNIV @ SY2243 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3072]) ).

thf(4474,plain,
    ! [SV99: $i] :
      ( ( ! [SY2244: $i,SY2245: $i] :
            ( ~ ( c_in @ SV99 @ ( c_Union @ SY2244 @ SY2245 ) @ SY2245 )
            | ( c_in @ ( c_Main_OUnionE__1 @ SV99 @ SY2244 @ SY2245 ) @ SY2244 @ ( tc_set @ SY2245 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3073]) ).

thf(4475,plain,
    ! [SV100: $i] :
      ( ( ! [SY2246: $i,SY2247: $i] :
            ( ~ ( c_in @ SV100 @ ( c_Union @ SY2246 @ SY2247 ) @ SY2247 )
            | ( c_in @ SV100 @ ( c_Main_OUnionE__1 @ SV100 @ SY2246 @ SY2247 ) @ SY2247 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3074]) ).

thf(4476,plain,
    ! [SV101: $i] :
      ( ( ! [SY2248: $i] : ( c_lessequals @ c_emptyset @ SV101 @ ( tc_set @ SY2248 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3075]) ).

thf(4477,plain,
    ! [SV102: $i] :
      ( ( ! [SY2249: $i,SY2250: $i] :
            ( ~ ( c_less @ SV102 @ SY2249 @ ( tc_set @ SY2250 ) )
            | ~ ( c_lessequals @ SY2249 @ SV102 @ ( tc_set @ SY2250 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3076]) ).

thf(4478,plain,
    ! [SV103: $i] :
      ( ( ! [SY2251: $i,SY2252: $i] :
            ( ~ ( c_less @ SV103 @ SY2251 @ ( tc_set @ SY2252 ) )
            | ( c_lessequals @ SV103 @ SY2251 @ ( tc_set @ SY2252 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3077]) ).

thf(4479,plain,
    ! [SV104: $i] :
      ( ( ! [SY2253: $i,SY2254: $i] :
            ( ~ ( c_lessequals @ SV104 @ SY2253 @ ( tc_set @ SY2254 ) )
            | ( SV104 = SY2253 )
            | ( c_less @ SV104 @ SY2253 @ ( tc_set @ SY2254 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3078]) ).

thf(4480,plain,
    ! [SV105: $i] :
      ( ( ! [SY2255: $i] :
            ( ! [SY2256: $i] :
                ~ ( c_in @ SV105 @ ( c_insert @ SY2255 @ c_emptyset @ SY2256 ) @ SY2256 )
            | ( SV105 = SY2255 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3079]) ).

thf(4481,plain,
    ! [SV106: $i] :
      ( ( ! [SY2257: $i] : ( c_in @ SV106 @ ( c_insert @ SV106 @ c_emptyset @ SY2257 ) @ SY2257 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3080]) ).

thf(4482,plain,
    ! [SV107: $i] :
      ( ( ! [SY2258: $i,SY2259: $i] :
            ( ( ( c_insert @ SV107 @ c_emptyset @ SY2258 )
             != ( c_insert @ SY2259 @ c_emptyset @ SY2258 ) )
            | ( SV107 = SY2259 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3081]) ).

thf(4483,plain,
    ! [SV108: $i] :
      ( ( ! [SY2260: $i,SY2261: $i] :
            ( ~ ( c_in @ SV108 @ SY2260 @ SY2261 )
            | ! [SY2262: $i] :
                ( ~ ( c_lessequals @ SY2260 @ SY2262 @ ( tc_set @ SY2261 ) )
                | ( c_in @ SV108 @ SY2262 @ SY2261 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3082]) ).

thf(4484,plain,
    ! [SV109: $i] :
      ( ( ! [SY2263: $i,SY2264: $i] :
            ( ( c_in @ ( c_Main_OsubsetI__1 @ SV109 @ SY2263 @ SY2264 ) @ SV109 @ SY2264 )
            | ( c_lessequals @ SV109 @ SY2263 @ ( tc_set @ SY2264 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3083]) ).

thf(4485,plain,
    ! [SV110: $i] :
      ( ( ! [SY2265: $i,SY2266: $i] :
            ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV110 @ SY2265 @ SY2266 ) @ SY2265 @ SY2266 )
            | ( c_lessequals @ SV110 @ SY2265 @ ( tc_set @ SY2266 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3084]) ).

thf(4486,plain,
    ! [SV111: $i] :
      ( ( ! [SY2267: $i,SY2268: $i] :
            ( ~ ( c_lessequals @ SV111 @ SY2267 @ ( tc_set @ SY2268 ) )
            | ~ ( c_lessequals @ SY2267 @ SV111 @ ( tc_set @ SY2268 ) )
            | ( SY2267 = SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3085]) ).

thf(4487,plain,
    ! [SV112: $i] :
      ( ( ! [SY2269: $i] : ( c_lessequals @ SV112 @ SV112 @ ( tc_set @ SY2269 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3086]) ).

thf(4488,plain,
    ! [SV113: $i] :
      ( ( ! [SY2270: $i,SY2271: $i] :
            ( ~ ( c_in @ SV113 @ SY2270 @ SY2271 )
            | ! [SY2272: $i,SY2273: $i] : ( c_in @ ( c_Sum__Type_OInl @ SV113 @ SY2271 @ SY2272 ) @ ( c_Sum__Type_OPlus @ SY2270 @ SY2273 @ SY2271 @ SY2272 ) @ ( tc_sum @ SY2271 @ SY2272 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3087]) ).

thf(4489,plain,
    ! [SV114: $i] :
      ( ( ! [SY2274: $i,SY2275: $i] :
            ( ~ ( c_in @ SV114 @ SY2274 @ SY2275 )
            | ! [SY2276: $i,SY2277: $i] : ( c_in @ ( c_Sum__Type_OInr @ SV114 @ SY2275 @ SY2276 ) @ ( c_Sum__Type_OPlus @ SY2277 @ SY2274 @ SY2276 @ SY2275 ) @ ( tc_sum @ SY2276 @ SY2275 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3088]) ).

thf(4490,plain,
    ! [SV115: $i] :
      ( ( ! [SY2278: $i,SY2279: $i,SY2280: $i,SY2281: $i] :
            ( ~ ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SY2278 @ SY2279 @ SY2280 @ SY2281 ) @ ( tc_sum @ SY2280 @ SY2281 ) )
            | ( SV115
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SY2278 @ SV115 @ SY2280 @ SY2281 ) @ SY2280 @ SY2281 ) )
            | ( SV115
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2279 @ SV115 @ SY2281 @ SY2280 ) @ SY2281 @ SY2280 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3089]) ).

thf(4491,plain,
    ! [SV116: $i] :
      ( ( ! [SY2282: $i,SY2283: $i,SY2284: $i,SY2285: $i] :
            ( ~ ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SY2282 @ SY2283 @ SY2284 @ SY2285 ) @ ( tc_sum @ SY2284 @ SY2285 ) )
            | ( SV116
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SY2282 @ SV116 @ SY2284 @ SY2285 ) @ SY2284 @ SY2285 ) )
            | ( c_in @ ( c_Main_OPlusE__2 @ SY2283 @ SV116 @ SY2285 @ SY2284 ) @ SY2283 @ SY2285 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3090]) ).

thf(4492,plain,
    ! [SV117: $i] :
      ( ( ! [SY2286: $i,SY2287: $i,SY2288: $i,SY2289: $i] :
            ( ~ ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SY2286 @ SY2287 @ SY2288 @ SY2289 ) @ ( tc_sum @ SY2288 @ SY2289 ) )
            | ( SV117
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2287 @ SV117 @ SY2289 @ SY2288 ) @ SY2289 @ SY2288 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SY2286 @ SV117 @ SY2288 @ SY2289 ) @ SY2286 @ SY2288 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3091]) ).

thf(4493,plain,
    ! [SV118: $i] :
      ( ( ! [SY2290: $i,SY2291: $i,SY2292: $i,SY2293: $i] :
            ( ~ ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SY2290 @ SY2291 @ SY2292 @ SY2293 ) @ ( tc_sum @ SY2292 @ SY2293 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SY2290 @ SV118 @ SY2292 @ SY2293 ) @ SY2290 @ SY2292 )
            | ( c_in @ ( c_Main_OPlusE__2 @ SY2291 @ SV118 @ SY2293 @ SY2292 ) @ SY2291 @ SY2293 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3092]) ).

thf(4494,plain,
    ! [SV119: $i] :
      ( ( ! [SY2294: $i,SY2295: $i] :
            ( ~ ( c_in @ SV119 @ SY2294 @ ( tc_prod @ SY2295 @ SY2295 ) )
            | ( c_in @ SV119 @ ( c_Transitive__Closure_Ortrancl @ SY2294 @ SY2295 ) @ ( tc_prod @ SY2295 @ SY2295 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3093]) ).

thf(4495,plain,
    ! [SV120: $i] :
      ( ( ! [SY2296: $i,SY2297: $i] : ( c_in @ ( c_Pair @ SV120 @ SV120 @ SY2296 @ SY2296 ) @ ( c_Transitive__Closure_Ortrancl @ SY2297 @ SY2296 ) @ ( tc_prod @ SY2296 @ SY2296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3094]) ).

thf(4496,plain,
    ! [SV121: $i] :
      ( ( ! [SY2298: $i,SY2299: $i,SY2300: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV121 @ SY2298 @ SY2299 @ SY2299 ) @ SY2300 @ ( tc_prod @ SY2299 @ SY2299 ) )
            | ( c_in @ ( c_Pair @ SV121 @ SY2298 @ SY2299 @ SY2299 ) @ ( c_Transitive__Closure_Otrancl @ SY2300 @ SY2299 ) @ ( tc_prod @ SY2299 @ SY2299 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3095]) ).

thf(4497,plain,
    ! [SV122: $i] :
      ( ( ! [SY2301: $i,SY2302: $i,SY2303: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV122 @ SY2301 @ SY2302 @ SY2302 ) @ ( c_Transitive__Closure_Otrancl @ SY2303 @ SY2302 ) @ ( tc_prod @ SY2302 @ SY2302 ) )
            | ( c_in @ ( c_Pair @ SV122 @ SY2301 @ SY2302 @ SY2302 ) @ ( c_Transitive__Closure_Ortrancl @ SY2303 @ SY2302 ) @ ( tc_prod @ SY2302 @ SY2302 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3096]) ).

thf(4498,plain,
    ! [SV123: $i] :
      ( ( c_Wellfounded__Recursion_Owf @ c_emptyset @ SV123 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3097]) ).

thf(4499,plain,
    ! [SV124: $i] :
      ( ( ! [SY2304: $i] :
            ( ~ ( c_Relation_Otrans @ SV124 @ SY2304 )
            | ! [SY2305: $i,SY2306: $i] :
                ( ~ ( c_Relation_Otrans @ SY2305 @ SY2306 )
                | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SY2305 @ SV124 @ SY2306 @ SY2304 ) @ ( tc_prod @ SY2306 @ SY2304 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3099]) ).

thf(4500,plain,
    ! [SV125: $i] :
      ( ( ! [SY2307: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ SV125 @ SY2307 )
            | ! [SY2308: $i,SY2309: $i] :
                ( ~ ( c_Wellfounded__Recursion_Owf @ SY2308 @ SY2309 )
                | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SY2308 @ SV125 @ SY2309 @ SY2307 ) @ ( tc_prod @ SY2309 @ SY2307 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3101]) ).

thf(4501,plain,
    ! [SV126: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ SV126 ) )
        | ~ ( class_Finite__Set_Ofinite @ SV126 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3102]) ).

thf(4502,plain,
    ! [SV127: $i] :
      ( ( ! [SY2310: $i] :
            ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV127 @ SY2310 ) )
            | ~ ( class_Finite__Set_Ofinite @ SY2310 )
            | ~ ( class_Finite__Set_Ofinite @ SV127 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3170]) ).

thf(4503,plain,
    ! [SV128: $i] :
      ( ( ! [SY2311: $i] : ( class_Nat_Opower @ ( tc_fun @ SV128 @ SY2311 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3171]) ).

thf(4504,plain,
    ! [SV129: $i] :
      ( ( ! [SY2312: $i] :
            ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV129 @ SY2312 ) )
            | ~ ( class_Finite__Set_Ofinite @ SY2312 )
            | ~ ( class_Finite__Set_Ofinite @ SV129 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3220]) ).

thf(4505,plain,
    ! [SV130: $i] :
      ( ( class_HOL_Ominus @ ( tc_set @ SV130 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3221]) ).

thf(4506,plain,
    ! [SV131: $i] :
      ( ( class_Orderings_Oord @ ( tc_set @ SV131 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3222]) ).

thf(4507,plain,
    ! [SV132: $i] :
      ( ( class_Orderings_Oorder @ ( tc_set @ SV132 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3223]) ).

thf(4508,plain,
    ! [SV133: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_set @ SV133 ) )
        | ~ ( class_Finite__Set_Ofinite @ SV133 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3224]) ).

thf(4509,plain,
    ! [SV134: $i] :
      ( ( class_Nat_Opower @ ( tc_set @ SV134 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3225]) ).

thf(4510,plain,
    ! [SV135: $i] :
      ( ( ! [SY2313: $i] :
            ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV135 @ SY2313 ) )
            | ~ ( class_Finite__Set_Ofinite @ SY2313 )
            | ~ ( class_Finite__Set_Ofinite @ SV135 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3226]) ).

thf(4511,plain,
    ! [SV136: $i] :
      ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV136 )
        | ( class_Orderings_Oord @ SV136 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3227]) ).

thf(4512,plain,
    ! [SV137: $i] :
      ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV137 )
        | ( class_Orderings_Oorder @ SV137 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3228]) ).

thf(4513,plain,
    ! [SV138: $i] :
      ( ( ~ ( class_LOrder_Olorder @ SV138 )
        | ( class_LOrder_Omeet__semilorder @ SV138 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3229]) ).

thf(4514,plain,
    ! [SV139: $i] :
      ( ( ~ ( class_LOrder_Olorder @ SV139 )
        | ( class_Orderings_Oord @ SV139 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3230]) ).

thf(4515,plain,
    ! [SV140: $i] :
      ( ( ~ ( class_LOrder_Olorder @ SV140 )
        | ( class_Orderings_Oorder @ SV140 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3231]) ).

thf(4516,plain,
    ! [SV141: $i] :
      ( ( ~ ( class_LOrder_Olorder @ SV141 )
        | ( class_LOrder_Ojoin__semilorder @ SV141 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3232]) ).

thf(4517,plain,
    ! [SV142: $i] :
      ( ( ~ ( class_LOrder_Omeet__semilorder @ SV142 )
        | ( class_Orderings_Oord @ SV142 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3233]) ).

thf(4518,plain,
    ! [SV143: $i] :
      ( ( ~ ( class_LOrder_Omeet__semilorder @ SV143 )
        | ( class_Orderings_Oorder @ SV143 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3234]) ).

thf(4519,plain,
    ! [SV144: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV144 )
        | ( class_HOL_Oplus @ SV144 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3235]) ).

thf(4520,plain,
    ! [SV145: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV145 )
        | ( class_OrderedGroup_Osemigroup__add @ SV145 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3236]) ).

thf(4521,plain,
    ! [SV146: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV146 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV146 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3237]) ).

thf(4522,plain,
    ! [SV147: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV147 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV147 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3238]) ).

thf(4523,plain,
    ! [SV148: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV148 )
        | ( class_HOL_Ominus @ SV148 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3239]) ).

thf(4524,plain,
    ! [SV149: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV149 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV149 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3240]) ).

thf(4525,plain,
    ! [SV150: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV150 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV150 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3241]) ).

thf(4526,plain,
    ! [SV151: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV151 )
        | ( class_OrderedGroup_Oab__group__add @ SV151 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3242]) ).

thf(4527,plain,
    ! [SV152: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV152 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV152 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3243]) ).

thf(4528,plain,
    ! [SV153: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV153 )
        | ( class_Ring__and__Field_Oring @ SV153 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3244]) ).

thf(4529,plain,
    ! [SV154: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV154 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV154 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3245]) ).

thf(4530,plain,
    ! [SV155: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV155 )
        | ( class_Ring__and__Field_Ocomm__ring @ SV155 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3246]) ).

thf(4531,plain,
    ! [SV156: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV156 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV156 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3247]) ).

thf(4532,plain,
    ! [SV157: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV157 )
        | ( class_HOL_Oone @ SV157 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3248]) ).

thf(4533,plain,
    ! [SV158: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV158 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV158 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3249]) ).

thf(4534,plain,
    ! [SV159: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV159 )
        | ( class_OrderedGroup_Omonoid__mult @ SV159 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3250]) ).

thf(4535,plain,
    ! [SV160: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV160 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV160 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3251]) ).

thf(4536,plain,
    ! [SV161: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV161 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV161 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3252]) ).

thf(4537,plain,
    ! [SV162: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV162 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3253]) ).

thf(4538,plain,
    ! [SV163: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV163 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV163 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3254]) ).

thf(4539,plain,
    ! [SV164: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV164 )
        | ( class_Ring__and__Field_Oring__1 @ SV164 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3255]) ).

thf(4540,plain,
    ! [SV165: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV165 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV165 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3256]) ).

thf(4541,plain,
    ! [SV166: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV166 )
        | ( class_Ring__and__Field_Ocomm__ring__1 @ SV166 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3257]) ).

thf(4542,plain,
    ! [SV167: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV167 )
        | ( class_HOL_Otimes @ SV167 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3258]) ).

thf(4543,plain,
    ! [SV168: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV168 )
        | ( class_Numeral_Onumber @ SV168 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3259]) ).

thf(4544,plain,
    ! [SV169: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV169 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV169 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3260]) ).

thf(4545,plain,
    ! [SV170: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV170 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV170 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3261]) ).

thf(4546,plain,
    ! [SV171: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV171 )
        | ( class_Ring__and__Field_Osemiring @ SV171 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3262]) ).

thf(4547,plain,
    ! [SV172: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV172 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV172 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3263]) ).

thf(4548,plain,
    ! [SV173: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV173 )
        | ( class_HOL_Ozero @ SV173 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3264]) ).

thf(4549,plain,
    ! [SV174: $i] :
      ( ( ~ ( class_Numeral_Onumber__ring @ SV174 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV174 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3265]) ).

thf(4550,plain,
    ! [SV175: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV175 )
        | ( class_HOL_Ominus @ SV175 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3266]) ).

thf(4551,plain,
    ! [SV176: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV176 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV176 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3267]) ).

thf(4552,plain,
    ! [SV177: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV177 )
        | ( class_HOL_Ozero @ SV177 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3268]) ).

thf(4553,plain,
    ! [SV178: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV178 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV178 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3269]) ).

thf(4554,plain,
    ! [SV179: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV179 )
        | ( class_OrderedGroup_Osemigroup__add @ SV179 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3270]) ).

thf(4555,plain,
    ! [SV180: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV180 )
        | ( class_HOL_Oplus @ SV180 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3271]) ).

thf(4556,plain,
    ! [SV181: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV181 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV181 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3272]) ).

thf(4557,plain,
    ! [SV182: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV182 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV182 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3273]) ).

thf(4558,plain,
    ! [SV183: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV183 )
        | ( class_OrderedGroup_Osemigroup__add @ SV183 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3274]) ).

thf(4559,plain,
    ! [SV184: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV184 )
        | ( class_HOL_Oplus @ SV184 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3275]) ).

thf(4560,plain,
    ! [SV185: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV185 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV185 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3276]) ).

thf(4561,plain,
    ! [SV186: $i] :
      ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV186 )
        | ( class_HOL_Otimes @ SV186 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3277]) ).

thf(4562,plain,
    ! [SV187: $i] :
      ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV187 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV187 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3278]) ).

thf(4563,plain,
    ! [SV188: $i] :
      ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV188 )
        | ( class_OrderedGroup_Osemigroup__add @ SV188 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3279]) ).

thf(4564,plain,
    ! [SV189: $i] :
      ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV189 )
        | ( class_HOL_Oplus @ SV189 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3280]) ).

thf(4565,plain,
    ! [SV190: $i] :
      ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV190 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV190 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3281]) ).

thf(4566,plain,
    ! [SV191: $i] :
      ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV191 )
        | ( class_OrderedGroup_Osemigroup__add @ SV191 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3282]) ).

thf(4567,plain,
    ! [SV192: $i] :
      ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV192 )
        | ( class_HOL_Oplus @ SV192 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3283]) ).

thf(4568,plain,
    ! [SV193: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV193 )
        | ( class_HOL_Ozero @ SV193 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3284]) ).

thf(4569,plain,
    ! [SV194: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV194 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV194 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3285]) ).

thf(4570,plain,
    ! [SV195: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV195 )
        | ( class_OrderedGroup_Osemigroup__add @ SV195 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3286]) ).

thf(4571,plain,
    ! [SV196: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV196 )
        | ( class_HOL_Oplus @ SV196 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3287]) ).

thf(4572,plain,
    ! [SV197: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV197 )
        | ( class_HOL_Oone @ SV197 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3288]) ).

thf(4573,plain,
    ! [SV198: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV198 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV198 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3289]) ).

thf(4574,plain,
    ! [SV199: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV199 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV199 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3290]) ).

thf(4575,plain,
    ! [SV200: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV200 )
        | ( class_HOL_Otimes @ SV200 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3291]) ).

thf(4576,plain,
    ! [SV201: $i] :
      ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV201 )
        | ( class_OrderedGroup_Omonoid__mult @ SV201 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3292]) ).

thf(4577,plain,
    ! [SV202: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV202 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV202 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3293]) ).

thf(4578,plain,
    ! [SV203: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV203 )
        | ( class_OrderedGroup_Oab__group__add @ SV203 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3294]) ).

thf(4579,plain,
    ! [SV204: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV204 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV204 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3295]) ).

thf(4580,plain,
    ! [SV205: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV205 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV205 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3296]) ).

thf(4581,plain,
    ! [SV206: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV206 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV206 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3297]) ).

thf(4582,plain,
    ! [SV207: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV207 )
        | ( class_OrderedGroup_Osemigroup__add @ SV207 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3298]) ).

thf(4583,plain,
    ! [SV208: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV208 )
        | ( class_HOL_Oplus @ SV208 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3299]) ).

thf(4584,plain,
    ! [SV209: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV209 )
        | ( class_LOrder_Olorder @ SV209 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3300]) ).

thf(4585,plain,
    ! [SV210: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV210 )
        | ( class_LOrder_Ojoin__semilorder @ SV210 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3301]) ).

thf(4586,plain,
    ! [SV211: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV211 )
        | ( class_LOrder_Omeet__semilorder @ SV211 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3302]) ).

thf(4587,plain,
    ! [SV212: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV212 )
        | ( class_HOL_Ominus @ SV212 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3303]) ).

thf(4588,plain,
    ! [SV213: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV213 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV213 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3304]) ).

thf(4589,plain,
    ! [SV214: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV214 )
        | ( class_HOL_Ozero @ SV214 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3305]) ).

thf(4590,plain,
    ! [SV215: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV215 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV215 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3306]) ).

thf(4591,plain,
    ! [SV216: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV216 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV216 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3307]) ).

thf(4592,plain,
    ! [SV217: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV217 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV217 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3308]) ).

thf(4593,plain,
    ! [SV218: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV218 )
        | ( class_Orderings_Oorder @ SV218 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3309]) ).

thf(4594,plain,
    ! [SV219: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV219 )
        | ( class_Orderings_Oord @ SV219 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3310]) ).

thf(4595,plain,
    ! [SV220: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV220 )
        | ( class_OrderedGroup_Olordered__ab__group @ SV220 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3311]) ).

thf(4596,plain,
    ! [SV221: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV221 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV221 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3312]) ).

thf(4597,plain,
    ! [SV222: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV222 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV222 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3313]) ).

thf(4598,plain,
    ! [SV223: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV223 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV223 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3314]) ).

thf(4599,plain,
    ! [SV224: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV224 )
        | ( class_OrderedGroup_Osemigroup__add @ SV224 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3315]) ).

thf(4600,plain,
    ! [SV225: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV225 )
        | ( class_HOL_Oplus @ SV225 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3316]) ).

thf(4601,plain,
    ! [SV226: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV226 )
        | ( class_LOrder_Olorder @ SV226 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3317]) ).

thf(4602,plain,
    ! [SV227: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV227 )
        | ( class_LOrder_Ojoin__semilorder @ SV227 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3318]) ).

thf(4603,plain,
    ! [SV228: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV228 )
        | ( class_LOrder_Omeet__semilorder @ SV228 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3319]) ).

thf(4604,plain,
    ! [SV229: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV229 )
        | ( class_Orderings_Oorder @ SV229 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3320]) ).

thf(4605,plain,
    ! [SV230: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV230 )
        | ( class_Orderings_Oord @ SV230 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3321]) ).

thf(4606,plain,
    ! [SV231: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV231 )
        | ( class_OrderedGroup_Oab__group__add @ SV231 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3322]) ).

thf(4607,plain,
    ! [SV232: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV232 )
        | ( class_HOL_Ominus @ SV232 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3323]) ).

thf(4608,plain,
    ! [SV233: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV233 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV233 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3324]) ).

thf(4609,plain,
    ! [SV234: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV234 )
        | ( class_HOL_Ozero @ SV234 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3325]) ).

thf(4610,plain,
    ! [SV235: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV235 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV235 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3326]) ).

thf(4611,plain,
    ! [SV236: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV236 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV236 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3327]) ).

thf(4612,plain,
    ! [SV237: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV237 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV237 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3328]) ).

thf(4613,plain,
    ! [SV238: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV238 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV238 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3329]) ).

thf(4614,plain,
    ! [SV239: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV239 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV239 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3330]) ).

thf(4615,plain,
    ! [SV240: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV240 )
        | ( class_OrderedGroup_Oab__group__add @ SV240 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3331]) ).

thf(4616,plain,
    ! [SV241: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV241 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV241 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3332]) ).

thf(4617,plain,
    ! [SV242: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV242 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV242 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3333]) ).

thf(4618,plain,
    ! [SV243: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV243 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV243 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3334]) ).

thf(4619,plain,
    ! [SV244: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV244 )
        | ( class_OrderedGroup_Osemigroup__add @ SV244 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3335]) ).

thf(4620,plain,
    ! [SV245: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV245 )
        | ( class_HOL_Oplus @ SV245 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3336]) ).

thf(4621,plain,
    ! [SV246: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV246 )
        | ( class_LOrder_Ojoin__semilorder @ SV246 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3337]) ).

thf(4622,plain,
    ! [SV247: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV247 )
        | ( class_OrderedGroup_Olordered__ab__group @ SV247 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3338]) ).

thf(4623,plain,
    ! [SV248: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV248 )
        | ( class_LOrder_Olorder @ SV248 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3339]) ).

thf(4624,plain,
    ! [SV249: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV249 )
        | ( class_LOrder_Omeet__semilorder @ SV249 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3340]) ).

thf(4625,plain,
    ! [SV250: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV250 )
        | ( class_HOL_Ominus @ SV250 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3341]) ).

thf(4626,plain,
    ! [SV251: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV251 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV251 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3342]) ).

thf(4627,plain,
    ! [SV252: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV252 )
        | ( class_HOL_Ozero @ SV252 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3343]) ).

thf(4628,plain,
    ! [SV253: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV253 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV253 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3344]) ).

thf(4629,plain,
    ! [SV254: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV254 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV254 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3345]) ).

thf(4630,plain,
    ! [SV255: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV255 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV255 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3346]) ).

thf(4631,plain,
    ! [SV256: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV256 )
        | ( class_Orderings_Oorder @ SV256 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3347]) ).

thf(4632,plain,
    ! [SV257: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV257 )
        | ( class_Orderings_Oord @ SV257 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3348]) ).

thf(4633,plain,
    ! [SV258: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV258 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV258 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3349]) ).

thf(4634,plain,
    ! [SV259: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV259 )
        | ( class_OrderedGroup_Oab__group__add @ SV259 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3350]) ).

thf(4635,plain,
    ! [SV260: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV260 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV260 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3351]) ).

thf(4636,plain,
    ! [SV261: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV261 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV261 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3352]) ).

thf(4637,plain,
    ! [SV262: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV262 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV262 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3353]) ).

thf(4638,plain,
    ! [SV263: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV263 )
        | ( class_OrderedGroup_Osemigroup__add @ SV263 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3354]) ).

thf(4639,plain,
    ! [SV264: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV264 )
        | ( class_HOL_Oplus @ SV264 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3355]) ).

thf(4640,plain,
    ! [SV265: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV265 )
        | ( class_LOrder_Omeet__semilorder @ SV265 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3356]) ).

thf(4641,plain,
    ! [SV266: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV266 )
        | ( class_OrderedGroup_Olordered__ab__group @ SV266 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3357]) ).

thf(4642,plain,
    ! [SV267: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV267 )
        | ( class_LOrder_Olorder @ SV267 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3358]) ).

thf(4643,plain,
    ! [SV268: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV268 )
        | ( class_LOrder_Ojoin__semilorder @ SV268 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3359]) ).

thf(4644,plain,
    ! [SV269: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV269 )
        | ( class_HOL_Ominus @ SV269 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3360]) ).

thf(4645,plain,
    ! [SV270: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV270 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV270 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3361]) ).

thf(4646,plain,
    ! [SV271: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV271 )
        | ( class_HOL_Ozero @ SV271 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3362]) ).

thf(4647,plain,
    ! [SV272: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV272 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV272 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3363]) ).

thf(4648,plain,
    ! [SV273: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV273 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV273 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3364]) ).

thf(4649,plain,
    ! [SV274: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV274 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV274 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3365]) ).

thf(4650,plain,
    ! [SV275: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV275 )
        | ( class_Orderings_Oorder @ SV275 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3366]) ).

thf(4651,plain,
    ! [SV276: $i] :
      ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV276 )
        | ( class_Orderings_Oord @ SV276 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3367]) ).

thf(4652,plain,
    ! [SV277: $i] :
      ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV277 )
        | ( class_HOL_Oone @ SV277 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3368]) ).

thf(4653,plain,
    ! [SV278: $i] :
      ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV278 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV278 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3369]) ).

thf(4654,plain,
    ! [SV279: $i] :
      ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV279 )
        | ( class_HOL_Otimes @ SV279 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3370]) ).

thf(4655,plain,
    ! [SV280: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV280 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV280 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3371]) ).

thf(4656,plain,
    ! [SV281: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV281 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV281 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3372]) ).

thf(4657,plain,
    ! [SV282: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV282 )
        | ( class_LOrder_Olorder @ SV282 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3373]) ).

thf(4658,plain,
    ! [SV283: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV283 )
        | ( class_LOrder_Ojoin__semilorder @ SV283 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3374]) ).

thf(4659,plain,
    ! [SV284: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV284 )
        | ( class_LOrder_Omeet__semilorder @ SV284 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3375]) ).

thf(4660,plain,
    ! [SV285: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV285 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV285 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3376]) ).

thf(4661,plain,
    ! [SV286: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV286 )
        | ( class_Orderings_Oorder @ SV286 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3377]) ).

thf(4662,plain,
    ! [SV287: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV287 )
        | ( class_Orderings_Oord @ SV287 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3378]) ).

thf(4663,plain,
    ! [SV288: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV288 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV288 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3379]) ).

thf(4664,plain,
    ! [SV289: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV289 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV289 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3380]) ).

thf(4665,plain,
    ! [SV290: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV290 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV290 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3381]) ).

thf(4666,plain,
    ! [SV291: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV291 )
        | ( class_OrderedGroup_Osemigroup__add @ SV291 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3382]) ).

thf(4667,plain,
    ! [SV292: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV292 )
        | ( class_HOL_Oplus @ SV292 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3383]) ).

thf(4668,plain,
    ! [SV293: $i] :
      ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV293 )
        | ( class_Orderings_Olinorder @ SV293 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3384]) ).

thf(4669,plain,
    ! [SV294: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV294 )
        | ( class_OrderedGroup_Oab__group__add @ SV294 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3385]) ).

thf(4670,plain,
    ! [SV295: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV295 )
        | ( class_HOL_Ominus @ SV295 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3386]) ).

thf(4671,plain,
    ! [SV296: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV296 )
        | ( class_Orderings_Oorder @ SV296 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3387]) ).

thf(4672,plain,
    ! [SV297: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV297 )
        | ( class_Orderings_Oord @ SV297 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3388]) ).

thf(4673,plain,
    ! [SV298: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV298 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV298 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3389]) ).

thf(4674,plain,
    ! [SV299: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV299 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV299 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3390]) ).

thf(4675,plain,
    ! [SV300: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV300 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV300 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3391]) ).

thf(4676,plain,
    ! [SV301: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV301 )
        | ( class_HOL_Ozero @ SV301 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3392]) ).

thf(4677,plain,
    ! [SV302: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV302 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV302 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3393]) ).

thf(4678,plain,
    ! [SV303: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV303 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV303 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3394]) ).

thf(4679,plain,
    ! [SV304: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV304 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV304 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3395]) ).

thf(4680,plain,
    ! [SV305: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV305 )
        | ( class_OrderedGroup_Osemigroup__add @ SV305 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3396]) ).

thf(4681,plain,
    ! [SV306: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV306 )
        | ( class_HOL_Oplus @ SV306 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3397]) ).

thf(4682,plain,
    ! [SV307: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV307 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3398]) ).

thf(4683,plain,
    ! [SV308: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV308 )
        | ( class_Orderings_Oorder @ SV308 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3399]) ).

thf(4684,plain,
    ! [SV309: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV309 )
        | ( class_Orderings_Oord @ SV309 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3400]) ).

thf(4685,plain,
    ! [SV310: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV310 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV310 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3401]) ).

thf(4686,plain,
    ! [SV311: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV311 )
        | ( class_OrderedGroup_Osemigroup__add @ SV311 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3402]) ).

thf(4687,plain,
    ! [SV312: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV312 )
        | ( class_HOL_Oplus @ SV312 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3403]) ).

thf(4688,plain,
    ! [SV313: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV313 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV313 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3404]) ).

thf(4689,plain,
    ! [SV314: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV314 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV314 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3405]) ).

thf(4690,plain,
    ! [SV315: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV315 )
        | ( class_Orderings_Oorder @ SV315 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3406]) ).

thf(4691,plain,
    ! [SV316: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV316 )
        | ( class_Orderings_Oord @ SV316 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3407]) ).

thf(4692,plain,
    ! [SV317: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV317 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV317 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3408]) ).

thf(4693,plain,
    ! [SV318: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV318 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV318 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3409]) ).

thf(4694,plain,
    ! [SV319: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV319 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV319 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3410]) ).

thf(4695,plain,
    ! [SV320: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV320 )
        | ( class_OrderedGroup_Osemigroup__add @ SV320 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3411]) ).

thf(4696,plain,
    ! [SV321: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV321 )
        | ( class_HOL_Oplus @ SV321 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3412]) ).

thf(4697,plain,
    ! [SV322: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV322 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV322 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3413]) ).

thf(4698,plain,
    ! [SV323: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV323 )
        | ( class_Orderings_Oorder @ SV323 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3414]) ).

thf(4699,plain,
    ! [SV324: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV324 )
        | ( class_Orderings_Oord @ SV324 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3415]) ).

thf(4700,plain,
    ! [SV325: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV325 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV325 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3416]) ).

thf(4701,plain,
    ! [SV326: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV326 )
        | ( class_OrderedGroup_Osemigroup__add @ SV326 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3417]) ).

thf(4702,plain,
    ! [SV327: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV327 )
        | ( class_HOL_Oplus @ SV327 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3418]) ).

thf(4703,plain,
    ! [SV328: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV328 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV328 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3419]) ).

thf(4704,plain,
    ! [SV329: $i] :
      ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV329 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV329 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3420]) ).

thf(4705,plain,
    ! [SV330: $i] :
      ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV330 )
        | ( class_HOL_Oplus @ SV330 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3421]) ).

thf(4706,plain,
    ! [SV331: $i] :
      ( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV331 )
        | ( class_HOL_Otimes @ SV331 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3422]) ).

thf(4707,plain,
    ! [SV332: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV332 )
        | ( class_LOrder_Olorder @ SV332 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3423]) ).

thf(4708,plain,
    ! [SV333: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV333 )
        | ( class_LOrder_Ojoin__semilorder @ SV333 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3424]) ).

thf(4709,plain,
    ! [SV334: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV334 )
        | ( class_LOrder_Omeet__semilorder @ SV334 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3425]) ).

thf(4710,plain,
    ! [SV335: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV335 )
        | ( class_Orderings_Oord @ SV335 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3426]) ).

thf(4711,plain,
    ! [SV336: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV336 )
        | ( class_Orderings_Oorder @ SV336 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3427]) ).

thf(4712,plain,
    ! [SV337: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV337 )
        | ( class_Orderings_Oord @ SV337 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3428]) ).

thf(4713,plain,
    ! [SV338: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV338 )
        | ( class_Nat_Opower @ SV338 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3429]) ).

thf(4714,plain,
    ! [SV339: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV339 )
        | ( class_HOL_Ozero @ SV339 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3430]) ).

thf(4715,plain,
    ! [SV340: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV340 )
        | ( class_Ring__and__Field_Osemiring @ SV340 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3431]) ).

thf(4716,plain,
    ! [SV341: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV341 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV341 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3432]) ).

thf(4717,plain,
    ! [SV342: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV342 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV342 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3433]) ).

thf(4718,plain,
    ! [SV343: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV343 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV343 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3434]) ).

thf(4719,plain,
    ! [SV344: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV344 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV344 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3435]) ).

thf(4720,plain,
    ! [SV345: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV345 )
        | ( class_OrderedGroup_Omonoid__mult @ SV345 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3436]) ).

thf(4721,plain,
    ! [SV346: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV346 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV346 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3437]) ).

thf(4722,plain,
    ! [SV347: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV347 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV347 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3438]) ).

thf(4723,plain,
    ! [SV348: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV348 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV348 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3439]) ).

thf(4724,plain,
    ! [SV349: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV349 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV349 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3440]) ).

thf(4725,plain,
    ! [SV350: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV350 )
        | ( class_HOL_Oone @ SV350 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3441]) ).

thf(4726,plain,
    ! [SV351: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV351 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV351 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3442]) ).

thf(4727,plain,
    ! [SV352: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV352 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV352 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3443]) ).

thf(4728,plain,
    ! [SV353: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV353 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV353 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3444]) ).

thf(4729,plain,
    ! [SV354: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV354 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV354 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3445]) ).

thf(4730,plain,
    ! [SV355: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV355 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV355 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3446]) ).

thf(4731,plain,
    ! [SV356: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV356 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV356 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3447]) ).

thf(4732,plain,
    ! [SV357: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV357 )
        | ( class_HOL_Oplus @ SV357 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3448]) ).

thf(4733,plain,
    ! [SV358: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV358 )
        | ( class_OrderedGroup_Osemigroup__add @ SV358 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3449]) ).

thf(4734,plain,
    ! [SV359: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV359 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV359 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3450]) ).

thf(4735,plain,
    ! [SV360: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV360 )
        | ( class_HOL_Otimes @ SV360 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3451]) ).

thf(4736,plain,
    ! [SV361: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV361 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV361 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3452]) ).

thf(4737,plain,
    ! [SV362: $i] :
      ( ( ~ ( class_Power_Orecpower @ SV362 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV362 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3453]) ).

thf(4738,plain,
    ! [SV363: $i] :
      ( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV363 )
        | ( class_HOL_Ozero @ SV363 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3454]) ).

thf(4739,plain,
    ! [SV364: $i] :
      ( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV364 )
        | ( class_HOL_Oone @ SV364 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3455]) ).

thf(4740,plain,
    ! [SV365: $i] :
      ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV365 )
        | ( class_HOL_Ominus @ SV365 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3456]) ).

thf(4741,plain,
    ! [SV366: $i] :
      ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV366 )
        | ( class_Orderings_Oord @ SV366 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3457]) ).

thf(4742,plain,
    ! [SV367: $i] :
      ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV367 )
        | ( class_HOL_Ozero @ SV367 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3458]) ).

thf(4743,plain,
    ! [SV368: $i] :
      ( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV368 )
        | ( class_HOL_Ozero @ SV368 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3459]) ).

thf(4744,plain,
    ! [SV369: $i] :
      ( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV369 )
        | ( class_HOL_Otimes @ SV369 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3460]) ).

thf(4745,plain,
    ! [SV370: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV370 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV370 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3461]) ).

thf(4746,plain,
    ! [SV371: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV371 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV371 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3462]) ).

thf(4747,plain,
    ! [SV372: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV372 )
        | ( class_HOL_Oplus @ SV372 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3463]) ).

thf(4748,plain,
    ! [SV373: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV373 )
        | ( class_HOL_Ozero @ SV373 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3464]) ).

thf(4749,plain,
    ! [SV374: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV374 )
        | ( class_OrderedGroup_Oab__group__add @ SV374 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3465]) ).

thf(4750,plain,
    ! [SV375: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV375 )
        | ( class_HOL_Ominus @ SV375 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3466]) ).

thf(4751,plain,
    ! [SV376: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV376 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV376 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3467]) ).

thf(4752,plain,
    ! [SV377: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV377 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV377 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3468]) ).

thf(4753,plain,
    ! [SV378: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV378 )
        | ( class_Ring__and__Field_Oring @ SV378 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3469]) ).

thf(4754,plain,
    ! [SV379: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV379 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV379 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3470]) ).

thf(4755,plain,
    ! [SV380: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV380 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV380 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3471]) ).

thf(4756,plain,
    ! [SV381: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV381 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV381 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3472]) ).

thf(4757,plain,
    ! [SV382: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV382 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV382 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3473]) ).

thf(4758,plain,
    ! [SV383: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV383 )
        | ( class_Ring__and__Field_Osemiring @ SV383 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3474]) ).

thf(4759,plain,
    ! [SV384: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV384 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV384 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3475]) ).

thf(4760,plain,
    ! [SV385: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV385 )
        | ( class_HOL_Otimes @ SV385 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3476]) ).

thf(4761,plain,
    ! [SV386: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV386 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV386 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3477]) ).

thf(4762,plain,
    ! [SV387: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV387 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV387 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3478]) ).

thf(4763,plain,
    ! [SV388: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV388 )
        | ( class_OrderedGroup_Osemigroup__add @ SV388 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3479]) ).

thf(4764,plain,
    ! [SV389: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV389 )
        | ( class_Ring__and__Field_Ocomm__ring @ SV389 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3480]) ).

thf(4765,plain,
    ! [SV390: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV390 )
        | ( class_Ring__and__Field_Oring @ SV390 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3481]) ).

thf(4766,plain,
    ! [SV391: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV391 )
        | ( class_Ring__and__Field_Osemiring @ SV391 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3482]) ).

thf(4767,plain,
    ! [SV392: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV392 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV392 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3483]) ).

thf(4768,plain,
    ! [SV393: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV393 )
        | ( class_HOL_Otimes @ SV393 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3484]) ).

thf(4769,plain,
    ! [SV394: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV394 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV394 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3485]) ).

thf(4770,plain,
    ! [SV395: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV395 )
        | ( class_HOL_Ozero @ SV395 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3486]) ).

thf(4771,plain,
    ! [SV396: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV396 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV396 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3487]) ).

thf(4772,plain,
    ! [SV397: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV397 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV397 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3488]) ).

thf(4773,plain,
    ! [SV398: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV398 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV398 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3489]) ).

thf(4774,plain,
    ! [SV399: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV399 )
        | ( class_OrderedGroup_Osemigroup__add @ SV399 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3490]) ).

thf(4775,plain,
    ! [SV400: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV400 )
        | ( class_HOL_Oplus @ SV400 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3491]) ).

thf(4776,plain,
    ! [SV401: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV401 )
        | ( class_OrderedGroup_Oab__group__add @ SV401 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3492]) ).

thf(4777,plain,
    ! [SV402: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV402 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3493]) ).

thf(4778,plain,
    ! [SV403: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV403 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV403 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3494]) ).

thf(4779,plain,
    ! [SV404: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV404 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV404 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3495]) ).

thf(4780,plain,
    ! [SV405: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV405 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV405 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3496]) ).

thf(4781,plain,
    ! [SV406: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV406 )
        | ( class_OrderedGroup_Omonoid__mult @ SV406 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3497]) ).

thf(4782,plain,
    ! [SV407: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV407 )
        | ( class_HOL_Oone @ SV407 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3498]) ).

thf(4783,plain,
    ! [SV408: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV408 )
        | ( class_Ring__and__Field_Oring__1 @ SV408 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3499]) ).

thf(4784,plain,
    ! [SV409: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV409 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV409 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3500]) ).

thf(4785,plain,
    ! [SV410: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV410 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV410 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3501]) ).

thf(4786,plain,
    ! [SV411: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV411 )
        | ( class_HOL_Ominus @ SV411 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3502]) ).

thf(4787,plain,
    ! [SV412: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV412 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV412 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3503]) ).

thf(4788,plain,
    ! [SV413: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV413 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV413 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3504]) ).

thf(4789,plain,
    ! [SV414: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV414 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV414 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3505]) ).

thf(4790,plain,
    ! [SV415: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV415 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV415 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3506]) ).

thf(4791,plain,
    ! [SV416: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV416 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV416 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3507]) ).

thf(4792,plain,
    ! [SV417: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV417 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV417 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3508]) ).

thf(4793,plain,
    ! [SV418: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV418 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV418 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3509]) ).

thf(4794,plain,
    ! [SV419: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV419 )
        | ( class_OrderedGroup_Osemigroup__add @ SV419 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3510]) ).

thf(4795,plain,
    ! [SV420: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV420 )
        | ( class_HOL_Oplus @ SV420 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3511]) ).

thf(4796,plain,
    ! [SV421: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV421 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV421 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3512]) ).

thf(4797,plain,
    ! [SV422: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV422 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV422 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3513]) ).

thf(4798,plain,
    ! [SV423: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV423 )
        | ( class_HOL_Otimes @ SV423 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3514]) ).

thf(4799,plain,
    ! [SV424: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV424 )
        | ( class_Ring__and__Field_Osemiring @ SV424 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3515]) ).

thf(4800,plain,
    ! [SV425: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV425 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV425 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3516]) ).

thf(4801,plain,
    ! [SV426: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV426 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV426 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3517]) ).

thf(4802,plain,
    ! [SV427: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV427 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV427 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3518]) ).

thf(4803,plain,
    ! [SV428: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV428 )
        | ( class_Ring__and__Field_Osemiring @ SV428 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3519]) ).

thf(4804,plain,
    ! [SV429: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV429 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV429 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3520]) ).

thf(4805,plain,
    ! [SV430: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV430 )
        | ( class_OrderedGroup_Osemigroup__add @ SV430 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3521]) ).

thf(4806,plain,
    ! [SV431: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV431 )
        | ( class_HOL_Oplus @ SV431 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3522]) ).

thf(4807,plain,
    ! [SV432: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV432 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV432 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3523]) ).

thf(4808,plain,
    ! [SV433: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV433 )
        | ( class_HOL_Otimes @ SV433 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3524]) ).

thf(4809,plain,
    ! [SV434: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV434 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV434 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3525]) ).

thf(4810,plain,
    ! [SV435: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV435 )
        | ( class_HOL_Ozero @ SV435 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3526]) ).

thf(4811,plain,
    ! [SV436: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV436 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV436 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3527]) ).

thf(4812,plain,
    ! [SV437: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV437 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV437 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3528]) ).

thf(4813,plain,
    ! [SV438: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV438 )
        | ( class_HOL_Oplus @ SV438 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3529]) ).

thf(4814,plain,
    ! [SV439: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV439 )
        | ( class_HOL_Ozero @ SV439 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3530]) ).

thf(4815,plain,
    ! [SV440: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV440 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV440 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3531]) ).

thf(4816,plain,
    ! [SV441: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV441 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV441 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3532]) ).

thf(4817,plain,
    ! [SV442: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV442 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV442 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3533]) ).

thf(4818,plain,
    ! [SV443: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV443 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV443 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3534]) ).

thf(4819,plain,
    ! [SV444: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV444 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV444 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3535]) ).

thf(4820,plain,
    ! [SV445: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV445 )
        | ( class_Ring__and__Field_Osemiring @ SV445 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3536]) ).

thf(4821,plain,
    ! [SV446: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV446 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV446 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3537]) ).

thf(4822,plain,
    ! [SV447: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV447 )
        | ( class_HOL_Otimes @ SV447 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3538]) ).

thf(4823,plain,
    ! [SV448: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV448 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV448 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3539]) ).

thf(4824,plain,
    ! [SV449: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV449 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV449 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3540]) ).

thf(4825,plain,
    ! [SV450: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV450 )
        | ( class_OrderedGroup_Osemigroup__add @ SV450 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3541]) ).

thf(4826,plain,
    ! [SV451: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV451 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV451 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3542]) ).

thf(4827,plain,
    ! [SV452: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV452 )
        | ( class_HOL_Ozero @ SV452 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3543]) ).

thf(4828,plain,
    ! [SV453: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV453 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV453 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3544]) ).

thf(4829,plain,
    ! [SV454: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV454 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV454 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3545]) ).

thf(4830,plain,
    ! [SV455: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV455 )
        | ( class_OrderedGroup_Osemigroup__add @ SV455 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3546]) ).

thf(4831,plain,
    ! [SV456: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV456 )
        | ( class_HOL_Oplus @ SV456 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3547]) ).

thf(4832,plain,
    ! [SV457: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV457 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV457 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3548]) ).

thf(4833,plain,
    ! [SV458: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV458 )
        | ( class_OrderedGroup_Omonoid__mult @ SV458 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3549]) ).

thf(4834,plain,
    ! [SV459: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV459 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV459 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3550]) ).

thf(4835,plain,
    ! [SV460: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV460 )
        | ( class_HOL_Oone @ SV460 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3551]) ).

thf(4836,plain,
    ! [SV461: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV461 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV461 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3552]) ).

thf(4837,plain,
    ! [SV462: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV462 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV462 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3553]) ).

thf(4838,plain,
    ! [SV463: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV463 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV463 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3554]) ).

thf(4839,plain,
    ! [SV464: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV464 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV464 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3555]) ).

thf(4840,plain,
    ! [SV465: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV465 )
        | ( class_Ring__and__Field_Osemiring @ SV465 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3556]) ).

thf(4841,plain,
    ! [SV466: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV466 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV466 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3557]) ).

thf(4842,plain,
    ! [SV467: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV467 )
        | ( class_HOL_Otimes @ SV467 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3558]) ).

thf(4843,plain,
    ! [SV468: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV468 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV468 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3559]) ).

thf(4844,plain,
    ! [SV469: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV469 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV469 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3560]) ).

thf(4845,plain,
    ! [SV470: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV470 )
        | ( class_HOL_Ozero @ SV470 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3561]) ).

thf(4846,plain,
    ! [SV471: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV471 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV471 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3562]) ).

thf(4847,plain,
    ! [SV472: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV472 )
        | ( class_OrderedGroup_Osemigroup__add @ SV472 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3563]) ).

thf(4848,plain,
    ! [SV473: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV473 )
        | ( class_HOL_Oplus @ SV473 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3564]) ).

thf(4849,plain,
    ! [SV474: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV474 )
        | ( class_OrderedGroup_Omonoid__mult @ SV474 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3565]) ).

thf(4850,plain,
    ! [SV475: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV475 )
        | ( class_HOL_Oone @ SV475 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3566]) ).

thf(4851,plain,
    ! [SV476: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV476 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV476 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3567]) ).

thf(4852,plain,
    ! [SV477: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV477 )
        | ( class_HOL_Otimes @ SV477 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3568]) ).

thf(4853,plain,
    ! [SV478: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV478 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV478 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3569]) ).

thf(4854,plain,
    ! [SV479: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV479 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV479 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3570]) ).

thf(4855,plain,
    ! [SV480: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV480 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV480 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3571]) ).

thf(4856,plain,
    ! [SV481: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV481 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV481 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3572]) ).

thf(4857,plain,
    ! [SV482: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV482 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV482 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3573]) ).

thf(4858,plain,
    ! [SV483: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV483 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV483 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3574]) ).

thf(4859,plain,
    ! [SV484: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV484 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV484 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3575]) ).

thf(4860,plain,
    ! [SV485: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV485 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV485 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3576]) ).

thf(4861,plain,
    ! [SV486: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV486 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV486 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3577]) ).

thf(4862,plain,
    ! [SV487: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV487 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV487 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3578]) ).

thf(4863,plain,
    ! [SV488: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV488 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV488 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3579]) ).

thf(4864,plain,
    ! [SV489: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV489 )
        | ( class_Ring__and__Field_Osemiring @ SV489 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3580]) ).

thf(4865,plain,
    ! [SV490: $i] :
      ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV490 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV490 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3581]) ).

thf(4866,plain,
    ! [SV491: $i] :
      ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV491 )
        | ( class_HOL_Ozero @ SV491 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3582]) ).

thf(4867,plain,
    ! [SV492: $i] :
      ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV492 )
        | ( class_HOL_Oinverse @ SV492 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3583]) ).

thf(4868,plain,
    ! [SV493: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV493 )
        | ( class_Ring__and__Field_Ocomm__ring__1 @ SV493 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3584]) ).

thf(4869,plain,
    ! [SV494: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV494 )
        | ( class_Ring__and__Field_Ocomm__ring @ SV494 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3585]) ).

thf(4870,plain,
    ! [SV495: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV495 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV495 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3586]) ).

thf(4871,plain,
    ! [SV496: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV496 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV496 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3587]) ).

thf(4872,plain,
    ! [SV497: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV497 )
        | ( class_OrderedGroup_Omonoid__mult @ SV497 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3588]) ).

thf(4873,plain,
    ! [SV498: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV498 )
        | ( class_HOL_Oone @ SV498 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3589]) ).

thf(4874,plain,
    ! [SV499: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV499 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV499 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3590]) ).

thf(4875,plain,
    ! [SV500: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV500 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV500 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3591]) ).

thf(4876,plain,
    ! [SV501: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV501 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV501 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3592]) ).

thf(4877,plain,
    ! [SV502: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV502 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV502 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3593]) ).

thf(4878,plain,
    ! [SV503: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV503 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV503 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3594]) ).

thf(4879,plain,
    ! [SV504: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV504 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV504 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3595]) ).

thf(4880,plain,
    ! [SV505: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV505 )
        | ( class_Ring__and__Field_Oring__1 @ SV505 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3596]) ).

thf(4881,plain,
    ! [SV506: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV506 )
        | ( class_Ring__and__Field_Osemiring @ SV506 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3597]) ).

thf(4882,plain,
    ! [SV507: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV507 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV507 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3598]) ).

thf(4883,plain,
    ! [SV508: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV508 )
        | ( class_HOL_Otimes @ SV508 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3599]) ).

thf(4884,plain,
    ! [SV509: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV509 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV509 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3600]) ).

thf(4885,plain,
    ! [SV510: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV510 )
        | ( class_HOL_Ozero @ SV510 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3601]) ).

thf(4886,plain,
    ! [SV511: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV511 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV511 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3602]) ).

thf(4887,plain,
    ! [SV512: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV512 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV512 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3603]) ).

thf(4888,plain,
    ! [SV513: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV513 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV513 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3604]) ).

thf(4889,plain,
    ! [SV514: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV514 )
        | ( class_OrderedGroup_Osemigroup__add @ SV514 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3605]) ).

thf(4890,plain,
    ! [SV515: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV515 )
        | ( class_HOL_Oplus @ SV515 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3606]) ).

thf(4891,plain,
    ! [SV516: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV516 )
        | ( class_Ring__and__Field_Oring @ SV516 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3607]) ).

thf(4892,plain,
    ! [SV517: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV517 )
        | ( class_HOL_Oinverse @ SV517 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3608]) ).

thf(4893,plain,
    ! [SV518: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV518 )
        | ( class_Ring__and__Field_Oidom @ SV518 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3609]) ).

thf(4894,plain,
    ! [SV519: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV519 )
        | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV519 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3610]) ).

thf(4895,plain,
    ! [SV520: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV520 )
        | ( class_OrderedGroup_Oab__group__add @ SV520 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3611]) ).

thf(4896,plain,
    ! [SV521: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV521 )
        | ( class_HOL_Ominus @ SV521 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3612]) ).

thf(4897,plain,
    ! [SV522: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV522 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV522 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3613]) ).

thf(4898,plain,
    ! [SV523: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV523 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV523 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3614]) ).

thf(4899,plain,
    ! [SV524: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV524 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV524 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3615]) ).

thf(4900,plain,
    ! [SV525: $i] :
      ( ( ~ ( class_Ring__and__Field_Ofield @ SV525 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV525 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3616]) ).

thf(4901,plain,
    ! [SV526: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV526 )
        | ( class_Ring__and__Field_Ocomm__ring__1 @ SV526 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3617]) ).

thf(4902,plain,
    ! [SV527: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV527 )
        | ( class_Ring__and__Field_Ocomm__ring @ SV527 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3618]) ).

thf(4903,plain,
    ! [SV528: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV528 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV528 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3619]) ).

thf(4904,plain,
    ! [SV529: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV529 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV529 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3620]) ).

thf(4905,plain,
    ! [SV530: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV530 )
        | ( class_OrderedGroup_Omonoid__mult @ SV530 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3621]) ).

thf(4906,plain,
    ! [SV531: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV531 )
        | ( class_HOL_Oone @ SV531 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3622]) ).

thf(4907,plain,
    ! [SV532: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV532 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV532 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3623]) ).

thf(4908,plain,
    ! [SV533: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV533 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV533 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3624]) ).

thf(4909,plain,
    ! [SV534: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV534 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV534 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3625]) ).

thf(4910,plain,
    ! [SV535: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV535 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV535 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3626]) ).

thf(4911,plain,
    ! [SV536: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV536 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV536 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3627]) ).

thf(4912,plain,
    ! [SV537: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV537 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV537 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3628]) ).

thf(4913,plain,
    ! [SV538: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV538 )
        | ( class_Ring__and__Field_Oring__1 @ SV538 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3629]) ).

thf(4914,plain,
    ! [SV539: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV539 )
        | ( class_Ring__and__Field_Osemiring @ SV539 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3630]) ).

thf(4915,plain,
    ! [SV540: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV540 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV540 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3631]) ).

thf(4916,plain,
    ! [SV541: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV541 )
        | ( class_HOL_Otimes @ SV541 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3632]) ).

thf(4917,plain,
    ! [SV542: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV542 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV542 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3633]) ).

thf(4918,plain,
    ! [SV543: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV543 )
        | ( class_HOL_Ozero @ SV543 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3634]) ).

thf(4919,plain,
    ! [SV544: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV544 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV544 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3635]) ).

thf(4920,plain,
    ! [SV545: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV545 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV545 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3636]) ).

thf(4921,plain,
    ! [SV546: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV546 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV546 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3637]) ).

thf(4922,plain,
    ! [SV547: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV547 )
        | ( class_OrderedGroup_Osemigroup__add @ SV547 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3638]) ).

thf(4923,plain,
    ! [SV548: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV548 )
        | ( class_HOL_Oplus @ SV548 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3639]) ).

thf(4924,plain,
    ! [SV549: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV549 )
        | ( class_Ring__and__Field_Oring @ SV549 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3640]) ).

thf(4925,plain,
    ! [SV550: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV550 )
        | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV550 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3641]) ).

thf(4926,plain,
    ! [SV551: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV551 )
        | ( class_OrderedGroup_Oab__group__add @ SV551 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3642]) ).

thf(4927,plain,
    ! [SV552: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV552 )
        | ( class_HOL_Ominus @ SV552 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3643]) ).

thf(4928,plain,
    ! [SV553: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV553 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV553 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3644]) ).

thf(4929,plain,
    ! [SV554: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV554 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV554 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3645]) ).

thf(4930,plain,
    ! [SV555: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV555 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV555 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3646]) ).

thf(4931,plain,
    ! [SV556: $i] :
      ( ( ~ ( class_Ring__and__Field_Oidom @ SV556 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV556 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3647]) ).

thf(4932,plain,
    ! [SV557: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV557 )
        | ( class_Ring__and__Field_Opordered__ring @ SV557 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3648]) ).

thf(4933,plain,
    ! [SV558: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV558 )
        | ( class_Ring__and__Field_Oring @ SV558 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3649]) ).

thf(4934,plain,
    ! [SV559: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV559 )
        | ( class_Orderings_Oorder @ SV559 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3650]) ).

thf(4935,plain,
    ! [SV560: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV560 )
        | ( class_Orderings_Oord @ SV560 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3651]) ).

thf(4936,plain,
    ! [SV561: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV561 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV561 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3652]) ).

thf(4937,plain,
    ! [SV562: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV562 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV562 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3653]) ).

thf(4938,plain,
    ! [SV563: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV563 )
        | ( class_Ring__and__Field_Osemiring @ SV563 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3654]) ).

thf(4939,plain,
    ! [SV564: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV564 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV564 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3655]) ).

thf(4940,plain,
    ! [SV565: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV565 )
        | ( class_HOL_Otimes @ SV565 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3656]) ).

thf(4941,plain,
    ! [SV566: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV566 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV566 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3657]) ).

thf(4942,plain,
    ! [SV567: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV567 )
        | ( class_HOL_Ozero @ SV567 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3658]) ).

thf(4943,plain,
    ! [SV568: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV568 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV568 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3659]) ).

thf(4944,plain,
    ! [SV569: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV569 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV569 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3660]) ).

thf(4945,plain,
    ! [SV570: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV570 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV570 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3661]) ).

thf(4946,plain,
    ! [SV571: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV571 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV571 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3662]) ).

thf(4947,plain,
    ! [SV572: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV572 )
        | ( class_OrderedGroup_Osemigroup__add @ SV572 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3663]) ).

thf(4948,plain,
    ! [SV573: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV573 )
        | ( class_HOL_Oplus @ SV573 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3664]) ).

thf(4949,plain,
    ! [SV574: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV574 )
        | ( class_OrderedGroup_Olordered__ab__group__abs @ SV574 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3665]) ).

thf(4950,plain,
    ! [SV575: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV575 )
        | ( class_OrderedGroup_Olordered__ab__group @ SV575 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3666]) ).

thf(4951,plain,
    ! [SV576: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV576 )
        | ( class_LOrder_Olorder @ SV576 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3667]) ).

thf(4952,plain,
    ! [SV577: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV577 )
        | ( class_LOrder_Ojoin__semilorder @ SV577 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3668]) ).

thf(4953,plain,
    ! [SV578: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV578 )
        | ( class_LOrder_Omeet__semilorder @ SV578 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3669]) ).

thf(4954,plain,
    ! [SV579: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV579 )
        | ( class_OrderedGroup_Olordered__ab__group__meet @ SV579 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3670]) ).

thf(4955,plain,
    ! [SV580: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV580 )
        | ( class_OrderedGroup_Oab__group__add @ SV580 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3671]) ).

thf(4956,plain,
    ! [SV581: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV581 )
        | ( class_OrderedGroup_Olordered__ab__group__join @ SV581 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3672]) ).

thf(4957,plain,
    ! [SV582: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV582 )
        | ( class_HOL_Ominus @ SV582 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3673]) ).

thf(4958,plain,
    ! [SV583: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV583 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV583 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3674]) ).

thf(4959,plain,
    ! [SV584: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV584 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV584 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3675]) ).

thf(4960,plain,
    ! [SV585: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV585 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV585 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3676]) ).

thf(4961,plain,
    ! [SV586: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV586 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV586 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3677]) ).

thf(4962,plain,
    ! [SV587: $i] :
      ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV587 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV587 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3678]) ).

thf(4963,plain,
    ! [SV588: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV588 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV588 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3679]) ).

thf(4964,plain,
    ! [SV589: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV589 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV589 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3680]) ).

thf(4965,plain,
    ! [SV590: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV590 )
        | ( class_HOL_Oplus @ SV590 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3681]) ).

thf(4966,plain,
    ! [SV591: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV591 )
        | ( class_HOL_Ozero @ SV591 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3682]) ).

thf(4967,plain,
    ! [SV592: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV592 )
        | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV592 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3683]) ).

thf(4968,plain,
    ! [SV593: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV593 )
        | ( class_Orderings_Olinorder @ SV593 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3684]) ).

thf(4969,plain,
    ! [SV594: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV594 )
        | ( class_LOrder_Olorder @ SV594 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3685]) ).

thf(4970,plain,
    ! [SV595: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV595 )
        | ( class_LOrder_Ojoin__semilorder @ SV595 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3686]) ).

thf(4971,plain,
    ! [SV596: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV596 )
        | ( class_LOrder_Omeet__semilorder @ SV596 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3687]) ).

thf(4972,plain,
    ! [SV597: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV597 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV597 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3688]) ).

thf(4973,plain,
    ! [SV598: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV598 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV598 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3689]) ).

thf(4974,plain,
    ! [SV599: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV599 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV599 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3690]) ).

thf(4975,plain,
    ! [SV600: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV600 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV600 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3691]) ).

thf(4976,plain,
    ! [SV601: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV601 )
        | ( class_Orderings_Oorder @ SV601 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3692]) ).

thf(4977,plain,
    ! [SV602: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV602 )
        | ( class_Orderings_Oord @ SV602 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3693]) ).

thf(4978,plain,
    ! [SV603: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV603 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV603 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3694]) ).

thf(4979,plain,
    ! [SV604: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV604 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV604 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3695]) ).

thf(4980,plain,
    ! [SV605: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV605 )
        | ( class_Ring__and__Field_Oordered__semiring__strict @ SV605 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3696]) ).

thf(4981,plain,
    ! [SV606: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV606 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV606 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3697]) ).

thf(4982,plain,
    ! [SV607: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV607 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV607 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3698]) ).

thf(4983,plain,
    ! [SV608: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV608 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV608 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3699]) ).

thf(4984,plain,
    ! [SV609: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV609 )
        | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV609 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3700]) ).

thf(4985,plain,
    ! [SV610: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV610 )
        | ( class_Ring__and__Field_Opordered__comm__semiring @ SV610 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3701]) ).

thf(4986,plain,
    ! [SV611: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV611 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV611 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3702]) ).

thf(4987,plain,
    ! [SV612: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV612 )
        | ( class_Ring__and__Field_Osemiring @ SV612 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3703]) ).

thf(4988,plain,
    ! [SV613: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV613 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV613 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3704]) ).

thf(4989,plain,
    ! [SV614: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV614 )
        | ( class_HOL_Otimes @ SV614 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3705]) ).

thf(4990,plain,
    ! [SV615: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV615 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV615 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3706]) ).

thf(4991,plain,
    ! [SV616: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV616 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV616 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3707]) ).

thf(4992,plain,
    ! [SV617: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV617 )
        | ( class_OrderedGroup_Osemigroup__add @ SV617 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3708]) ).

thf(4993,plain,
    ! [SV618: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV618 )
        | ( class_Ring__and__Field_Ofield @ SV618 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3709]) ).

thf(4994,plain,
    ! [SV619: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV619 )
        | ( class_HOL_Oinverse @ SV619 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3710]) ).

thf(4995,plain,
    ! [SV620: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV620 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV620 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3711]) ).

thf(4996,plain,
    ! [SV621: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV621 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV621 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3712]) ).

thf(4997,plain,
    ! [SV622: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV622 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV622 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3713]) ).

thf(4998,plain,
    ! [SV623: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV623 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV623 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3714]) ).

thf(4999,plain,
    ! [SV624: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV624 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV624 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3715]) ).

thf(5000,plain,
    ! [SV625: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV625 )
        | ( class_OrderedGroup_Omonoid__mult @ SV625 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3716]) ).

thf(5001,plain,
    ! [SV626: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV626 )
        | ( class_HOL_Oone @ SV626 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3717]) ).

thf(5002,plain,
    ! [SV627: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV627 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV627 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3718]) ).

thf(5003,plain,
    ! [SV628: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV628 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV628 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3719]) ).

thf(5004,plain,
    ! [SV629: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV629 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV629 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3720]) ).

thf(5005,plain,
    ! [SV630: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV630 )
        | ( class_Ring__and__Field_Oidom @ SV630 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3721]) ).

thf(5006,plain,
    ! [SV631: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV631 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV631 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3722]) ).

thf(5007,plain,
    ! [SV632: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV632 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV632 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3723]) ).

thf(5008,plain,
    ! [SV633: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV633 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV633 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3724]) ).

thf(5009,plain,
    ! [SV634: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV634 )
        | ( class_Ring__and__Field_Osemiring @ SV634 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3725]) ).

thf(5010,plain,
    ! [SV635: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV635 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV635 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3726]) ).

thf(5011,plain,
    ! [SV636: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV636 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV636 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3727]) ).

thf(5012,plain,
    ! [SV637: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV637 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV637 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3728]) ).

thf(5013,plain,
    ! [SV638: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV638 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV638 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3729]) ).

thf(5014,plain,
    ! [SV639: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV639 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV639 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3730]) ).

thf(5015,plain,
    ! [SV640: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV640 )
        | ( class_OrderedGroup_Osemigroup__add @ SV640 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3731]) ).

thf(5016,plain,
    ! [SV641: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV641 )
        | ( class_Ring__and__Field_Ocomm__ring__1 @ SV641 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3732]) ).

thf(5017,plain,
    ! [SV642: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV642 )
        | ( class_HOL_Oplus @ SV642 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3733]) ).

thf(5018,plain,
    ! [SV643: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV643 )
        | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV643 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3734]) ).

thf(5019,plain,
    ! [SV644: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV644 )
        | ( class_HOL_Ozero @ SV644 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3735]) ).

thf(5020,plain,
    ! [SV645: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV645 )
        | ( class_HOL_Otimes @ SV645 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3736]) ).

thf(5021,plain,
    ! [SV646: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV646 )
        | ( class_Ring__and__Field_Oordered__idom @ SV646 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3737]) ).

thf(5022,plain,
    ! [SV647: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV647 )
        | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV647 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3738]) ).

thf(5023,plain,
    ! [SV648: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV648 )
        | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV648 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3739]) ).

thf(5024,plain,
    ! [SV649: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV649 )
        | ( class_Ring__and__Field_Opordered__comm__semiring @ SV649 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3740]) ).

thf(5025,plain,
    ! [SV650: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV650 )
        | ( class_Ring__and__Field_Oordered__ring__strict @ SV650 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3741]) ).

thf(5026,plain,
    ! [SV651: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV651 )
        | ( class_Ring__and__Field_Oordered__semiring__strict @ SV651 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3742]) ).

thf(5027,plain,
    ! [SV652: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV652 )
        | ( class_Ring__and__Field_Ocomm__ring @ SV652 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3743]) ).

thf(5028,plain,
    ! [SV653: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV653 )
        | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV653 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3744]) ).

thf(5029,plain,
    ! [SV654: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV654 )
        | ( class_Orderings_Olinorder @ SV654 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3745]) ).

thf(5030,plain,
    ! [SV655: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV655 )
        | ( class_Ring__and__Field_Oaxclass__abs__if @ SV655 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3746]) ).

thf(5031,plain,
    ! [SV656: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV656 )
        | ( class_Ring__and__Field_Olordered__ring @ SV656 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3747]) ).

thf(5032,plain,
    ! [SV657: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV657 )
        | ( class_Ring__and__Field_Opordered__ring @ SV657 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3748]) ).

thf(5033,plain,
    ! [SV658: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV658 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV658 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3749]) ).

thf(5034,plain,
    ! [SV659: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV659 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV659 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3750]) ).

thf(5035,plain,
    ! [SV660: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV660 )
        | ( class_OrderedGroup_Olordered__ab__group__abs @ SV660 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3751]) ).

thf(5036,plain,
    ! [SV661: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV661 )
        | ( class_OrderedGroup_Olordered__ab__group__meet @ SV661 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3752]) ).

thf(5037,plain,
    ! [SV662: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV662 )
        | ( class_OrderedGroup_Olordered__ab__group__join @ SV662 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3753]) ).

thf(5038,plain,
    ! [SV663: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV663 )
        | ( class_Ring__and__Field_Oring__1 @ SV663 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3754]) ).

thf(5039,plain,
    ! [SV664: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV664 )
        | ( class_OrderedGroup_Olordered__ab__group @ SV664 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3755]) ).

thf(5040,plain,
    ! [SV665: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV665 )
        | ( class_LOrder_Olorder @ SV665 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3756]) ).

thf(5041,plain,
    ! [SV666: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV666 )
        | ( class_LOrder_Ojoin__semilorder @ SV666 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3757]) ).

thf(5042,plain,
    ! [SV667: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV667 )
        | ( class_LOrder_Omeet__semilorder @ SV667 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3758]) ).

thf(5043,plain,
    ! [SV668: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV668 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV668 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3759]) ).

thf(5044,plain,
    ! [SV669: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV669 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV669 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3760]) ).

thf(5045,plain,
    ! [SV670: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV670 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV670 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3761]) ).

thf(5046,plain,
    ! [SV671: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV671 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV671 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3762]) ).

thf(5047,plain,
    ! [SV672: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV672 )
        | ( class_Orderings_Oorder @ SV672 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3763]) ).

thf(5048,plain,
    ! [SV673: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV673 )
        | ( class_Orderings_Oord @ SV673 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3764]) ).

thf(5049,plain,
    ! [SV674: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV674 )
        | ( class_Ring__and__Field_Oring @ SV674 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3765]) ).

thf(5050,plain,
    ! [SV675: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV675 )
        | ( class_Ring__and__Field_Oordered__semidom @ SV675 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3766]) ).

thf(5051,plain,
    ! [SV676: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV676 )
        | ( class_OrderedGroup_Oab__group__add @ SV676 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3767]) ).

thf(5052,plain,
    ! [SV677: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV677 )
        | ( class_HOL_Ominus @ SV677 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3768]) ).

thf(5053,plain,
    ! [SV678: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV678 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV678 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3769]) ).

thf(5054,plain,
    ! [SV679: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV679 )
        | ( class_Ring__and__Field_Ocomm__ring__1 @ SV679 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3770]) ).

thf(5055,plain,
    ! [SV680: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV680 )
        | ( class_Ring__and__Field_Ocomm__ring @ SV680 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3771]) ).

thf(5056,plain,
    ! [SV681: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV681 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV681 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3772]) ).

thf(5057,plain,
    ! [SV682: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV682 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV682 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3773]) ).

thf(5058,plain,
    ! [SV683: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV683 )
        | ( class_OrderedGroup_Omonoid__mult @ SV683 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3774]) ).

thf(5059,plain,
    ! [SV684: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 )
        | ( class_HOL_Oone @ SV684 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3775]) ).

thf(5060,plain,
    ! [SV685: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV685 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV685 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3776]) ).

thf(5061,plain,
    ! [SV686: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV686 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV686 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3777]) ).

thf(5062,plain,
    ! [SV687: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV687 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV687 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3778]) ).

thf(5063,plain,
    ! [SV688: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV688 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV688 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3779]) ).

thf(5064,plain,
    ! [SV689: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV689 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV689 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3780]) ).

thf(5065,plain,
    ! [SV690: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV690 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV690 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3781]) ).

thf(5066,plain,
    ! [SV691: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV691 )
        | ( class_Ring__and__Field_Oring__1 @ SV691 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3782]) ).

thf(5067,plain,
    ! [SV692: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV692 )
        | ( class_Ring__and__Field_Osemiring @ SV692 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3783]) ).

thf(5068,plain,
    ! [SV693: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV693 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV693 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3784]) ).

thf(5069,plain,
    ! [SV694: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV694 )
        | ( class_HOL_Otimes @ SV694 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3785]) ).

thf(5070,plain,
    ! [SV695: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV695 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV695 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3786]) ).

thf(5071,plain,
    ! [SV696: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV696 )
        | ( class_HOL_Ozero @ SV696 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3787]) ).

thf(5072,plain,
    ! [SV697: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV697 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV697 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3788]) ).

thf(5073,plain,
    ! [SV698: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV698 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV698 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3789]) ).

thf(5074,plain,
    ! [SV699: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV699 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV699 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3790]) ).

thf(5075,plain,
    ! [SV700: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV700 )
        | ( class_OrderedGroup_Osemigroup__add @ SV700 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3791]) ).

thf(5076,plain,
    ! [SV701: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV701 )
        | ( class_HOL_Oplus @ SV701 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3792]) ).

thf(5077,plain,
    ! [SV702: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV702 )
        | ( class_Ring__and__Field_Oring @ SV702 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3793]) ).

thf(5078,plain,
    ! [SV703: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV703 )
        | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV703 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3794]) ).

thf(5079,plain,
    ! [SV704: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV704 )
        | ( class_Ring__and__Field_Oordered__semiring__strict @ SV704 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3795]) ).

thf(5080,plain,
    ! [SV705: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV705 )
        | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV705 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3796]) ).

thf(5081,plain,
    ! [SV706: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV706 )
        | ( class_Orderings_Olinorder @ SV706 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3797]) ).

thf(5082,plain,
    ! [SV707: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV707 )
        | ( class_LOrder_Olorder @ SV707 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3798]) ).

thf(5083,plain,
    ! [SV708: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV708 )
        | ( class_LOrder_Ojoin__semilorder @ SV708 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3799]) ).

thf(5084,plain,
    ! [SV709: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV709 )
        | ( class_LOrder_Omeet__semilorder @ SV709 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3800]) ).

thf(5085,plain,
    ! [SV710: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV710 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV710 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3801]) ).

thf(5086,plain,
    ! [SV711: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV711 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV711 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3802]) ).

thf(5087,plain,
    ! [SV712: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV712 )
        | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV712 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3803]) ).

thf(5088,plain,
    ! [SV713: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV713 )
        | ( class_OrderedGroup_Oab__group__add @ SV713 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3804]) ).

thf(5089,plain,
    ! [SV714: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV714 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV714 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3805]) ).

thf(5090,plain,
    ! [SV715: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV715 )
        | ( class_Ring__and__Field_Opordered__comm__semiring @ SV715 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3806]) ).

thf(5091,plain,
    ! [SV716: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV716 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV716 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3807]) ).

thf(5092,plain,
    ! [SV717: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV717 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV717 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3808]) ).

thf(5093,plain,
    ! [SV718: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV718 )
        | ( class_Orderings_Oorder @ SV718 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3809]) ).

thf(5094,plain,
    ! [SV719: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV719 )
        | ( class_Orderings_Oord @ SV719 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3810]) ).

thf(5095,plain,
    ! [SV720: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV720 )
        | ( class_Ring__and__Field_Oaxclass__abs__if @ SV720 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3811]) ).

thf(5096,plain,
    ! [SV721: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV721 )
        | ( class_Ring__and__Field_Oordered__ring__strict @ SV721 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3812]) ).

thf(5097,plain,
    ! [SV722: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV722 )
        | ( class_Ring__and__Field_Olordered__ring @ SV722 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3813]) ).

thf(5098,plain,
    ! [SV723: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV723 )
        | ( class_Ring__and__Field_Opordered__ring @ SV723 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3814]) ).

thf(5099,plain,
    ! [SV724: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV724 )
        | ( class_HOL_Ominus @ SV724 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3815]) ).

thf(5100,plain,
    ! [SV725: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV725 )
        | ( class_OrderedGroup_Olordered__ab__group__abs @ SV725 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3816]) ).

thf(5101,plain,
    ! [SV726: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV726 )
        | ( class_OrderedGroup_Olordered__ab__group__meet @ SV726 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3817]) ).

thf(5102,plain,
    ! [SV727: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV727 )
        | ( class_OrderedGroup_Olordered__ab__group__join @ SV727 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3818]) ).

thf(5103,plain,
    ! [SV728: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV728 )
        | ( class_OrderedGroup_Olordered__ab__group @ SV728 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3819]) ).

thf(5104,plain,
    ! [SV729: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV729 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV729 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3820]) ).

thf(5105,plain,
    ! [SV730: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV730 )
        | ( class_Ring__and__Field_Oordered__semidom @ SV730 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3821]) ).

thf(5106,plain,
    ! [SV731: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV731 )
        | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV731 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3822]) ).

thf(5107,plain,
    ! [SV732: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV732 )
        | ( class_Ring__and__Field_Oidom @ SV732 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3823]) ).

thf(5108,plain,
    ! [SV733: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV733 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV733 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3824]) ).

thf(5109,plain,
    ! [SV734: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV734 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV734 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3825]) ).

thf(5110,plain,
    ! [SV735: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV735 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV735 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3826]) ).

thf(5111,plain,
    ! [SV736: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV736 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV736 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3827]) ).

thf(5112,plain,
    ! [SV737: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV737 )
        | ( class_Ring__and__Field_Oring @ SV737 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3828]) ).

thf(5113,plain,
    ! [SV738: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV738 )
        | ( class_OrderedGroup_Oab__group__add @ SV738 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3829]) ).

thf(5114,plain,
    ! [SV739: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV739 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV739 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3830]) ).

thf(5115,plain,
    ! [SV740: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV740 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV740 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3831]) ).

thf(5116,plain,
    ! [SV741: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV741 )
        | ( class_OrderedGroup_Osemigroup__add @ SV741 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3832]) ).

thf(5117,plain,
    ! [SV742: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV742 )
        | ( class_HOL_Oplus @ SV742 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3833]) ).

thf(5118,plain,
    ! [SV743: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV743 )
        | ( class_HOL_Ozero @ SV743 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3834]) ).

thf(5119,plain,
    ! [SV744: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV744 )
        | ( class_Ring__and__Field_Oordered__semiring__strict @ SV744 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3835]) ).

thf(5120,plain,
    ! [SV745: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV745 )
        | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV745 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3836]) ).

thf(5121,plain,
    ! [SV746: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV746 )
        | ( class_Orderings_Olinorder @ SV746 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3837]) ).

thf(5122,plain,
    ! [SV747: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
        | ( class_LOrder_Olorder @ SV747 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3838]) ).

thf(5123,plain,
    ! [SV748: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV748 )
        | ( class_LOrder_Ojoin__semilorder @ SV748 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3839]) ).

thf(5124,plain,
    ! [SV749: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV749 )
        | ( class_HOL_Ominus @ SV749 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3840]) ).

thf(5125,plain,
    ! [SV750: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV750 )
        | ( class_LOrder_Omeet__semilorder @ SV750 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3841]) ).

thf(5126,plain,
    ! [SV751: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV751 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV751 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3842]) ).

thf(5127,plain,
    ! [SV752: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV752 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV752 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3843]) ).

thf(5128,plain,
    ! [SV753: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV753 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV753 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3844]) ).

thf(5129,plain,
    ! [SV754: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV754 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV754 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3845]) ).

thf(5130,plain,
    ! [SV755: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV755 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV755 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3846]) ).

thf(5131,plain,
    ! [SV756: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV756 )
        | ( class_Orderings_Oorder @ SV756 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3847]) ).

thf(5132,plain,
    ! [SV757: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV757 )
        | ( class_Orderings_Oord @ SV757 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3848]) ).

thf(5133,plain,
    ! [SV758: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV758 )
        | ( class_Ring__and__Field_Oaxclass__abs__if @ SV758 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3849]) ).

thf(5134,plain,
    ! [SV759: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV759 )
        | ( class_OrderedGroup_Olordered__ab__group @ SV759 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3850]) ).

thf(5135,plain,
    ! [SV760: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV760 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV760 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3851]) ).

thf(5136,plain,
    ! [SV761: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV761 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV761 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3852]) ).

thf(5137,plain,
    ! [SV762: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV762 )
        | ( class_Ring__and__Field_Olordered__ring @ SV762 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3853]) ).

thf(5138,plain,
    ! [SV763: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV763 )
        | ( class_Ring__and__Field_Opordered__ring @ SV763 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3854]) ).

thf(5139,plain,
    ! [SV764: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV764 )
        | ( class_OrderedGroup_Olordered__ab__group__abs @ SV764 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3855]) ).

thf(5140,plain,
    ! [SV765: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV765 )
        | ( class_OrderedGroup_Olordered__ab__group__meet @ SV765 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3856]) ).

thf(5141,plain,
    ! [SV766: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV766 )
        | ( class_OrderedGroup_Olordered__ab__group__join @ SV766 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3857]) ).

thf(5142,plain,
    ! [SV767: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV767 )
        | ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV767 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3858]) ).

thf(5143,plain,
    ! [SV768: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV768 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV768 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3859]) ).

thf(5144,plain,
    ! [SV769: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV769 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV769 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3860]) ).

thf(5145,plain,
    ! [SV770: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV770 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV770 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3861]) ).

thf(5146,plain,
    ! [SV771: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV771 )
        | ( class_Ring__and__Field_Osemiring @ SV771 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3862]) ).

thf(5147,plain,
    ! [SV772: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV772 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV772 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3863]) ).

thf(5148,plain,
    ! [SV773: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV773 )
        | ( class_HOL_Otimes @ SV773 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3864]) ).

thf(5149,plain,
    ! [SV774: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV774 )
        | ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV774 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3865]) ).

thf(5150,plain,
    ! [SV775: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV775 )
        | ( class_Ring__and__Field_Ocomm__semiring__1 @ SV775 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3866]) ).

thf(5151,plain,
    ! [SV776: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV776 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV776 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3867]) ).

thf(5152,plain,
    ! [SV777: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV777 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV777 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3868]) ).

thf(5153,plain,
    ! [SV778: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV778 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV778 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3869]) ).

thf(5154,plain,
    ! [SV779: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV779 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV779 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3870]) ).

thf(5155,plain,
    ! [SV780: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV780 )
        | ( class_Ring__and__Field_Osemiring @ SV780 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3871]) ).

thf(5156,plain,
    ! [SV781: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV781 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV781 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3872]) ).

thf(5157,plain,
    ! [SV782: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV782 )
        | ( class_HOL_Otimes @ SV782 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3873]) ).

thf(5158,plain,
    ! [SV783: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV783 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV783 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3874]) ).

thf(5159,plain,
    ! [SV784: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV784 )
        | ( class_HOL_Ozero @ SV784 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3875]) ).

thf(5160,plain,
    ! [SV785: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV785 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV785 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3876]) ).

thf(5161,plain,
    ! [SV786: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV786 )
        | ( class_OrderedGroup_Ocomm__monoid__mult @ SV786 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3877]) ).

thf(5162,plain,
    ! [SV787: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV787 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV787 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3878]) ).

thf(5163,plain,
    ! [SV788: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV788 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV788 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3879]) ).

thf(5164,plain,
    ! [SV789: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV789 )
        | ( class_OrderedGroup_Osemigroup__add @ SV789 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3880]) ).

thf(5165,plain,
    ! [SV790: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV790 )
        | ( class_HOL_Oplus @ SV790 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3881]) ).

thf(5166,plain,
    ! [SV791: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV791 )
        | ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV791 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3882]) ).

thf(5167,plain,
    ! [SV792: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV792 )
        | ( class_Ring__and__Field_Oordered__semiring__strict @ SV792 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3883]) ).

thf(5168,plain,
    ! [SV793: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV793 )
        | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV793 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3884]) ).

thf(5169,plain,
    ! [SV794: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV794 )
        | ( class_Orderings_Olinorder @ SV794 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3885]) ).

thf(5170,plain,
    ! [SV795: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV795 )
        | ( class_LOrder_Olorder @ SV795 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3886]) ).

thf(5171,plain,
    ! [SV796: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV796 )
        | ( class_LOrder_Ojoin__semilorder @ SV796 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3887]) ).

thf(5172,plain,
    ! [SV797: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV797 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV797 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3888]) ).

thf(5173,plain,
    ! [SV798: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV798 )
        | ( class_LOrder_Omeet__semilorder @ SV798 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3889]) ).

thf(5174,plain,
    ! [SV799: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV799 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV799 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3890]) ).

thf(5175,plain,
    ! [SV800: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV800 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV800 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3891]) ).

thf(5176,plain,
    ! [SV801: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV801 )
        | ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV801 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3892]) ).

thf(5177,plain,
    ! [SV802: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV802 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV802 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3893]) ).

thf(5178,plain,
    ! [SV803: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV803 )
        | ( class_Ring__and__Field_Opordered__comm__semiring @ SV803 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3894]) ).

thf(5179,plain,
    ! [SV804: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV804 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV804 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3895]) ).

thf(5180,plain,
    ! [SV805: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV805 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV805 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3896]) ).

thf(5181,plain,
    ! [SV806: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV806 )
        | ( class_Orderings_Oorder @ SV806 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3897]) ).

thf(5182,plain,
    ! [SV807: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV807 )
        | ( class_Orderings_Oord @ SV807 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3898]) ).

thf(5183,plain,
    ! [SV808: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV808 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV808 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3899]) ).

thf(5184,plain,
    ! [SV809: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV809 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV809 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3900]) ).

thf(5185,plain,
    ! [SV810: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV810 )
        | ( class_OrderedGroup_Omonoid__mult @ SV810 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3901]) ).

thf(5186,plain,
    ! [SV811: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV811 )
        | ( class_HOL_Oone @ SV811 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3902]) ).

thf(5187,plain,
    ! [SV812: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV812 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV812 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3903]) ).

thf(5188,plain,
    ! [SV813: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV813 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV813 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3904]) ).

thf(5189,plain,
    ! [SV814: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV814 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV814 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3905]) ).

thf(5190,plain,
    ! [SV815: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV815 )
        | ( class_Ring__and__Field_Osemiring @ SV815 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3906]) ).

thf(5191,plain,
    ! [SV816: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV816 )
        | ( class_Orderings_Olinorder @ SV816 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3907]) ).

thf(5192,plain,
    ! [SV817: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV817 )
        | ( class_LOrder_Olorder @ SV817 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3908]) ).

thf(5193,plain,
    ! [SV818: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV818 )
        | ( class_LOrder_Ojoin__semilorder @ SV818 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3909]) ).

thf(5194,plain,
    ! [SV819: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV819 )
        | ( class_LOrder_Omeet__semilorder @ SV819 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3910]) ).

thf(5195,plain,
    ! [SV820: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV820 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV820 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3911]) ).

thf(5196,plain,
    ! [SV821: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV821 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV821 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3912]) ).

thf(5197,plain,
    ! [SV822: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV822 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV822 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3913]) ).

thf(5198,plain,
    ! [SV823: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV823 )
        | ( class_Orderings_Oorder @ SV823 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3914]) ).

thf(5199,plain,
    ! [SV824: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV824 )
        | ( class_Orderings_Oord @ SV824 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3915]) ).

thf(5200,plain,
    ! [SV825: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV825 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV825 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3916]) ).

thf(5201,plain,
    ! [SV826: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV826 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV826 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3917]) ).

thf(5202,plain,
    ! [SV827: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV827 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV827 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3918]) ).

thf(5203,plain,
    ! [SV828: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV828 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV828 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3919]) ).

thf(5204,plain,
    ! [SV829: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV829 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV829 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3920]) ).

thf(5205,plain,
    ! [SV830: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV830 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV830 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3921]) ).

thf(5206,plain,
    ! [SV831: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV831 )
        | ( class_HOL_Otimes @ SV831 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3922]) ).

thf(5207,plain,
    ! [SV832: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV832 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV832 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3923]) ).

thf(5208,plain,
    ! [SV833: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV833 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV833 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3924]) ).

thf(5209,plain,
    ! [SV834: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV834 )
        | ( class_OrderedGroup_Osemigroup__add @ SV834 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3925]) ).

thf(5210,plain,
    ! [SV835: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV835 )
        | ( class_HOL_Oplus @ SV835 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3926]) ).

thf(5211,plain,
    ! [SV836: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV836 )
        | ( class_HOL_Ozero @ SV836 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3927]) ).

thf(5212,plain,
    ! [SV837: $i] :
      ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV837 )
        | ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV837 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3928]) ).

thf(5213,plain,
    ! [SV838: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV838 )
        | ( class_Ring__and__Field_Opordered__comm__semiring @ SV838 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3929]) ).

thf(5214,plain,
    ! [SV839: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV839 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV839 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3930]) ).

thf(5215,plain,
    ! [SV840: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV840 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV840 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3931]) ).

thf(5216,plain,
    ! [SV841: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV841 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV841 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3932]) ).

thf(5217,plain,
    ! [SV842: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV842 )
        | ( class_OrderedGroup_Osemigroup__add @ SV842 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3933]) ).

thf(5218,plain,
    ! [SV843: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV843 )
        | ( class_HOL_Oplus @ SV843 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3934]) ).

thf(5219,plain,
    ! [SV844: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV844 )
        | ( class_Orderings_Oorder @ SV844 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3935]) ).

thf(5220,plain,
    ! [SV845: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV845 )
        | ( class_Orderings_Oord @ SV845 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3936]) ).

thf(5221,plain,
    ! [SV846: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV846 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV846 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3937]) ).

thf(5222,plain,
    ! [SV847: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV847 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV847 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3938]) ).

thf(5223,plain,
    ! [SV848: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV848 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV848 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3939]) ).

thf(5224,plain,
    ! [SV849: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV849 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV849 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3940]) ).

thf(5225,plain,
    ! [SV850: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV850 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV850 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3941]) ).

thf(5226,plain,
    ! [SV851: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV851 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV851 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3942]) ).

thf(5227,plain,
    ! [SV852: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV852 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV852 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3943]) ).

thf(5228,plain,
    ! [SV853: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV853 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV853 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3944]) ).

thf(5229,plain,
    ! [SV854: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV854 )
        | ( class_Ring__and__Field_Osemiring @ SV854 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3945]) ).

thf(5230,plain,
    ! [SV855: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV855 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV855 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3946]) ).

thf(5231,plain,
    ! [SV856: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV856 )
        | ( class_HOL_Otimes @ SV856 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3947]) ).

thf(5232,plain,
    ! [SV857: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV857 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV857 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3948]) ).

thf(5233,plain,
    ! [SV858: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV858 )
        | ( class_HOL_Ozero @ SV858 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3949]) ).

thf(5234,plain,
    ! [SV859: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV859 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV859 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3950]) ).

thf(5235,plain,
    ! [SV860: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV860 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV860 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3951]) ).

thf(5236,plain,
    ! [SV861: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV861 )
        | ( class_HOL_Oplus @ SV861 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3952]) ).

thf(5237,plain,
    ! [SV862: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV862 )
        | ( class_Orderings_Oorder @ SV862 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3953]) ).

thf(5238,plain,
    ! [SV863: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV863 )
        | ( class_Orderings_Oord @ SV863 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3954]) ).

thf(5239,plain,
    ! [SV864: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV864 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV864 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3955]) ).

thf(5240,plain,
    ! [SV865: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV865 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV865 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3956]) ).

thf(5241,plain,
    ! [SV866: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV866 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV866 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3957]) ).

thf(5242,plain,
    ! [SV867: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV867 )
        | ( class_Ring__and__Field_Osemiring @ SV867 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3958]) ).

thf(5243,plain,
    ! [SV868: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV868 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV868 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3959]) ).

thf(5244,plain,
    ! [SV869: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV869 )
        | ( class_HOL_Otimes @ SV869 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3960]) ).

thf(5245,plain,
    ! [SV870: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV870 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV870 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3961]) ).

thf(5246,plain,
    ! [SV871: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV871 )
        | ( class_HOL_Ozero @ SV871 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3962]) ).

thf(5247,plain,
    ! [SV872: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV872 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV872 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3963]) ).

thf(5248,plain,
    ! [SV873: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV873 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV873 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3964]) ).

thf(5249,plain,
    ! [SV874: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV874 )
        | ( class_OrderedGroup_Osemigroup__add @ SV874 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3965]) ).

thf(5250,plain,
    ! [SV875: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV875 )
        | ( class_Ring__and__Field_Ocomm__ring @ SV875 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3966]) ).

thf(5251,plain,
    ! [SV876: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV876 )
        | ( class_Ring__and__Field_Oring @ SV876 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3967]) ).

thf(5252,plain,
    ! [SV877: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV877 )
        | ( class_Ring__and__Field_Osemiring @ SV877 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3968]) ).

thf(5253,plain,
    ! [SV878: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV878 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV878 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3969]) ).

thf(5254,plain,
    ! [SV879: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV879 )
        | ( class_HOL_Otimes @ SV879 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3970]) ).

thf(5255,plain,
    ! [SV880: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV880 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV880 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3971]) ).

thf(5256,plain,
    ! [SV881: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV881 )
        | ( class_HOL_Ozero @ SV881 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3972]) ).

thf(5257,plain,
    ! [SV882: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV882 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV882 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3973]) ).

thf(5258,plain,
    ! [SV883: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV883 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV883 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3974]) ).

thf(5259,plain,
    ! [SV884: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV884 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV884 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3975]) ).

thf(5260,plain,
    ! [SV885: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV885 )
        | ( class_OrderedGroup_Osemigroup__add @ SV885 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3976]) ).

thf(5261,plain,
    ! [SV886: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV886 )
        | ( class_HOL_Oplus @ SV886 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3977]) ).

thf(5262,plain,
    ! [SV887: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV887 )
        | ( class_OrderedGroup_Oab__group__add @ SV887 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3978]) ).

thf(5263,plain,
    ! [SV888: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV888 )
        | ( class_Ring__and__Field_Opordered__comm__semiring @ SV888 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3979]) ).

thf(5264,plain,
    ! [SV889: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV889 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV889 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3980]) ).

thf(5265,plain,
    ! [SV890: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV890 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV890 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3981]) ).

thf(5266,plain,
    ! [SV891: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV891 )
        | ( class_Orderings_Oorder @ SV891 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3982]) ).

thf(5267,plain,
    ! [SV892: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV892 )
        | ( class_Orderings_Oord @ SV892 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3983]) ).

thf(5268,plain,
    ! [SV893: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV893 )
        | ( class_HOL_Ominus @ SV893 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3984]) ).

thf(5269,plain,
    ! [SV894: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV894 )
        | ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV894 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3985]) ).

thf(5270,plain,
    ! [SV895: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV895 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV895 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3986]) ).

thf(5271,plain,
    ! [SV896: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV896 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV896 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3987]) ).

thf(5272,plain,
    ! [SV897: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV897 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV897 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3988]) ).

thf(5273,plain,
    ! [SV898: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV898 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV898 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3989]) ).

thf(5274,plain,
    ! [SV899: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV899 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV899 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3990]) ).

thf(5275,plain,
    ! [SV900: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV900 )
        | ( class_Ring__and__Field_Ocomm__semiring__0 @ SV900 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3991]) ).

thf(5276,plain,
    ! [SV901: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV901 )
        | ( class_Ring__and__Field_Ocomm__semiring @ SV901 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3992]) ).

thf(5277,plain,
    ! [SV902: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV902 )
        | ( class_HOL_Oplus @ SV902 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3993]) ).

thf(5278,plain,
    ! [SV903: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV903 )
        | ( class_HOL_Ozero @ SV903 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3994]) ).

thf(5279,plain,
    ! [SV904: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV904 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV904 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3995]) ).

thf(5280,plain,
    ! [SV905: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV905 )
        | ( class_Orderings_Oorder @ SV905 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3996]) ).

thf(5281,plain,
    ! [SV906: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV906 )
        | ( class_Orderings_Oord @ SV906 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3997]) ).

thf(5282,plain,
    ! [SV907: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV907 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV907 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3998]) ).

thf(5283,plain,
    ! [SV908: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV908 )
        | ( class_OrderedGroup_Oab__semigroup__mult @ SV908 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3999]) ).

thf(5284,plain,
    ! [SV909: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV909 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV909 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4000]) ).

thf(5285,plain,
    ! [SV910: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV910 )
        | ( class_Ring__and__Field_Osemiring @ SV910 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4001]) ).

thf(5286,plain,
    ! [SV911: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV911 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV911 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4002]) ).

thf(5287,plain,
    ! [SV912: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV912 )
        | ( class_HOL_Otimes @ SV912 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4003]) ).

thf(5288,plain,
    ! [SV913: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV913 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV913 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4004]) ).

thf(5289,plain,
    ! [SV914: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV914 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV914 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4005]) ).

thf(5290,plain,
    ! [SV915: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV915 )
        | ( class_OrderedGroup_Osemigroup__add @ SV915 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4006]) ).

thf(5291,plain,
    ! [SV916: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV916 )
        | ( class_Ring__and__Field_Oring @ SV916 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4007]) ).

thf(5292,plain,
    ! [SV917: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV917 )
        | ( class_OrderedGroup_Oab__group__add @ SV917 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4008]) ).

thf(5293,plain,
    ! [SV918: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV918 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV918 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4009]) ).

thf(5294,plain,
    ! [SV919: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV919 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV919 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4010]) ).

thf(5295,plain,
    ! [SV920: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV920 )
        | ( class_OrderedGroup_Osemigroup__add @ SV920 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4011]) ).

thf(5296,plain,
    ! [SV921: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV921 )
        | ( class_HOL_Oplus @ SV921 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4012]) ).

thf(5297,plain,
    ! [SV922: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV922 )
        | ( class_HOL_Ozero @ SV922 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4013]) ).

thf(5298,plain,
    ! [SV923: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV923 )
        | ( class_Ring__and__Field_Opordered__semiring @ SV923 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4014]) ).

thf(5299,plain,
    ! [SV924: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV924 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV924 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4015]) ).

thf(5300,plain,
    ! [SV925: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV925 )
        | ( class_Orderings_Oorder @ SV925 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4016]) ).

thf(5301,plain,
    ! [SV926: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV926 )
        | ( class_Orderings_Oord @ SV926 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4017]) ).

thf(5302,plain,
    ! [SV927: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV927 )
        | ( class_OrderedGroup_Opordered__ab__group__add @ SV927 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4018]) ).

thf(5303,plain,
    ! [SV928: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV928 )
        | ( class_HOL_Ominus @ SV928 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4019]) ).

thf(5304,plain,
    ! [SV929: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV929 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV929 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4020]) ).

thf(5305,plain,
    ! [SV930: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV930 )
        | ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV930 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4021]) ).

thf(5306,plain,
    ! [SV931: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV931 )
        | ( class_Ring__and__Field_Opordered__cancel__semiring @ SV931 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4022]) ).

thf(5307,plain,
    ! [SV932: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV932 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV932 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4023]) ).

thf(5308,plain,
    ! [SV933: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV933 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV933 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4024]) ).

thf(5309,plain,
    ! [SV934: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV934 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV934 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4025]) ).

thf(5310,plain,
    ! [SV935: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV935 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV935 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4026]) ).

thf(5311,plain,
    ! [SV936: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV936 )
        | ( class_Ring__and__Field_Osemiring @ SV936 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4027]) ).

thf(5312,plain,
    ! [SV937: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV937 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV937 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4028]) ).

thf(5313,plain,
    ! [SV938: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV938 )
        | ( class_HOL_Otimes @ SV938 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4029]) ).

thf(5314,plain,
    ! [SV939: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV939 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV939 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4030]) ).

thf(5315,plain,
    ! [SV940: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV940 )
        | ( class_Ring__and__Field_Osemiring @ SV940 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4031]) ).

thf(5316,plain,
    ! [SV941: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV941 )
        | ( class_Orderings_Oorder @ SV941 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4032]) ).

thf(5317,plain,
    ! [SV942: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV942 )
        | ( class_Orderings_Oord @ SV942 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4033]) ).

thf(5318,plain,
    ! [SV943: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV943 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV943 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4034]) ).

thf(5319,plain,
    ! [SV944: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV944 )
        | ( class_HOL_Otimes @ SV944 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4035]) ).

thf(5320,plain,
    ! [SV945: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV945 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV945 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4036]) ).

thf(5321,plain,
    ! [SV946: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV946 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV946 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4037]) ).

thf(5322,plain,
    ! [SV947: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV947 )
        | ( class_OrderedGroup_Osemigroup__add @ SV947 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4038]) ).

thf(5323,plain,
    ! [SV948: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV948 )
        | ( class_HOL_Oplus @ SV948 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4039]) ).

thf(5324,plain,
    ! [SV949: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV949 )
        | ( class_HOL_Ozero @ SV949 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4040]) ).

thf(5325,plain,
    ! [SV950: $i] :
      ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV950 )
        | ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV950 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4041]) ).

thf(5326,plain,
    ! [SV951: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV951 )
        | ( class_Ring__and__Field_Osemiring @ SV951 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4042]) ).

thf(5327,plain,
    ! [SV952: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV952 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV952 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4043]) ).

thf(5328,plain,
    ! [SV953: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV953 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV953 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4044]) ).

thf(5329,plain,
    ! [SV954: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV954 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV954 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4045]) ).

thf(5330,plain,
    ! [SV955: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV955 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV955 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4046]) ).

thf(5331,plain,
    ! [SV956: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV956 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV956 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4047]) ).

thf(5332,plain,
    ! [SV957: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV957 )
        | ( class_OrderedGroup_Osemigroup__add @ SV957 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4048]) ).

thf(5333,plain,
    ! [SV958: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV958 )
        | ( class_HOL_Oplus @ SV958 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4049]) ).

thf(5334,plain,
    ! [SV959: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV959 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV959 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4050]) ).

thf(5335,plain,
    ! [SV960: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV960 )
        | ( class_HOL_Otimes @ SV960 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4051]) ).

thf(5336,plain,
    ! [SV961: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV961 )
        | ( class_OrderedGroup_Oab__group__add @ SV961 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4052]) ).

thf(5337,plain,
    ! [SV962: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV962 )
        | ( class_HOL_Ominus @ SV962 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4053]) ).

thf(5338,plain,
    ! [SV963: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV963 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV963 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4054]) ).

thf(5339,plain,
    ! [SV964: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring @ SV964 )
        | ( class_HOL_Ozero @ SV964 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4055]) ).

thf(5340,plain,
    ! [SV965: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV965 )
        | ( class_Ring__and__Field_Oring @ SV965 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4056]) ).

thf(5341,plain,
    ! [SV966: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV966 )
        | ( class_OrderedGroup_Oab__group__add @ SV966 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4057]) ).

thf(5342,plain,
    ! [SV967: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV967 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV967 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4058]) ).

thf(5343,plain,
    ! [SV968: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV968 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV968 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4059]) ).

thf(5344,plain,
    ! [SV969: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV969 )
        | ( class_OrderedGroup_Osemigroup__add @ SV969 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4060]) ).

thf(5345,plain,
    ! [SV970: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV970 )
        | ( class_HOL_Oplus @ SV970 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4061]) ).

thf(5346,plain,
    ! [SV971: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV971 )
        | ( class_HOL_Ozero @ SV971 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4062]) ).

thf(5347,plain,
    ! [SV972: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV972 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV972 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4063]) ).

thf(5348,plain,
    ! [SV973: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV973 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV973 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4064]) ).

thf(5349,plain,
    ! [SV974: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV974 )
        | ( class_OrderedGroup_Omonoid__mult @ SV974 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4065]) ).

thf(5350,plain,
    ! [SV975: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV975 )
        | ( class_HOL_Oone @ SV975 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4066]) ).

thf(5351,plain,
    ! [SV976: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV976 )
        | ( class_Ring__and__Field_Osemiring__1__cancel @ SV976 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4067]) ).

thf(5352,plain,
    ! [SV977: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV977 )
        | ( class_HOL_Ominus @ SV977 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4068]) ).

thf(5353,plain,
    ! [SV978: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV978 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV978 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4069]) ).

thf(5354,plain,
    ! [SV979: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV979 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV979 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4070]) ).

thf(5355,plain,
    ! [SV980: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV980 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV980 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4071]) ).

thf(5356,plain,
    ! [SV981: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV981 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV981 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4072]) ).

thf(5357,plain,
    ! [SV982: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV982 )
        | ( class_Ring__and__Field_Osemiring @ SV982 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4073]) ).

thf(5358,plain,
    ! [SV983: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV983 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV983 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4074]) ).

thf(5359,plain,
    ! [SV984: $i] :
      ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV984 )
        | ( class_HOL_Otimes @ SV984 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4075]) ).

thf(5360,plain,
    ! [SV985: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring @ SV985 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV985 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4076]) ).

thf(5361,plain,
    ! [SV986: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring @ SV986 )
        | ( class_OrderedGroup_Osemigroup__add @ SV986 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4077]) ).

thf(5362,plain,
    ! [SV987: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring @ SV987 )
        | ( class_HOL_Oplus @ SV987 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4078]) ).

thf(5363,plain,
    ! [SV988: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring @ SV988 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV988 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4079]) ).

thf(5364,plain,
    ! [SV989: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring @ SV989 )
        | ( class_HOL_Otimes @ SV989 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4080]) ).

thf(5365,plain,
    ! [SV990: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV990 )
        | ( class_Ring__and__Field_Osemiring @ SV990 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4081]) ).

thf(5366,plain,
    ! [SV991: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV991 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV991 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4082]) ).

thf(5367,plain,
    ! [SV992: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV992 )
        | ( class_OrderedGroup_Osemigroup__add @ SV992 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4083]) ).

thf(5368,plain,
    ! [SV993: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV993 )
        | ( class_HOL_Oplus @ SV993 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4084]) ).

thf(5369,plain,
    ! [SV994: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV994 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV994 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4085]) ).

thf(5370,plain,
    ! [SV995: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV995 )
        | ( class_HOL_Otimes @ SV995 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4086]) ).

thf(5371,plain,
    ! [SV996: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV996 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV996 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4087]) ).

thf(5372,plain,
    ! [SV997: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV997 )
        | ( class_HOL_Ozero @ SV997 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4088]) ).

thf(5373,plain,
    ! [SV998: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV998 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV998 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4089]) ).

thf(5374,plain,
    ! [SV999: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV999 )
        | ( class_Ring__and__Field_Osemiring @ SV999 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4090]) ).

thf(5375,plain,
    ! [SV1000: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1000 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV1000 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4091]) ).

thf(5376,plain,
    ! [SV1001: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1001 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV1001 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4092]) ).

thf(5377,plain,
    ! [SV1002: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1002 )
        | ( class_HOL_Otimes @ SV1002 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4093]) ).

thf(5378,plain,
    ! [SV1003: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1003 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV1003 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4094]) ).

thf(5379,plain,
    ! [SV1004: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1004 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV1004 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4095]) ).

thf(5380,plain,
    ! [SV1005: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1005 )
        | ( class_OrderedGroup_Osemigroup__add @ SV1005 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4096]) ).

thf(5381,plain,
    ! [SV1006: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1006 )
        | ( class_HOL_Oplus @ SV1006 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4097]) ).

thf(5382,plain,
    ! [SV1007: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1007 )
        | ( class_HOL_Ozero @ SV1007 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4098]) ).

thf(5383,plain,
    ! [SV1008: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1008 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1008 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4099]) ).

thf(5384,plain,
    ! [SV1009: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1009 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1009 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4100]) ).

thf(5385,plain,
    ! [SV1010: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1010 )
        | ( class_HOL_Ozero @ SV1010 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4101]) ).

thf(5386,plain,
    ! [SV1011: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1011 )
        | ( class_HOL_Oplus @ SV1011 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4102]) ).

thf(5387,plain,
    ! [SV1012: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1012 )
        | ( class_OrderedGroup_Omonoid__mult @ SV1012 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4103]) ).

thf(5388,plain,
    ! [SV1013: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1013 )
        | ( class_HOL_Oone @ SV1013 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4104]) ).

thf(5389,plain,
    ! [SV1014: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1014 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV1014 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4105]) ).

thf(5390,plain,
    ! [SV1015: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1015 )
        | ( class_Ring__and__Field_Osemiring @ SV1015 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4106]) ).

thf(5391,plain,
    ! [SV1016: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1016 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV1016 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4107]) ).

thf(5392,plain,
    ! [SV1017: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1017 )
        | ( class_HOL_Otimes @ SV1017 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4108]) ).

thf(5393,plain,
    ! [SV1018: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1018 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV1018 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4109]) ).

thf(5394,plain,
    ! [SV1019: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1019 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV1019 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4110]) ).

thf(5395,plain,
    ! [SV1020: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1020 )
        | ( class_OrderedGroup_Osemigroup__add @ SV1020 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4111]) ).

thf(5396,plain,
    ! [SV1021: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1021 )
        | ( class_Ring__and__Field_Osemiring__1 @ SV1021 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4112]) ).

thf(5397,plain,
    ! [SV1022: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1022 )
        | ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1022 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4113]) ).

thf(5398,plain,
    ! [SV1023: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1023 )
        | ( class_HOL_Oone @ SV1023 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4114]) ).

thf(5399,plain,
    ! [SV1024: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1024 )
        | ( class_OrderedGroup_Osemigroup__mult @ SV1024 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4115]) ).

thf(5400,plain,
    ! [SV1025: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1025 )
        | ( class_HOL_Otimes @ SV1025 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4116]) ).

thf(5401,plain,
    ! [SV1026: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1026 )
        | ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1026 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4117]) ).

thf(5402,plain,
    ! [SV1027: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1027 )
        | ( class_OrderedGroup_Ocancel__semigroup__add @ SV1027 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4118]) ).

thf(5403,plain,
    ! [SV1028: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1028 )
        | ( class_Ring__and__Field_Osemiring__0__cancel @ SV1028 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4119]) ).

thf(5404,plain,
    ! [SV1029: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1029 )
        | ( class_Ring__and__Field_Osemiring__0 @ SV1029 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4120]) ).

thf(5405,plain,
    ! [SV1030: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1030 )
        | ( class_Ring__and__Field_Osemiring @ SV1030 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4121]) ).

thf(5406,plain,
    ! [SV1031: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1031 )
        | ( class_OrderedGroup_Ocomm__monoid__add @ SV1031 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4122]) ).

thf(5407,plain,
    ! [SV1032: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1032 )
        | ( class_HOL_Ozero @ SV1032 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4123]) ).

thf(5408,plain,
    ! [SV1033: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1033 )
        | ( class_OrderedGroup_Oab__semigroup__add @ SV1033 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4124]) ).

thf(5409,plain,
    ! [SV1034: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1034 )
        | ( class_OrderedGroup_Osemigroup__add @ SV1034 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4125]) ).

thf(5410,plain,
    ! [SV1035: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1035 )
        | ( class_HOL_Oplus @ SV1035 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4126]) ).

thf(5411,plain,
    ! [SV1036: $i] :
      ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1036 )
        | ( class_OrderedGroup_Omonoid__mult @ SV1036 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4127]) ).

thf(5412,plain,
    ! [SV1037: $i] :
      ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1037 )
        | ( class_Orderings_Oord @ SV1037 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4128]) ).

thf(5413,plain,
    ! [SV1038: $i] :
      ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1038 )
        | ( class_Orderings_Oorder @ SV1038 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4129]) ).

thf(5414,plain,
    ! [SV1039: $i] :
      ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1039 )
        | ( class_LOrder_Omeet__semilorder @ SV1039 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4130]) ).

thf(5415,plain,
    ! [SV1040: $i] :
      ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1040 )
        | ( class_LOrder_Ojoin__semilorder @ SV1040 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4131]) ).

thf(5416,plain,
    ! [SV1041: $i] :
      ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1041 )
        | ( class_LOrder_Olorder @ SV1041 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4132]) ).

thf(5417,plain,
    ! [SV1042: $i] :
      ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1042 )
        | ( class_Orderings_Olinorder @ SV1042 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4133]) ).

thf(5418,plain,
    ! [SV1043: $i] :
      ( ( ! [SY2314: $i,SY2315: $i] :
            ( ~ ( c_in @ SV1043 @ ( c_Datatype_Oo2s @ SY2314 @ SY2315 ) @ SY2315 )
            | ( SY2314
              = ( c_Datatype_Ooption_OSome @ SV1043 @ SY2315 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4134]) ).

thf(5419,plain,
    ! [SV1044: $i] :
      ( ( ! [SY2316: $i] : ( c_in @ SV1044 @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ SV1044 @ SY2316 ) @ SY2316 ) @ SY2316 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4135]) ).

thf(5420,plain,
    ! [SV1045: $i] :
      ( ( ( SV1045 = c_Datatype_Ooption_ONone )
        | ! [SY2317: $i] :
            ( SV1045
            = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ SV1045 @ SY2317 ) @ SY2317 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4136]) ).

thf(5421,plain,
    ! [SV1046: $i] :
      ( ( ( SV1046 = c_Datatype_Ooption_ONone )
        | ! [SY2318: $i] :
            ( SV1046
            = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ SV1046 @ SY2318 ) @ SY2318 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4137]) ).

thf(5422,plain,
    ! [SV1047: $i] :
      ( ( ! [SY2319: $i] :
            ( c_Datatype_Ooption_ONone
           != ( c_Datatype_Ooption_OSome @ SV1047 @ SY2319 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4138]) ).

thf(5423,plain,
    ! [SV1048: $i] :
      ( ( ! [SY2320: $i] :
            ( ( c_Datatype_Ooption_OSome @ SV1048 @ SY2320 )
           != c_Datatype_Ooption_ONone ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4139]) ).

thf(5424,plain,
    ! [SV1049: $i] :
      ( ( ! [SY2321: $i,SY2322: $i] :
            ( ( ( c_Datatype_Ooption_OSome @ SV1049 @ SY2321 )
             != ( c_Datatype_Ooption_OSome @ SY2322 @ SY2321 ) )
            | ( SV1049 = SY2322 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4140]) ).

thf(5425,plain,
    ! [SV1050: $i] :
      ( ( ! [SY2323: $i,SY2324: $i,SY2325: $i] :
            ( ( ( c_Datatype__Universe_OAtom @ SV1050 @ SY2323 @ SY2324 )
             != ( c_Datatype__Universe_OAtom @ SY2325 @ SY2323 @ SY2324 ) )
            | ( SV1050 = SY2325 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4141]) ).

thf(5426,plain,
    ! [SV1051: $i] :
      ( ( ! [SY2326: $i,SY2327: $i,SY2328: $i,SY2329: $i] :
            ( ( c_Datatype__Universe_OAtom @ SV1051 @ SY2326 @ SY2327 )
           != ( c_Datatype__Universe_OScons @ SY2328 @ SY2329 @ SY2326 @ SY2327 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4142]) ).

thf(5427,plain,
    ! [SV1052: $i] :
      ( ( ! [SY2330: $i,SY2331: $i,SY2332: $i] :
            ( ( ( c_Datatype__Universe_OIn0 @ SV1052 @ SY2330 @ SY2331 )
             != ( c_Datatype__Universe_OIn0 @ SY2332 @ SY2330 @ SY2331 ) )
            | ( SV1052 = SY2332 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4143]) ).

thf(5428,plain,
    ! [SV1053: $i] :
      ( ( ! [SY2333: $i,SY2334: $i,SY2335: $i] :
            ( ( c_Datatype__Universe_OIn0 @ SV1053 @ SY2333 @ SY2334 )
           != ( c_Datatype__Universe_OIn1 @ SY2335 @ SY2333 @ SY2334 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4144]) ).

thf(5429,plain,
    ! [SV1054: $i] :
      ( ( ! [SY2336: $i,SY2337: $i,SY2338: $i] :
            ( ( ( c_Datatype__Universe_OIn1 @ SV1054 @ SY2336 @ SY2337 )
             != ( c_Datatype__Universe_OIn1 @ SY2338 @ SY2336 @ SY2337 ) )
            | ( SV1054 = SY2338 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4145]) ).

thf(5430,plain,
    ! [SV1055: $i] :
      ( ( ! [SY2339: $i,SY2340: $i,SY2341: $i] :
            ( ( c_Datatype__Universe_OIn1 @ SV1055 @ SY2339 @ SY2340 )
           != ( c_Datatype__Universe_OIn0 @ SY2341 @ SY2339 @ SY2340 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4146]) ).

thf(5431,plain,
    ! [SV1056: $i] :
      ( ( ! [SY2342: $i,SY2343: $i,SY2344: $i] :
            ( ( c_Datatype__Universe_OLeaf @ SV1056 @ SY2342 @ SY2343 )
           != ( c_Datatype__Universe_ONumb @ SY2344 @ SY2342 @ SY2343 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4147]) ).

thf(5432,plain,
    ! [SV1057: $i] :
      ( ( ! [SY2345: $i,SY2346: $i,SY2347: $i,SY2348: $i] :
            ( ( c_Datatype__Universe_OLeaf @ SV1057 @ SY2345 @ SY2346 )
           != ( c_Datatype__Universe_OScons @ SY2347 @ SY2348 @ SY2345 @ SY2346 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4148]) ).

thf(5433,plain,
    ! [SV1058: $i] :
      ( ( ! [SY2349: $i,SY2350: $i,SY2351: $i] :
            ( ( c_Datatype__Universe_ONumb @ SV1058 @ SY2349 @ SY2350 )
           != ( c_Datatype__Universe_OLeaf @ SY2351 @ SY2349 @ SY2350 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4149]) ).

thf(5434,plain,
    ! [SV1059: $i] :
      ( ( ! [SY2352: $i,SY2353: $i,SY2354: $i,SY2355: $i] :
            ( ( c_Datatype__Universe_ONumb @ SV1059 @ SY2352 @ SY2353 )
           != ( c_Datatype__Universe_OScons @ SY2354 @ SY2355 @ SY2352 @ SY2353 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4150]) ).

thf(5435,plain,
    ! [SV1060: $i] :
      ( ( ! [SY2356: $i,SY2357: $i,SY2358: $i,SY2359: $i] :
            ( ! [SY2360: $i] :
                ( ( c_Datatype__Universe_OScons @ SV1060 @ SY2356 @ SY2357 @ SY2358 )
               != ( c_Datatype__Universe_OScons @ SY2359 @ SY2360 @ SY2357 @ SY2358 ) )
            | ( SV1060 = SY2359 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4151]) ).

thf(5436,plain,
    ! [SV1061: $i] :
      ( ( ! [SY2361: $i,SY2362: $i,SY2363: $i,SY2364: $i,SY2365: $i] :
            ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SY2361 @ SY2362 @ SY2363 )
             != ( c_Datatype__Universe_OScons @ SY2364 @ SY2365 @ SY2362 @ SY2363 ) )
            | ( SY2361 = SY2365 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4152]) ).

thf(5437,plain,
    ! [SV1062: $i] :
      ( ( ! [SY2366: $i,SY2367: $i,SY2368: $i,SY2369: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1062 @ SY2366 @ SY2367 @ SY2368 )
           != ( c_Datatype__Universe_OAtom @ SY2369 @ SY2367 @ SY2368 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4153]) ).

thf(5438,plain,
    ! [SV1063: $i] :
      ( ( ! [SY2370: $i,SY2371: $i,SY2372: $i,SY2373: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1063 @ SY2370 @ SY2371 @ SY2372 )
           != ( c_Datatype__Universe_OLeaf @ SY2373 @ SY2371 @ SY2372 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4154]) ).

thf(5439,plain,
    ! [SV1064: $i] :
      ( ( ! [SY2374: $i,SY2375: $i,SY2376: $i,SY2377: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1064 @ SY2374 @ SY2375 @ SY2376 )
           != ( c_Datatype__Universe_ONumb @ SY2377 @ SY2375 @ SY2376 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4155]) ).

thf(5440,plain,
    ! [SV1065: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1065 @ tc_nat )
        | ( SV1065 = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4156]) ).

thf(5441,plain,
    ! [SV1066: $i] :
      ( ( ! [SY2378: $i,SY2379: $i] :
            ( c_emptyset
           != ( c_Equiv__Relations_Oquotient @ SV1066 @ SY2378 @ SY2379 ) )
        | ( SV1066 = c_emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4158]) ).

thf(5442,plain,
    ! [SV1067: $i] :
      ( ( ! [SY2380: $i] :
            ( c_emptyset
            = ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1067 @ SY2380 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4159]) ).

thf(5443,plain,
    ! [SV1068: $i] :
      ( ( ! [SY2381: $i,SY2382: $i] :
            ( ( c_Equiv__Relations_Oquotient @ SV1068 @ SY2381 @ SY2382 )
           != c_emptyset )
        | ( SV1068 = c_emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4160]) ).

thf(5444,plain,
    ! [SV1069: $i] :
      ( ( ! [SY2383: $i] :
            ( ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1069 @ SY2383 )
            = c_emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4161]) ).

thf(5445,plain,
    ( ( c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4162]) ).

thf(5446,plain,
    ( ( c_Extraction_Osumbool_ORight = c_Extraction_Osumbool_OLeft )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4163]) ).

thf(5447,plain,
    ! [SV1070: $i] :
      ( ( ! [SY2384: $i,SY2385: $i,SY2386: $i] :
            ( ~ ( c_in @ ( c_minus @ SV1070 @ ( c_insert @ SY2384 @ SY2385 @ SY2386 ) @ ( tc_set @ SY2386 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2386 ) )
            | ( c_in @ ( c_minus @ SV1070 @ SY2385 @ ( tc_set @ SY2386 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2386 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4164]) ).

thf(5448,plain,
    ! [SV1071: $i] :
      ( ( ! [SY2387: $i,SY2388: $i] :
            ( ~ ( c_in @ ( c_minus @ SV1071 @ SY2387 @ ( tc_set @ SY2388 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2388 ) )
            | ! [SY2389: $i] : ( c_in @ ( c_minus @ SV1071 @ ( c_insert @ SY2389 @ SY2387 @ SY2388 ) @ ( tc_set @ SY2388 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2388 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4165]) ).

thf(5449,plain,
    ! [SV1072: $i] :
      ( ( ! [SY2390: $i] :
            ( ~ ( c_in @ ( c_Pow @ SV1072 @ SY2390 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2390 ) ) )
            | ( c_in @ SV1072 @ c_Finite__Set_OFinites @ ( tc_set @ SY2390 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4166]) ).

thf(5450,plain,
    ! [SV1073: $i] :
      ( ( ! [SY2391: $i] :
            ( ~ ( c_in @ SV1073 @ c_Finite__Set_OFinites @ ( tc_set @ SY2391 ) )
            | ( c_in @ ( c_Pow @ SV1073 @ SY2391 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2391 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4167]) ).

thf(5451,plain,
    ! [SV1074: $i] :
      ( ( ! [SY2392: $i,SY2393: $i] :
            ( ~ ( c_in @ ( c_union @ SV1074 @ SY2392 @ SY2393 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2393 ) )
            | ( c_in @ SV1074 @ c_Finite__Set_OFinites @ ( tc_set @ SY2393 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4168]) ).

thf(5452,plain,
    ! [SV1075: $i] :
      ( ( ! [SY2394: $i,SY2395: $i] :
            ( ~ ( c_in @ ( c_union @ SV1075 @ SY2394 @ SY2395 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2395 ) )
            | ( c_in @ SY2394 @ c_Finite__Set_OFinites @ ( tc_set @ SY2395 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4169]) ).

thf(5453,plain,
    ! [SV1076: $i] :
      ( ( ! [SY2396: $i] :
            ( ~ ( c_in @ SV1076 @ c_Finite__Set_OFinites @ ( tc_set @ SY2396 ) )
            | ! [SY2397: $i] :
                ( ~ ( c_in @ SY2397 @ c_Finite__Set_OFinites @ ( tc_set @ SY2396 ) )
                | ( c_in @ ( c_union @ SY2397 @ SV1076 @ SY2396 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2396 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4170]) ).

thf(5454,plain,
    ! [SV1077: $i] :
      ( ( ! [SY2398: $i,SY2399: $i] :
            ( ~ ( c_in @ ( c_Relation_Oconverse @ SV1077 @ SY2398 @ SY2399 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2399 @ SY2398 ) ) )
            | ( c_in @ SV1077 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2398 @ SY2399 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4171]) ).

thf(5455,plain,
    ! [SV1078: $i] :
      ( ( ! [SY2400: $i,SY2401: $i] :
            ( ~ ( c_in @ SV1078 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2400 @ SY2401 ) ) )
            | ( c_in @ ( c_Relation_Oconverse @ SV1078 @ SY2400 @ SY2401 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2401 @ SY2400 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4172]) ).

thf(5456,plain,
    ! [SV1079: $i] :
      ( ( ! [SY2402: $i] :
            ( ! [SY2403: $i] :
                ~ ( c_Divides_Oop_Advd @ SV1079 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2402 @ SY2403 @ tc_nat @ tc_nat ) ) @ tc_nat )
            | ( c_Divides_Oop_Advd @ SV1079 @ SY2402 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4173]) ).

thf(5457,plain,
    ! [SV1080: $i] :
      ( ( ! [SY2404: $i,SY2405: $i] :
            ( ~ ( c_Divides_Oop_Advd @ SV1080 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2404 @ SY2405 @ tc_nat @ tc_nat ) ) @ tc_nat )
            | ( c_Divides_Oop_Advd @ SV1080 @ SY2405 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4174]) ).

thf(5458,plain,
    ! [SV1081: $i] :
      ( ( ! [SY2406: $i] :
            ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SY2406 @ tc_nat )
            | ! [SY2407: $i] :
                ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SY2407 @ tc_nat )
                | ( c_Divides_Oop_Advd @ SV1081 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2407 @ SY2406 @ tc_nat @ tc_nat ) ) @ tc_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4175]) ).

thf(5459,plain,
    ( ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4176]) ).

thf(5460,plain,
    ! [SV1082: $i] :
      ( ( ! [SY2408: $i] :
            ( ( ( c_IntDef_Oint @ SV1082 )
             != ( c_IntDef_Oint @ SY2408 ) )
            | ( SV1082 = SY2408 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4177]) ).

thf(5461,plain,
    ! [SV1083: $i] :
      ( ( ! [SY2409: $i] :
            ( ~ ( c_Divides_Oop_Advd @ SV1083 @ ( c_uminus @ SY2409 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
            | ( c_Divides_Oop_Advd @ SV1083 @ SY2409 @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4178]) ).

thf(5462,plain,
    ! [SV1084: $i] :
      ( ( ! [SY2410: $i] :
            ( ~ ( c_Divides_Oop_Advd @ SV1084 @ SY2410 @ tc_IntDef_Oint )
            | ( c_Divides_Oop_Advd @ SV1084 @ ( c_uminus @ SY2410 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4179]) ).

thf(5463,plain,
    ! [SV1085: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1085 @ tc_IntDef_Oint )
        | ( SV1085 = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4180]) ).

thf(5464,plain,
    ! [SV1086: $i] :
      ( ( ! [SY2411: $i] :
            ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ SV1086 @ tc_IntDef_Oint ) @ SY2411 @ tc_IntDef_Oint )
            | ( c_Divides_Oop_Advd @ SV1086 @ SY2411 @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4182]) ).

thf(5465,plain,
    ! [SV1087: $i] :
      ( ( ! [SY2412: $i] :
            ( ~ ( c_Divides_Oop_Advd @ SV1087 @ SY2412 @ tc_IntDef_Oint )
            | ( c_Divides_Oop_Advd @ ( c_uminus @ SV1087 @ tc_IntDef_Oint ) @ SY2412 @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4183]) ).

thf(5466,plain,
    ! [SV1088: $i] :
      ( ( ! [SY2413: $i,SY2414: $i] :
            ~ ( c_in @ ( c_Pair @ SV1088 @ c_List_Olist_ONil @ ( tc_List_Olist @ SY2413 ) @ ( tc_List_Olist @ SY2413 ) ) @ ( c_List_Olex @ SY2414 @ SY2413 ) @ ( tc_prod @ ( tc_List_Olist @ SY2413 ) @ ( tc_List_Olist @ SY2413 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4184]) ).

thf(5467,plain,
    ! [SV1089: $i] :
      ( ( ! [SY2415: $i,SY2416: $i] :
            ( c_List_Olist_ONil
           != ( c_append @ SV1089 @ SY2415 @ SY2416 ) )
        | ( SV1089 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4185]) ).

thf(5468,plain,
    ! [SV1090: $i] :
      ( ( ! [SY2417: $i] :
            ( ! [SY2418: $i] :
                ( c_List_Olist_ONil
               != ( c_append @ SV1090 @ SY2417 @ SY2418 ) )
            | ( SY2417 = c_List_Olist_ONil ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4186]) ).

thf(5469,plain,
    ! [SV1091: $i] :
      ( ( c_List_Olist_ONil
        = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ SV1091 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4187]) ).

thf(5470,plain,
    ! [SV1092: $i] :
      ( ( ! [SY2419: $i] :
            ( c_List_Olist_ONil
           != ( c_List_Orev @ SV1092 @ SY2419 ) )
        | ( SV1092 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4188]) ).

thf(5471,plain,
    ! [SV1093: $i] :
      ( ( c_List_Olist_ONil
        = ( c_List_Orev @ c_List_Olist_ONil @ SV1093 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4189]) ).

thf(5472,plain,
    ! [SV1094: $i] :
      ( ( ! [SY2420: $i,SY2421: $i] :
            ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1094 @ ( tc_List_Olist @ SY2420 ) @ ( tc_List_Olist @ SY2420 ) ) @ ( c_List_Olex @ SY2421 @ SY2420 ) @ ( tc_prod @ ( tc_List_Olist @ SY2420 ) @ ( tc_List_Olist @ SY2420 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4190]) ).

thf(5473,plain,
    ! [SV1095: $i] :
      ( ( ! [SY2422: $i,SY2423: $i,SY2424: $i] :
            ( ! [SY2425: $i] :
                ( ( c_append @ SV1095 @ ( c_List_Olist_OCons @ SY2422 @ c_List_Olist_ONil @ SY2423 ) @ SY2423 )
               != ( c_append @ SY2424 @ ( c_List_Olist_OCons @ SY2425 @ c_List_Olist_ONil @ SY2423 ) @ SY2423 ) )
            | ( SV1095 = SY2424 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4191]) ).

thf(5474,plain,
    ! [SV1096: $i] :
      ( ( ! [SY2426: $i,SY2427: $i,SY2428: $i,SY2429: $i] :
            ( ( ( c_append @ SV1096 @ ( c_List_Olist_OCons @ SY2426 @ c_List_Olist_ONil @ SY2427 ) @ SY2427 )
             != ( c_append @ SY2428 @ ( c_List_Olist_OCons @ SY2429 @ c_List_Olist_ONil @ SY2427 ) @ SY2427 ) )
            | ( SY2426 = SY2429 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4192]) ).

thf(5475,plain,
    ! [SV1097: $i] :
      ( ( ! [SY2430: $i,SY2431: $i,SY2432: $i] :
            ( ~ ( c_in @ ( c_append @ SV1097 @ SY2430 @ SY2431 ) @ ( c_List_Olists @ SY2432 @ SY2431 ) @ ( tc_List_Olist @ SY2431 ) )
            | ( c_in @ SV1097 @ ( c_List_Olists @ SY2432 @ SY2431 ) @ ( tc_List_Olist @ SY2431 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4193]) ).

thf(5476,plain,
    ! [SV1098: $i] :
      ( ( ! [SY2433: $i,SY2434: $i,SY2435: $i] :
            ( ~ ( c_in @ ( c_append @ SV1098 @ SY2433 @ SY2434 ) @ ( c_List_Olists @ SY2435 @ SY2434 ) @ ( tc_List_Olist @ SY2434 ) )
            | ( c_in @ SY2433 @ ( c_List_Olists @ SY2435 @ SY2434 ) @ ( tc_List_Olist @ SY2434 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4194]) ).

thf(5477,plain,
    ! [SV1099: $i] :
      ( ( ! [SY2436: $i,SY2437: $i] :
            ( ~ ( c_in @ SV1099 @ ( c_List_Olists @ SY2436 @ SY2437 ) @ ( tc_List_Olist @ SY2437 ) )
            | ! [SY2438: $i] :
                ( ~ ( c_in @ SY2438 @ ( c_List_Olists @ SY2436 @ SY2437 ) @ ( tc_List_Olist @ SY2437 ) )
                | ( c_in @ ( c_append @ SY2438 @ SV1099 @ SY2437 ) @ ( c_List_Olists @ SY2436 @ SY2437 ) @ ( tc_List_Olist @ SY2437 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4195]) ).

thf(5478,plain,
    ! [SV1100: $i] :
      ( ( ! [SY2439: $i,SY2440: $i] :
            ( ( c_append @ SV1100 @ SY2439 @ SY2440 )
           != c_List_Olist_ONil )
        | ( SV1100 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4196]) ).

thf(5479,plain,
    ! [SV1101: $i] :
      ( ( ! [SY2441: $i] :
            ( ! [SY2442: $i] :
                ( ( c_append @ SV1101 @ SY2441 @ SY2442 )
               != c_List_Olist_ONil )
            | ( SY2441 = c_List_Olist_ONil ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4197]) ).

thf(5480,plain,
    ! [SV1102: $i] :
      ( ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ SV1102 )
        = c_List_Olist_ONil )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4198]) ).

thf(5481,plain,
    ! [SV1103: $i] :
      ( ( ! [SY2443: $i,SY2444: $i,SY2445: $i] :
            ( ( ( c_append @ SV1103 @ SY2443 @ SY2444 )
             != ( c_append @ SY2445 @ SY2443 @ SY2444 ) )
            | ( SV1103 = SY2445 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4199]) ).

thf(5482,plain,
    ! [SV1104: $i] :
      ( ( ! [SY2446: $i,SY2447: $i] :
            ( ( c_append @ SV1104 @ SY2446 @ SY2447 )
           != SY2446 )
        | ( SV1104 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4200]) ).

thf(5483,plain,
    ! [SV1105: $i] :
      ( ( ! [SY2448: $i] :
            ( ( c_append @ c_List_Olist_ONil @ SV1105 @ SY2448 )
            = SV1105 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4201]) ).

thf(5484,plain,
    ! [SV1106: $i] :
      ( ( ! [SY2449: $i] :
            ( ! [SY2450: $i] :
                ( ( c_append @ SV1106 @ SY2449 @ SY2450 )
               != SV1106 )
            | ( SY2449 = c_List_Olist_ONil ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4202]) ).

thf(5485,plain,
    ! [SV1107: $i] :
      ( ( ! [SY2451: $i] :
            ( ( c_append @ SV1107 @ c_List_Olist_ONil @ SY2451 )
            = SV1107 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4203]) ).

thf(5486,plain,
    ! [SV1108: $i] :
      ( ( ! [SY2452: $i,SY2453: $i] :
            ( ! [SY2454: $i] :
                ( ( c_List_Ochar_OChar @ SV1108 @ SY2452 )
               != ( c_List_Ochar_OChar @ SY2453 @ SY2454 ) )
            | ( SV1108 = SY2453 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4204]) ).

thf(5487,plain,
    ! [SV1109: $i] :
      ( ( ! [SY2455: $i,SY2456: $i,SY2457: $i] :
            ( ( ( c_List_Ochar_OChar @ SV1109 @ SY2455 )
             != ( c_List_Ochar_OChar @ SY2456 @ SY2457 ) )
            | ( SY2455 = SY2457 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4205]) ).

thf(5488,plain,
    ! [SV1110: $i] :
      ( ( ! [SY2458: $i] :
            ( ( c_Nat_Osize @ SV1110 @ ( tc_List_Olist @ SY2458 ) )
           != c_0 )
        | ( SV1110 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4206]) ).

thf(5489,plain,
    ! [SV1111: $i] :
      ( ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1111 ) )
        = c_0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4207]) ).

thf(5490,plain,
    ! [SV1112: $i] :
      ( ( ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1112 ) ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4208]) ).

thf(5491,plain,
    ! [SV1113: $i] :
      ( ( ( SV1113 = c_List_Olist_ONil )
        | ! [SY2459: $i] : ( c_less @ c_0 @ ( c_Nat_Osize @ SV1113 @ ( tc_List_Olist @ SY2459 ) ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4209]) ).

thf(5492,plain,
    ! [SV1114: $i] :
      ( ( ! [SY2460: $i] :
            ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1114 @ SY2460 ) @ ( tc_List_Olist @ SY2460 ) )
             != ( c_Nat_Osize @ SV1114 @ ( tc_List_Olist @ SY2460 ) ) )
            | ( ( c_List_Oremdups @ SV1114 @ SY2460 )
              = SV1114 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4210]) ).

thf(5493,plain,
    ! [SV1115: $i] :
      ( ( ! [SY2461: $i] :
            ( ( ( c_List_Oremdups @ SV1115 @ SY2461 )
             != SV1115 )
            | ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1115 @ SY2461 ) @ ( tc_List_Olist @ SY2461 ) )
              = ( c_Nat_Osize @ SV1115 @ ( tc_List_Olist @ SY2461 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4211]) ).

thf(5494,plain,
    ! [SV1116: $i] :
      ( ( ! [SY2462: $i,SY2463: $i] :
            ( c_List_Olist_ONil
           != ( c_List_Olist_OCons @ SV1116 @ SY2462 @ SY2463 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4212]) ).

thf(5495,plain,
    ! [SV1117: $i] :
      ( ( ! [SY2464: $i,SY2465: $i] :
            ( ( c_List_Olist_OCons @ SV1117 @ SY2464 @ SY2465 )
           != c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4213]) ).

thf(5496,plain,
    ! [SV1118: $i] :
      ( ( ! [SY2466: $i,SY2467: $i,SY2468: $i] :
            ( ! [SY2469: $i] :
                ( ( c_List_Olist_OCons @ SV1118 @ SY2466 @ SY2467 )
               != ( c_List_Olist_OCons @ SY2468 @ SY2469 @ SY2467 ) )
            | ( SV1118 = SY2468 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4214]) ).

thf(5497,plain,
    ! [SV1119: $i] :
      ( ( ! [SY2470: $i,SY2471: $i,SY2472: $i,SY2473: $i] :
            ( ( ( c_List_Olist_OCons @ SV1119 @ SY2470 @ SY2471 )
             != ( c_List_Olist_OCons @ SY2472 @ SY2473 @ SY2471 ) )
            | ( SY2470 = SY2473 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4215]) ).

thf(5498,plain,
    ! [SV1120: $i] :
      ( ( ! [SY2474: $i,SY2475: $i,SY2476: $i] :
            ( ( ( c_List_Orev @ SV1120 @ SY2474 )
             != ( c_List_Olist_OCons @ SY2475 @ SY2476 @ SY2474 ) )
            | ( SV1120
              = ( c_append @ ( c_List_Orev @ SY2476 @ SY2474 ) @ ( c_List_Olist_OCons @ SY2475 @ c_List_Olist_ONil @ SY2474 ) @ SY2474 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4216]) ).

thf(5499,plain,
    ! [SV1121: $i] :
      ( ( ! [SY2477: $i,SY2478: $i] :
            ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ SV1121 @ SY2477 ) @ ( c_List_Olist_OCons @ SY2478 @ c_List_Olist_ONil @ SY2477 ) @ SY2477 ) @ SY2477 )
            = ( c_List_Olist_OCons @ SY2478 @ SV1121 @ SY2477 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4217]) ).

thf(5500,plain,
    ! [SV1122: $i] :
      ( ( ! [SY2479: $i] :
            ( ( c_List_Orev @ SV1122 @ SY2479 )
           != c_List_Olist_ONil )
        | ( SV1122 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4218]) ).

thf(5501,plain,
    ! [SV1123: $i] :
      ( ( ( c_List_Orev @ c_List_Olist_ONil @ SV1123 )
        = c_List_Olist_ONil )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4219]) ).

thf(5502,plain,
    ! [SV1124: $i] :
      ( ( ! [SY2480: $i,SY2481: $i] :
            ( ( ( c_List_Orev @ SV1124 @ SY2480 )
             != ( c_List_Orev @ SY2481 @ SY2480 ) )
            | ( SV1124 = SY2481 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4220]) ).

thf(5503,plain,
    ! [SV1125: $i] :
      ( ( ! [SY2482: $i,SY2483: $i,SY2484: $i] :
            ( ( ( c_append @ SV1125 @ SY2482 @ SY2483 )
             != ( c_append @ SV1125 @ SY2484 @ SY2483 ) )
            | ( SY2482 = SY2484 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4221]) ).

thf(5504,plain,
    ! [SV1126: $i] :
      ( ( ! [SY2485: $i] :
            ( ! [SY2486: $i] :
                ( SV1126
               != ( c_append @ SY2485 @ SV1126 @ SY2486 ) )
            | ( SY2485 = c_List_Olist_ONil ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4222]) ).

thf(5505,plain,
    ! [SV1127: $i] :
      ( ( ! [SY2487: $i] :
            ( SV1127
            = ( c_append @ c_List_Olist_ONil @ SV1127 @ SY2487 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4223]) ).

thf(5506,plain,
    ! [SV1128: $i] :
      ( ( ! [SY2488: $i] :
            ( ! [SY2489: $i] :
                ( SV1128
               != ( c_append @ SV1128 @ SY2488 @ SY2489 ) )
            | ( SY2488 = c_List_Olist_ONil ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4224]) ).

thf(5507,plain,
    ! [SV1129: $i] :
      ( ( ! [SY2490: $i] :
            ( SV1129
            = ( c_append @ SV1129 @ c_List_Olist_ONil @ SY2490 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4225]) ).

thf(5508,plain,
    ! [SV1130: $i] :
      ( ( ! [SY2491: $i] :
            ( c_emptyset
           != ( c_List_Oset @ SV1130 @ SY2491 ) )
        | ( SV1130 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4226]) ).

thf(5509,plain,
    ! [SV1131: $i] :
      ( ( c_emptyset
        = ( c_List_Oset @ c_List_Olist_ONil @ SV1131 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4227]) ).

thf(5510,plain,
    ! [SV1132: $i] :
      ( ( ! [SY2492: $i] :
            ( ( c_List_Oset @ SV1132 @ SY2492 )
           != c_emptyset )
        | ( SV1132 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4228]) ).

thf(5511,plain,
    ! [SV1133: $i] :
      ( ( ( c_List_Oset @ c_List_Olist_ONil @ SV1133 )
        = c_emptyset )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4229]) ).

thf(5512,plain,
    ! [SV1134: $i] :
      ( ( ! [SY2493: $i] :
            ( ( ( c_Suc @ SV1134 )
             != ( c_Suc @ SY2493 ) )
            | ( SV1134 = SY2493 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4230]) ).

thf(5513,plain,
    ! [SV1135: $i] :
      ( ( ! [SY2494: $i] :
            ( ~ ( c_lessequals @ ( c_Suc @ SV1135 ) @ ( c_Suc @ SY2494 ) @ tc_nat )
            | ( c_lessequals @ SV1135 @ SY2494 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4231]) ).

thf(5514,plain,
    ! [SV1136: $i] :
      ( ( ! [SY2495: $i] :
            ( ~ ( c_lessequals @ SV1136 @ SY2495 @ tc_nat )
            | ( c_lessequals @ ( c_Suc @ SV1136 ) @ ( c_Suc @ SY2495 ) @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4232]) ).

thf(5515,plain,
    ! [SV1137: $i] :
      ( ( ! [SY2496: $i] :
            ( ~ ( c_less @ ( c_Suc @ SV1137 ) @ ( c_Suc @ SY2496 ) @ tc_nat )
            | ( c_less @ SV1137 @ SY2496 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4233]) ).

thf(5516,plain,
    ! [SV1138: $i] :
      ( ( ! [SY2497: $i] :
            ( ~ ( c_less @ SV1138 @ SY2497 @ tc_nat )
            | ( c_less @ ( c_Suc @ SV1138 ) @ ( c_Suc @ SY2497 ) @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4234]) ).

thf(5517,plain,
    ! [SV1139: $i] :
      ( ( ( c_Suc @ SV1139 )
       != c_0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4235]) ).

thf(5518,plain,
    ! [SV1140: $i] :
      ( ( c_0
       != ( c_Suc @ SV1140 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4236]) ).

thf(5519,plain,
    ! [SV1141: $i] :
      ( ( ! [SY2498: $i] :
            ( ~ ( c_less @ c_0 @ ( c_plus @ SV1141 @ SY2498 @ tc_nat ) @ tc_nat )
            | ( c_less @ c_0 @ SY2498 @ tc_nat )
            | ( c_less @ c_0 @ SV1141 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4237]) ).

thf(5520,plain,
    ! [SV1142: $i] :
      ( ( ~ ( c_less @ c_0 @ SV1142 @ tc_nat )
        | ! [SY2499: $i] : ( c_less @ c_0 @ ( c_plus @ SV1142 @ SY2499 @ tc_nat ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4238]) ).

thf(5521,plain,
    ! [SV1143: $i] :
      ( ( ~ ( c_less @ c_0 @ SV1143 @ tc_nat )
        | ! [SY2500: $i] : ( c_less @ c_0 @ ( c_plus @ SY2500 @ SV1143 @ tc_nat ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4239]) ).

thf(5522,plain,
    ! [SV1144: $i] :
      ( ( ! [SY2501: $i] :
            ( ( c_plus @ SV1144 @ SY2501 @ tc_nat )
           != c_0 )
        | ( SV1144 = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4240]) ).

thf(5523,plain,
    ! [SV1145: $i] :
      ( ( ! [SY2502: $i] :
            ( ( ( c_plus @ SV1145 @ SY2502 @ tc_nat )
             != c_0 )
            | ( SY2502 = c_0 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4241]) ).

thf(5524,plain,
    ! [SV1146: $i] :
      ( ( ~ ( c_lessequals @ SV1146 @ c_0 @ tc_nat )
        | ( SV1146 = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4243]) ).

thf(5525,plain,
    ! [SV1147: $i] :
      ( ( ~ ( c_less @ SV1147 @ ( c_Suc @ c_0 ) @ tc_nat )
        | ( SV1147 = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4245]) ).

thf(5526,plain,
    ! [SV1148: $i] :
      ( ( ~ ( c_less @ SV1148 @ c_1 @ tc_nat )
        | ( SV1148 = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4247]) ).

thf(5527,plain,
    ! [SV1149: $i] :
      ( ( ( SV1149 = c_0 )
        | ( c_less @ c_0 @ SV1149 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4249]) ).

thf(5528,plain,
    ( ( c_less @ c_0 @ c_0 @ tc_nat )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4250]) ).

thf(5529,plain,
    ! [SV1150: $i] :
      ( ( ! [SY2503: $i] :
            ~ ( c_less @ ( c_plus @ SV1150 @ SY2503 @ tc_nat ) @ SV1150 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4251]) ).

thf(5530,plain,
    ! [SV1151: $i] :
      ( ( ! [SY2504: $i] :
            ~ ( c_less @ ( c_plus @ SV1151 @ SY2504 @ tc_nat ) @ SY2504 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4252]) ).

thf(5531,plain,
    ! [SV1152: $i] :
      ( ( ~ ( c_less @ SV1152 @ c_0 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4253]) ).

thf(5532,plain,
    ( ( c_Numeral_Obit_OB0 = c_Numeral_Obit_OB1 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4254]) ).

thf(5533,plain,
    ( ( c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4255]) ).

thf(5534,plain,
    ! [SV1153: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV1153 )
        | ! [SY2505: $i] :
            ~ ( c_less @ SY2505 @ SY2505 @ SV1153 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4256]) ).

thf(5535,plain,
    ! [SV1154: $i] :
      ( ( ! [SY2506: $i,SY2507: $i,SY2508: $i,SY2509: $i] :
            ( ! [SY2510: $i] :
                ( ( c_Pair @ SV1154 @ SY2506 @ SY2507 @ SY2508 )
               != ( c_Pair @ SY2509 @ SY2510 @ SY2507 @ SY2508 ) )
            | ( SV1154 = SY2509 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4257]) ).

thf(5536,plain,
    ! [SV1155: $i] :
      ( ( ! [SY2511: $i,SY2512: $i,SY2513: $i,SY2514: $i,SY2515: $i] :
            ( ( ( c_Pair @ SV1155 @ SY2511 @ SY2512 @ SY2513 )
             != ( c_Pair @ SY2514 @ SY2515 @ SY2512 @ SY2513 ) )
            | ( SY2511 = SY2515 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4258]) ).

thf(5537,plain,
    ! [SV1156: $i] :
      ( ( ! [SY2516: $i] : ( c_in @ ( c_Pair @ SV1156 @ SV1156 @ SY2516 @ SY2516 ) @ c_Relation_OId @ ( tc_prod @ SY2516 @ SY2516 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4259]) ).

thf(5538,plain,
    ! [SV1157: $i] :
      ( ( ! [SY2517: $i,SY2518: $i,SY2519: $i,SY2520: $i] :
            ( ~ ( c_in @ SV1157 @ ( c_Relation_OImage @ SY2517 @ ( c_insert @ SY2518 @ c_emptyset @ SY2519 ) @ SY2519 @ SY2520 ) @ SY2520 )
            | ( c_in @ ( c_Pair @ SY2518 @ SV1157 @ SY2519 @ SY2520 ) @ SY2517 @ ( tc_prod @ SY2519 @ SY2520 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4260]) ).

thf(5539,plain,
    ! [SV1158: $i] :
      ( ( ! [SY2521: $i,SY2522: $i,SY2523: $i,SY2524: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1158 @ SY2521 @ SY2522 @ SY2523 ) @ SY2524 @ ( tc_prod @ SY2522 @ SY2523 ) )
            | ( c_in @ SY2521 @ ( c_Relation_OImage @ SY2524 @ ( c_insert @ SV1158 @ c_emptyset @ SY2522 ) @ SY2522 @ SY2523 ) @ SY2523 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4261]) ).

thf(5540,plain,
    ! [SV1159: $i] :
      ( ( ! [SY2525: $i,SY2526: $i,SY2527: $i,SY2528: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1159 @ SY2525 @ SY2526 @ SY2527 ) @ ( c_Relation_Oconverse @ SY2528 @ SY2527 @ SY2526 ) @ ( tc_prod @ SY2526 @ SY2527 ) )
            | ( c_in @ ( c_Pair @ SY2525 @ SV1159 @ SY2527 @ SY2526 ) @ SY2528 @ ( tc_prod @ SY2527 @ SY2526 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4262]) ).

thf(5541,plain,
    ! [SV1160: $i] :
      ( ( ! [SY2529: $i,SY2530: $i,SY2531: $i,SY2532: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1160 @ SY2529 @ SY2530 @ SY2531 ) @ SY2532 @ ( tc_prod @ SY2530 @ SY2531 ) )
            | ( c_in @ ( c_Pair @ SY2529 @ SV1160 @ SY2531 @ SY2530 ) @ ( c_Relation_Oconverse @ SY2532 @ SY2530 @ SY2531 ) @ ( tc_prod @ SY2531 @ SY2530 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4263]) ).

thf(5542,plain,
    ! [SV1161: $i] :
      ( ( ! [SY2533: $i] :
            ( ! [SY2534: $i] :
                ~ ( c_in @ ( c_Pair @ SV1161 @ SY2533 @ SY2534 @ SY2534 ) @ c_Relation_OId @ ( tc_prod @ SY2534 @ SY2534 ) )
            | ( SV1161 = SY2533 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4264]) ).

thf(5543,plain,
    ! [SV1162: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1162 )
        | ! [SY2535: $i,SY2536: $i] :
            ( ( ( c_SetInterval_OatLeast @ SY2535 @ SV1162 )
             != ( c_SetInterval_OatLeast @ SY2536 @ SV1162 ) )
            | ( SY2535 = SY2536 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4265]) ).

thf(5544,plain,
    ! [SV1163: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1163 )
        | ! [SY2537: $i,SY2538: $i] :
            ( ~ ( c_in @ SY2537 @ ( c_SetInterval_OatLeast @ SY2538 @ SV1163 ) @ SV1163 )
            | ( c_lessequals @ SY2538 @ SY2537 @ SV1163 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4266]) ).

thf(5545,plain,
    ! [SV1164: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1164 )
        | ! [SY2539: $i,SY2540: $i] :
            ( ~ ( c_lessequals @ SY2539 @ SY2540 @ SV1164 )
            | ( c_in @ SY2540 @ ( c_SetInterval_OatLeast @ SY2539 @ SV1164 ) @ SV1164 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4267]) ).

thf(5546,plain,
    ! [SV1165: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV1165 )
        | ! [SY2541: $i,SY2542: $i] :
            ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2541 @ SV1165 ) @ ( c_SetInterval_OatLeast @ SY2542 @ SV1165 ) @ ( tc_set @ SV1165 ) )
            | ( c_lessequals @ SY2542 @ SY2541 @ SV1165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4268]) ).

thf(5547,plain,
    ! [SV1166: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV1166 )
        | ! [SY2543: $i,SY2544: $i] :
            ( ~ ( c_lessequals @ SY2543 @ SY2544 @ SV1166 )
            | ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2544 @ SV1166 ) @ ( c_SetInterval_OatLeast @ SY2543 @ SV1166 ) @ ( tc_set @ SV1166 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4269]) ).

thf(5548,plain,
    ! [SV1167: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1167 )
        | ! [SY2545: $i,SY2546: $i] :
            ( ( ( c_SetInterval_OatMost @ SY2545 @ SV1167 )
             != ( c_SetInterval_OatMost @ SY2546 @ SV1167 ) )
            | ( SY2545 = SY2546 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4270]) ).

thf(5549,plain,
    ! [SV1168: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1168 )
        | ! [SY2547: $i,SY2548: $i] :
            ( ~ ( c_in @ SY2547 @ ( c_SetInterval_OatMost @ SY2548 @ SV1168 ) @ SV1168 )
            | ( c_lessequals @ SY2547 @ SY2548 @ SV1168 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4271]) ).

thf(5550,plain,
    ! [SV1169: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1169 )
        | ! [SY2549: $i,SY2550: $i] :
            ( ~ ( c_lessequals @ SY2549 @ SY2550 @ SV1169 )
            | ( c_in @ SY2549 @ ( c_SetInterval_OatMost @ SY2550 @ SV1169 ) @ SV1169 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4272]) ).

thf(5551,plain,
    ! [SV1170: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV1170 )
        | ! [SY2551: $i,SY2552: $i] :
            ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SY2551 @ SV1170 ) @ ( c_SetInterval_OatMost @ SY2552 @ SV1170 ) @ ( tc_set @ SV1170 ) )
            | ( c_lessequals @ SY2551 @ SY2552 @ SV1170 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4273]) ).

thf(5552,plain,
    ! [SV1171: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV1171 )
        | ! [SY2553: $i,SY2554: $i] :
            ( ~ ( c_lessequals @ SY2553 @ SY2554 @ SV1171 )
            | ( c_lessequals @ ( c_SetInterval_OatMost @ SY2553 @ SV1171 ) @ ( c_SetInterval_OatMost @ SY2554 @ SV1171 ) @ ( tc_set @ SV1171 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4274]) ).

thf(5553,plain,
    ! [SV1172: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1172 )
        | ! [SY2555: $i,SY2556: $i] :
            ( ( ( c_SetInterval_OgreaterThan @ SY2555 @ SV1172 )
             != ( c_SetInterval_OgreaterThan @ SY2556 @ SV1172 ) )
            | ( SY2555 = SY2556 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4275]) ).

thf(5554,plain,
    ! [SV1173: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1173 )
        | ! [SY2557: $i,SY2558: $i] :
            ( ~ ( c_in @ SY2557 @ ( c_SetInterval_OgreaterThan @ SY2558 @ SV1173 ) @ SV1173 )
            | ( c_less @ SY2558 @ SY2557 @ SV1173 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4276]) ).

thf(5555,plain,
    ! [SV1174: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1174 )
        | ! [SY2559: $i,SY2560: $i] :
            ( ~ ( c_less @ SY2559 @ SY2560 @ SV1174 )
            | ( c_in @ SY2560 @ ( c_SetInterval_OgreaterThan @ SY2559 @ SV1174 ) @ SV1174 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4277]) ).

thf(5556,plain,
    ! [SV1175: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1175 )
        | ! [SY2561: $i,SY2562: $i] :
            ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2561 @ SV1175 ) @ ( c_SetInterval_OgreaterThan @ SY2562 @ SV1175 ) @ ( tc_set @ SV1175 ) )
            | ( c_lessequals @ SY2562 @ SY2561 @ SV1175 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4278]) ).

thf(5557,plain,
    ! [SV1176: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1176 )
        | ! [SY2563: $i,SY2564: $i] :
            ( ~ ( c_lessequals @ SY2563 @ SY2564 @ SV1176 )
            | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2564 @ SV1176 ) @ ( c_SetInterval_OgreaterThan @ SY2563 @ SV1176 ) @ ( tc_set @ SV1176 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4279]) ).

thf(5558,plain,
    ! [SV1177: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1177 )
        | ! [SY2565: $i,SY2566: $i] :
            ( ( ( c_SetInterval_OlessThan @ SY2565 @ SV1177 )
             != ( c_SetInterval_OlessThan @ SY2566 @ SV1177 ) )
            | ( SY2565 = SY2566 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4280]) ).

thf(5559,plain,
    ! [SV1178: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1178 )
        | ! [SY2567: $i,SY2568: $i] :
            ( ~ ( c_in @ SY2567 @ ( c_SetInterval_OlessThan @ SY2568 @ SV1178 ) @ SV1178 )
            | ( c_less @ SY2567 @ SY2568 @ SV1178 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4281]) ).

thf(5560,plain,
    ! [SV1179: $i] :
      ( ( ~ ( class_Orderings_Oord @ SV1179 )
        | ! [SY2569: $i,SY2570: $i] :
            ( ~ ( c_less @ SY2569 @ SY2570 @ SV1179 )
            | ( c_in @ SY2569 @ ( c_SetInterval_OlessThan @ SY2570 @ SV1179 ) @ SV1179 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4282]) ).

thf(5561,plain,
    ! [SV1180: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1180 )
        | ! [SY2571: $i,SY2572: $i] :
            ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2571 @ SV1180 ) @ ( c_SetInterval_OlessThan @ SY2572 @ SV1180 ) @ ( tc_set @ SV1180 ) )
            | ( c_lessequals @ SY2571 @ SY2572 @ SV1180 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4283]) ).

thf(5562,plain,
    ! [SV1181: $i] :
      ( ( ~ ( class_Orderings_Olinorder @ SV1181 )
        | ! [SY2573: $i,SY2574: $i] :
            ( ~ ( c_lessequals @ SY2573 @ SY2574 @ SV1181 )
            | ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2573 @ SV1181 ) @ ( c_SetInterval_OlessThan @ SY2574 @ SV1181 ) @ ( tc_set @ SV1181 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4284]) ).

thf(5563,plain,
    ! [SV1182: $i] :
      ( ( ! [SY2575: $i,SY2576: $i] :
            ( ~ ( c_in @ SV1182 @ SY2575 @ SY2576 )
            | ~ ( c_in @ SV1182 @ ( c_uminus @ SY2575 @ ( tc_set @ SY2576 ) ) @ SY2576 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4285]) ).

thf(5564,plain,
    ! [SV1183: $i] :
      ( ( ! [SY2577: $i,SY2578: $i] :
            ( ( c_in @ SV1183 @ SY2577 @ SY2578 )
            | ( c_in @ SV1183 @ ( c_uminus @ SY2577 @ ( tc_set @ SY2578 ) ) @ SY2578 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4286]) ).

thf(5565,plain,
    ! [SV1184: $i] :
      ( ( ! [SY2579: $i,SY2580: $i] :
            ( ( ( c_uminus @ SV1184 @ ( tc_set @ SY2579 ) )
             != ( c_uminus @ SY2580 @ ( tc_set @ SY2579 ) ) )
            | ( SV1184 = SY2580 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4287]) ).

thf(5566,plain,
    ! [SV1185: $i] :
      ( ( ! [SY2581: $i,SY2582: $i] :
            ( ~ ( c_lessequals @ ( c_uminus @ SV1185 @ ( tc_set @ SY2581 ) ) @ ( c_uminus @ SY2582 @ ( tc_set @ SY2581 ) ) @ ( tc_set @ SY2581 ) )
            | ( c_lessequals @ SY2582 @ SV1185 @ ( tc_set @ SY2581 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4288]) ).

thf(5567,plain,
    ! [SV1186: $i] :
      ( ( ! [SY2583: $i,SY2584: $i] :
            ( ~ ( c_lessequals @ SV1186 @ SY2583 @ ( tc_set @ SY2584 ) )
            | ( c_lessequals @ ( c_uminus @ SY2583 @ ( tc_set @ SY2584 ) ) @ ( c_uminus @ SV1186 @ ( tc_set @ SY2584 ) ) @ ( tc_set @ SY2584 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4289]) ).

thf(5568,plain,
    ! [SV1187: $i] :
      ( ( ! [SY2585: $i,SY2586: $i] :
            ( ~ ( c_in @ SV1187 @ SY2585 @ SY2586 )
            | ! [SY2587: $i] :
                ~ ( c_in @ SV1187 @ ( c_minus @ SY2587 @ SY2585 @ ( tc_set @ SY2586 ) ) @ SY2586 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4290]) ).

thf(5569,plain,
    ! [SV1188: $i] :
      ( ( ! [SY2588: $i,SY2589: $i,SY2590: $i] :
            ( ~ ( c_in @ SV1188 @ ( c_minus @ SY2588 @ SY2589 @ ( tc_set @ SY2590 ) ) @ SY2590 )
            | ( c_in @ SV1188 @ SY2588 @ SY2590 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4291]) ).

thf(5570,plain,
    ! [SV1189: $i] :
      ( ( ! [SY2591: $i,SY2592: $i] :
            ( ~ ( c_in @ SV1189 @ SY2591 @ SY2592 )
            | ! [SY2593: $i] :
                ( ( c_in @ SV1189 @ SY2593 @ SY2592 )
                | ( c_in @ SV1189 @ ( c_minus @ SY2591 @ SY2593 @ ( tc_set @ SY2592 ) ) @ SY2592 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4292]) ).

thf(5571,plain,
    ! [SV1190: $i] :
      ( ( ! [SY2594: $i,SY2595: $i,SY2596: $i] :
            ( ~ ( c_in @ SV1190 @ ( c_inter @ SY2594 @ SY2595 @ SY2596 ) @ SY2596 )
            | ( c_in @ SV1190 @ SY2595 @ SY2596 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4293]) ).

thf(5572,plain,
    ! [SV1191: $i] :
      ( ( ! [SY2597: $i,SY2598: $i,SY2599: $i] :
            ( ~ ( c_in @ SV1191 @ ( c_inter @ SY2597 @ SY2598 @ SY2599 ) @ SY2599 )
            | ( c_in @ SV1191 @ SY2597 @ SY2599 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4294]) ).

thf(5573,plain,
    ! [SV1192: $i] :
      ( ( ! [SY2600: $i,SY2601: $i] :
            ( ~ ( c_in @ SV1192 @ SY2600 @ SY2601 )
            | ! [SY2602: $i] :
                ( ~ ( c_in @ SV1192 @ SY2602 @ SY2601 )
                | ( c_in @ SV1192 @ ( c_inter @ SY2602 @ SY2600 @ SY2601 ) @ SY2601 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4295]) ).

thf(5574,plain,
    ! [SV1193: $i] :
      ( ( ! [SY2603: $i,SY2604: $i] :
            ( ~ ( c_in @ SV1193 @ SY2603 @ ( tc_set @ SY2604 ) )
            | ! [SY2605: $i] :
                ( ~ ( c_in @ SY2605 @ ( c_Inter @ SY2603 @ SY2604 ) @ SY2604 )
                | ( c_in @ SY2605 @ SV1193 @ SY2604 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4296]) ).

thf(5575,plain,
    ! [SV1194: $i] :
      ( ( ! [SY2606: $i,SY2607: $i] :
            ( ~ ( c_in @ SV1194 @ ( c_Pow @ SY2606 @ SY2607 ) @ ( tc_set @ SY2607 ) )
            | ( c_lessequals @ SV1194 @ SY2606 @ ( tc_set @ SY2607 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4297]) ).

thf(5576,plain,
    ! [SV1195: $i] :
      ( ( ! [SY2608: $i,SY2609: $i] :
            ( ~ ( c_lessequals @ SV1195 @ SY2608 @ ( tc_set @ SY2609 ) )
            | ( c_in @ SV1195 @ ( c_Pow @ SY2608 @ SY2609 ) @ ( tc_set @ SY2609 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4298]) ).

thf(5577,plain,
    ( ( c_UNIV = c_emptyset )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4299]) ).

thf(5578,plain,
    ! [SV1196: $i] :
      ( ( ! [SY2610: $i,SY2611: $i] :
            ( ~ ( c_in @ SV1196 @ SY2610 @ SY2611 )
            | ! [SY2612: $i] : ( c_in @ SV1196 @ ( c_union @ SY2612 @ SY2610 @ SY2611 ) @ SY2611 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4300]) ).

thf(5579,plain,
    ! [SV1197: $i] :
      ( ( ! [SY2613: $i,SY2614: $i] :
            ( ~ ( c_in @ SV1197 @ SY2613 @ SY2614 )
            | ! [SY2615: $i] : ( c_in @ SV1197 @ ( c_union @ SY2613 @ SY2615 @ SY2614 ) @ SY2614 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4301]) ).

thf(5580,plain,
    ! [SV1198: $i] :
      ( ( ! [SY2616: $i,SY2617: $i,SY2618: $i] :
            ( ~ ( c_in @ SV1198 @ ( c_union @ SY2616 @ SY2617 @ SY2618 ) @ SY2618 )
            | ( c_in @ SV1198 @ SY2617 @ SY2618 )
            | ( c_in @ SV1198 @ SY2616 @ SY2618 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4302]) ).

thf(5581,plain,
    ! [SV1199: $i] :
      ( ( ! [SY2619: $i,SY2620: $i] :
            ( ( c_union @ SV1199 @ SY2619 @ SY2620 )
           != c_emptyset )
        | ( SV1199 = c_emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4303]) ).

thf(5582,plain,
    ! [SV1200: $i] :
      ( ( ! [SY2621: $i] :
            ( ! [SY2622: $i] :
                ( ( c_union @ SV1200 @ SY2621 @ SY2622 )
               != c_emptyset )
            | ( SY2621 = c_emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4304]) ).

thf(5583,plain,
    ! [SV1201: $i] :
      ( ( ( c_union @ c_emptyset @ c_emptyset @ SV1201 )
        = c_emptyset )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4305]) ).

thf(5584,plain,
    ! [SV1202: $i] :
      ( ( ! [SY2623: $i,SY2624: $i] :
            ( ~ ( c_in @ SV1202 @ SY2623 @ SY2624 )
            | ! [SY2625: $i] :
                ( ~ ( c_in @ SY2623 @ SY2625 @ ( tc_set @ SY2624 ) )
                | ( c_in @ SV1202 @ ( c_Union @ SY2625 @ SY2624 ) @ SY2624 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4306]) ).

thf(5585,plain,
    ! [SV1203: $i] :
      ( ( ! [SY2626: $i] :
            ~ ( c_in @ SV1203 @ c_emptyset @ SY2626 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4307]) ).

thf(5586,plain,
    ! [SV1204: $i] :
      ( ( ! [SY2627: $i,SY2628: $i] :
            ( ~ ( c_in @ SV1204 @ SY2627 @ SY2628 )
            | ! [SY2629: $i] : ( c_in @ SV1204 @ ( c_insert @ SY2629 @ SY2627 @ SY2628 ) @ SY2628 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4308]) ).

thf(5587,plain,
    ! [SV1205: $i] :
      ( ( ! [SY2630: $i,SY2631: $i] : ( c_in @ SV1205 @ ( c_insert @ SV1205 @ SY2630 @ SY2631 ) @ SY2631 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4309]) ).

thf(5588,plain,
    ! [SV1206: $i] :
      ( ( ! [SY2632: $i,SY2633: $i,SY2634: $i] :
            ( ~ ( c_in @ SV1206 @ ( c_insert @ SY2632 @ SY2633 @ SY2634 ) @ SY2634 )
            | ( SV1206 = SY2632 )
            | ( c_in @ SV1206 @ SY2633 @ SY2634 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4310]) ).

thf(5589,plain,
    ! [SV1207: $i] :
      ( ( ! [SY2635: $i] :
            ~ ( c_less @ SV1207 @ c_emptyset @ ( tc_set @ SY2635 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4311]) ).

thf(5590,plain,
    ! [SV1208: $i] :
      ( ( ! [SY2636: $i,SY2637: $i,SY2638: $i] :
            ( ( ( c_insert @ SV1208 @ SY2636 @ SY2637 )
             != ( c_insert @ SY2638 @ c_emptyset @ SY2637 ) )
            | ( SV1208 = SY2638 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4312]) ).

thf(5591,plain,
    ! [SV1209: $i] :
      ( ( ! [SY2639: $i,SY2640: $i,SY2641: $i] :
            ( ( ( c_insert @ SV1209 @ SY2639 @ SY2640 )
             != ( c_insert @ SY2641 @ c_emptyset @ SY2640 ) )
            | ( c_lessequals @ SY2639 @ ( c_insert @ SY2641 @ c_emptyset @ SY2640 ) @ ( tc_set @ SY2640 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4313]) ).

thf(5592,plain,
    ! [SV1210: $i] :
      ( ( ! [SY2642: $i,SY2643: $i] :
            ( ~ ( c_lessequals @ SV1210 @ ( c_insert @ SY2642 @ c_emptyset @ SY2643 ) @ ( tc_set @ SY2643 ) )
            | ( ( c_insert @ SY2642 @ SV1210 @ SY2643 )
              = ( c_insert @ SY2642 @ c_emptyset @ SY2643 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4314]) ).

thf(5593,plain,
    ! [SV1211: $i] :
      ( ( ! [SY2644: $i,SY2645: $i] :
            ( ! [SY2646: $i] :
                ( ( c_insert @ SV1211 @ c_emptyset @ SY2644 )
               != ( c_insert @ SY2645 @ SY2646 @ SY2644 ) )
            | ( SY2645 = SV1211 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4315]) ).

thf(5594,plain,
    ! [SV1212: $i] :
      ( ( ! [SY2647: $i,SY2648: $i,SY2649: $i] :
            ( ( ( c_insert @ SV1212 @ c_emptyset @ SY2647 )
             != ( c_insert @ SY2648 @ SY2649 @ SY2647 ) )
            | ( c_lessequals @ SY2649 @ ( c_insert @ SV1212 @ c_emptyset @ SY2647 ) @ ( tc_set @ SY2647 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4316]) ).

thf(5595,plain,
    ! [SV1213: $i] :
      ( ( ! [SY2650: $i,SY2651: $i] :
            ( ~ ( c_lessequals @ SV1213 @ ( c_insert @ SY2650 @ c_emptyset @ SY2651 ) @ ( tc_set @ SY2651 ) )
            | ( ( c_insert @ SY2650 @ c_emptyset @ SY2651 )
              = ( c_insert @ SY2650 @ SV1213 @ SY2651 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4317]) ).

thf(5596,plain,
    ! [SV1214: $i] :
      ( ( ! [SY2652: $i,SY2653: $i,SY2654: $i] :
            ( ( ( c_Sum__Type_OInl @ SV1214 @ SY2652 @ SY2653 )
             != ( c_Sum__Type_OInl @ SY2654 @ SY2652 @ SY2653 ) )
            | ( SV1214 = SY2654 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4318]) ).

thf(5597,plain,
    ! [SV1215: $i] :
      ( ( ! [SY2655: $i,SY2656: $i,SY2657: $i] :
            ( ( c_Sum__Type_OInl @ SV1215 @ SY2655 @ SY2656 )
           != ( c_Sum__Type_OInr @ SY2657 @ SY2656 @ SY2655 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4319]) ).

thf(5598,plain,
    ! [SV1216: $i] :
      ( ( ! [SY2658: $i,SY2659: $i,SY2660: $i] :
            ( ( ( c_Sum__Type_OInr @ SV1216 @ SY2658 @ SY2659 )
             != ( c_Sum__Type_OInr @ SY2660 @ SY2658 @ SY2659 ) )
            | ( SV1216 = SY2660 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4320]) ).

thf(5599,plain,
    ! [SV1217: $i] :
      ( ( ! [SY2661: $i,SY2662: $i,SY2663: $i] :
            ( ( c_Sum__Type_OInr @ SV1217 @ SY2661 @ SY2662 )
           != ( c_Sum__Type_OInl @ SY2663 @ SY2662 @ SY2661 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4321]) ).

thf(5600,plain,
    ! [SV1218: $i] :
      ( ( ! [SY2664: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1218 @ SY2664 @ SY2664 ) @ SY2664 )
            | ( c_Wellfounded__Recursion_Oacyclic @ SV1218 @ SY2664 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4322]) ).

thf(5601,plain,
    ! [SV1219: $i] :
      ( ( ! [SY2665: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1219 @ SY2665 )
            | ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1219 @ SY2665 @ SY2665 ) @ SY2665 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4323]) ).

thf(5602,plain,
    ! [SV1220: $i] :
      ( ( ! [SY2666: $i,SY2667: $i,SY2668: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1220 @ SY2666 @ SY2667 @ SY2667 ) @ SY2668 @ ( tc_prod @ SY2667 @ SY2667 ) ) @ SY2667 )
            | ( c_Wellfounded__Recursion_Oacyclic @ SY2668 @ SY2667 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4324]) ).

thf(5603,plain,
    ! [SV1221: $i] :
      ( ( ! [SY2669: $i,SY2670: $i,SY2671: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1221 @ SY2669 @ SY2670 @ SY2670 ) @ SY2671 @ ( tc_prod @ SY2670 @ SY2670 ) ) @ SY2670 )
            | ~ ( c_in @ ( c_Pair @ SY2669 @ SV1221 @ SY2670 @ SY2670 ) @ ( c_Transitive__Closure_Ortrancl @ SY2671 @ SY2670 ) @ ( tc_prod @ SY2670 @ SY2670 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4325]) ).

thf(5604,plain,
    ! [SV1222: $i] :
      ( ( ! [SY2672: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1222 @ SY2672 )
            | ! [SY2673: $i,SY2674: $i] :
                ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SY2673 @ SY2674 @ SY2672 @ SY2672 ) @ SV1222 @ ( tc_prod @ SY2672 @ SY2672 ) ) @ SY2672 )
                | ( c_in @ ( c_Pair @ SY2674 @ SY2673 @ SY2672 @ SY2672 ) @ ( c_Transitive__Closure_Ortrancl @ SV1222 @ SY2672 ) @ ( tc_prod @ SY2672 @ SY2672 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4326]) ).

thf(5605,plain,
    ! [SV1223: $i] :
      ( ( ! [SY2675: $i,SY2676: $i,SY2677: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1223 @ SY2675 @ SY2676 @ SY2676 ) @ SY2677 @ ( tc_prod @ SY2676 @ SY2676 ) ) @ SY2676 )
            | ( c_Wellfounded__Recursion_Owf @ SY2677 @ SY2676 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4327]) ).

thf(5606,plain,
    ! [SV1224: $i] :
      ( ( ! [SY2678: $i,SY2679: $i,SY2680: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1224 @ SY2678 @ SY2679 @ SY2679 ) @ SY2680 @ ( tc_prod @ SY2679 @ SY2679 ) ) @ SY2679 )
            | ~ ( c_in @ ( c_Pair @ SY2678 @ SV1224 @ SY2679 @ SY2679 ) @ ( c_Transitive__Closure_Ortrancl @ SY2680 @ SY2679 ) @ ( tc_prod @ SY2679 @ SY2679 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4328]) ).

thf(5607,plain,
    ! [SV1225: $i] :
      ( ( ! [SY2681: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ SV1225 @ SY2681 )
            | ! [SY2682: $i,SY2683: $i] :
                ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SY2682 @ SY2683 @ SY2681 @ SY2681 ) @ SV1225 @ ( tc_prod @ SY2681 @ SY2681 ) ) @ SY2681 )
                | ( c_in @ ( c_Pair @ SY2683 @ SY2682 @ SY2681 @ SY2681 ) @ ( c_Transitive__Closure_Ortrancl @ SV1225 @ SY2681 ) @ ( tc_prod @ SY2681 @ SY2681 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4329]) ).

thf(5608,plain,
    ! [SV1226: $i] :
      ( ( ! [SY2684: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1226 @ SY2684 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
            | ( c_less @ SV1226 @ SY2684 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4330]) ).

thf(5609,plain,
    ! [SV1227: $i] :
      ( ( ! [SY2685: $i] :
            ( ~ ( c_less @ SV1227 @ SY2685 @ tc_nat )
            | ( c_in @ ( c_Pair @ SV1227 @ SY2685 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4331]) ).

thf(5610,plain,
    ! [SV1228: $i] :
      ( ( ! [SY2686: $i,SY2687: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SY2686 ) @ ( c_Message_Osynth @ SY2687 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SY2686 ) @ SY2687 @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OKey @ SV1228 ) @ SY2687 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4332]) ).

thf(5611,plain,
    ! [SV1229: $i] :
      ( ( ! [SY2688: $i,SY2689: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SY2688 ) @ ( c_Message_Osynth @ SY2689 ) @ tc_Message_Omsg )
            | ( c_in @ SY2688 @ ( c_Message_Osynth @ SY2689 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SY2688 ) @ SY2689 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4333]) ).

thf(5612,plain,
    ! [SV1230: $i] :
      ( ( ! [SY2690: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ ( c_Message_Osynth @ SY2690 ) @ tc_Message_Omsg )
            | ( c_in @ SV1230 @ ( c_Message_Osynth @ SY2690 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ SY2690 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4334]) ).

thf(5613,plain,
    ! [SV1231: $i] :
      ( ( ! [SY2691: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ ( c_Message_Osynth @ SY2691 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ SY2691 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4335]) ).

thf(5614,plain,
    ! [SV1232: $i] :
      ( ( ! [SY2692: $i,SY2693: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1232 @ SY2692 ) @ ( c_Message_Oanalz @ SY2693 ) @ tc_Message_Omsg )
            | ( c_in @ SY2692 @ ( c_Message_Oanalz @ SY2693 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4336]) ).

thf(5615,plain,
    ! [SV1233: $i] :
      ( ( ! [SY2694: $i,SY2695: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1233 @ SY2694 ) @ ( c_Message_Oanalz @ SY2695 ) @ tc_Message_Omsg )
            | ( c_in @ SV1233 @ ( c_Message_Oanalz @ SY2695 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4337]) ).

thf(5616,plain,
    ! [SV1234: $i] :
      ( ( ! [SY2696: $i,SY2697: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1234 @ SY2696 ) @ ( c_Message_Oparts @ SY2697 ) @ tc_Message_Omsg )
            | ( c_in @ SY2696 @ ( c_Message_Oparts @ SY2697 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4338]) ).

thf(5617,plain,
    ! [SV1235: $i] :
      ( ( ! [SY2698: $i,SY2699: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1235 @ SY2698 ) @ ( c_Message_Oparts @ SY2699 ) @ tc_Message_Omsg )
            | ( c_in @ SV1235 @ ( c_Message_Oparts @ SY2699 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4339]) ).

thf(5618,plain,
    ! [SV1236: $i] :
      ( ( ! [SY2700: $i,SY2701: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SY2700 ) @ ( c_Message_Osynth @ SY2701 ) @ tc_Message_Omsg )
            | ( c_in @ SY2700 @ ( c_Message_Osynth @ SY2701 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SY2700 ) @ SY2701 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4340]) ).

thf(5619,plain,
    ! [SV1237: $i] :
      ( ( ! [SY2702: $i,SY2703: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SY2702 ) @ ( c_Message_Osynth @ SY2703 ) @ tc_Message_Omsg )
            | ( c_in @ SV1237 @ ( c_Message_Osynth @ SY2703 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SY2702 ) @ SY2703 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4341]) ).

thf(5620,plain,
    ! [SV1238: $i] :
      ( ( ! [SY2704: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ ( c_Message_Osynth @ SY2704 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ SY2704 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4342]) ).

thf(5621,plain,
    ! [SV1239: $i] :
      ( ( c_Message_Oagent_OServer
       != ( c_Message_Oagent_OFriend @ SV1239 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4343]) ).

thf(5622,plain,
    ! [SV1240: $i] :
      ( ( ( c_Message_Oagent_OFriend @ SV1240 )
       != c_Message_Oagent_OServer )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4344]) ).

thf(5623,plain,
    ( ( c_Message_Oagent_OServer = c_Message_Oagent_OSpy )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4345]) ).

thf(5624,plain,
    ( ( c_Message_Oagent_OSpy = c_Message_Oagent_OServer )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[4346]) ).

thf(5625,plain,
    ! [SV1241: $i] :
      ( ( ( c_Message_Oagent_OFriend @ SV1241 )
       != c_Message_Oagent_OSpy )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4347]) ).

thf(5626,plain,
    ! [SV1242: $i] :
      ( ( c_Message_Oagent_OSpy
       != ( c_Message_Oagent_OFriend @ SV1242 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4348]) ).

thf(5627,plain,
    ! [SV1243: $i] :
      ( ( ! [SY2705: $i] :
            ( ( ( c_Message_Oagent_OFriend @ SV1243 )
             != ( c_Message_Oagent_OFriend @ SY2705 ) )
            | ( SV1243 = SY2705 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4349]) ).

thf(5628,plain,
    ! [SV1244: $i] :
      ( ( ! [SY2706: $i,SY2707: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1244 @ SY2706 ) @ ( c_Message_Oanalz @ SY2707 ) @ tc_Message_Omsg )
            | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1244 ) ) @ ( c_Message_Oanalz @ SY2707 ) @ tc_Message_Omsg )
            | ( c_in @ SY2706 @ ( c_Message_Oanalz @ SY2707 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4350]) ).

thf(5629,plain,
    ! [SV1245: $i] :
      ( ( ! [SY2708: $i] :
            ( ~ ( c_in @ SV1245 @ SY2708 @ tc_Message_Omsg )
            | ( c_in @ SV1245 @ ( c_Message_Oanalz @ SY2708 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4351]) ).

thf(5630,plain,
    ! [SV1246: $i] :
      ( ( ! [SY2709: $i] :
            ( ~ ( c_in @ SV1246 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SY2709 ) ) @ tc_Message_Omsg )
            | ( c_in @ SV1246 @ ( c_Message_Oanalz @ SY2709 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4352]) ).

thf(5631,plain,
    ! [SV1247: $i] :
      ( ( ! [SY2710: $i,SY2711: $i] :
            ( ~ ( c_in @ SV1247 @ ( c_Message_Oparts @ ( c_union @ SY2710 @ SY2711 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
            | ( c_in @ SV1247 @ ( c_Message_Oparts @ SY2711 ) @ tc_Message_Omsg )
            | ( c_in @ SV1247 @ ( c_Message_Oparts @ SY2710 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4353]) ).

thf(5632,plain,
    ! [SV1248: $i] :
      ( ( ! [SY2712: $i] :
            ( ( ( c_Message_Omsg_OAgent @ SV1248 )
             != ( c_Message_Omsg_OAgent @ SY2712 ) )
            | ( SV1248 = SY2712 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4354]) ).

thf(5633,plain,
    ! [SV1249: $i] :
      ( ( ! [SY2713: $i] :
            ( ( ( c_Message_Omsg_ONumber @ SV1249 )
             != ( c_Message_Omsg_ONumber @ SY2713 ) )
            | ( SV1249 = SY2713 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4355]) ).

thf(5634,plain,
    ! [SV1250: $i] :
      ( ( ! [SY2714: $i] :
            ( ( ( c_Message_Omsg_ONonce @ SV1250 )
             != ( c_Message_Omsg_ONonce @ SY2714 ) )
            | ( SV1250 = SY2714 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4356]) ).

thf(5635,plain,
    ! [SV1251: $i] :
      ( ( ! [SY2715: $i] :
            ( ( ( c_Message_Omsg_OKey @ SV1251 )
             != ( c_Message_Omsg_OKey @ SY2715 ) )
            | ( SV1251 = SY2715 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4357]) ).

thf(5636,plain,
    ! [SV1252: $i] :
      ( ( ! [SY2716: $i] :
            ( ( ( c_Message_Omsg_OHash @ SV1252 )
             != ( c_Message_Omsg_OHash @ SY2716 ) )
            | ( SV1252 = SY2716 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4358]) ).

thf(5637,plain,
    ! [SV1253: $i] :
      ( ( ! [SY2717: $i,SY2718: $i] :
            ( ! [SY2719: $i] :
                ( ( c_Message_Omsg_OMPair @ SV1253 @ SY2717 )
               != ( c_Message_Omsg_OMPair @ SY2718 @ SY2719 ) )
            | ( SV1253 = SY2718 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4359]) ).

thf(5638,plain,
    ! [SV1254: $i] :
      ( ( ! [SY2720: $i,SY2721: $i,SY2722: $i] :
            ( ( ( c_Message_Omsg_OMPair @ SV1254 @ SY2720 )
             != ( c_Message_Omsg_OMPair @ SY2721 @ SY2722 ) )
            | ( SY2720 = SY2722 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4360]) ).

thf(5639,plain,
    ! [SV1255: $i] :
      ( ( ! [SY2723: $i,SY2724: $i] :
            ( ! [SY2725: $i] :
                ( ( c_Message_Omsg_OCrypt @ SV1255 @ SY2723 )
               != ( c_Message_Omsg_OCrypt @ SY2724 @ SY2725 ) )
            | ( SV1255 = SY2724 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4361]) ).

thf(5640,plain,
    ! [SV1256: $i] :
      ( ( ! [SY2726: $i,SY2727: $i,SY2728: $i] :
            ( ( ( c_Message_Omsg_OCrypt @ SV1256 @ SY2726 )
             != ( c_Message_Omsg_OCrypt @ SY2727 @ SY2728 ) )
            | ( SY2726 = SY2728 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4362]) ).

thf(5641,plain,
    ! [SV1257: $i] :
      ( ( ! [SY2729: $i] :
            ( ~ ( c_in @ SV1257 @ SY2729 @ tc_Message_Omsg )
            | ( c_in @ SV1257 @ ( c_Message_Oparts @ SY2729 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4363]) ).

thf(5642,plain,
    ! [SV1258: $i] :
      ( ( ~ ( c_in @ SV1258 @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4364]) ).

thf(5643,plain,
    ! [SV1259: $i] :
      ( ( ! [SY2730: $i] :
            ( ~ ( c_in @ SV1259 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SY2730 ) ) @ tc_Message_Omsg )
            | ( c_in @ SV1259 @ ( c_Message_Oparts @ SY2730 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4365]) ).

thf(5644,plain,
    ! [SV1260: $i] :
      ( ( ! [SY2731: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ SV1260 ) @ ( c_Message_Osynth @ SY2731 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4366]) ).

thf(5645,plain,
    ! [SV1261: $i] :
      ( ( ! [SY2732: $i] :
            ( ~ ( c_in @ SV1261 @ ( c_Message_Osynth @ SY2732 ) @ tc_Message_Omsg )
            | ! [SY2733: $i] :
                ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SY2733 ) @ SY2732 @ tc_Message_Omsg )
                | ( c_in @ ( c_Message_Omsg_OCrypt @ SY2733 @ SV1261 ) @ ( c_Message_Osynth @ SY2732 ) @ tc_Message_Omsg ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4367]) ).

thf(5646,plain,
    ! [SV1262: $i] :
      ( ( ! [SY2734: $i] :
            ( ~ ( c_in @ SV1262 @ ( c_Message_Osynth @ SY2734 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OHash @ SV1262 ) @ ( c_Message_Osynth @ SY2734 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4368]) ).

thf(5647,plain,
    ! [SV1263: $i] :
      ( ( ! [SY2735: $i] :
            ( ~ ( c_in @ SV1263 @ SY2735 @ tc_Message_Omsg )
            | ( c_in @ SV1263 @ ( c_Message_Osynth @ SY2735 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4369]) ).

thf(5648,plain,
    ! [SV1264: $i] :
      ( ( ! [SY2736: $i] :
            ( ~ ( c_in @ SV1264 @ ( c_Message_Osynth @ SY2736 ) @ tc_Message_Omsg )
            | ! [SY2737: $i] :
                ( ~ ( c_in @ SY2737 @ ( c_Message_Osynth @ SY2736 ) @ tc_Message_Omsg )
                | ( c_in @ ( c_Message_Omsg_OMPair @ SY2737 @ SV1264 ) @ ( c_Message_Osynth @ SY2736 ) @ tc_Message_Omsg ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4370]) ).

thf(5649,plain,
    ! [SV1265: $i] :
      ( ( ! [SY2738: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ SV1265 ) @ ( c_Message_Osynth @ SY2738 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4371]) ).

thf(5650,plain,
    ! [SV1266: $i] :
      ( ( ! [SY2739: $i] :
            ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SY2739 ) @ ( tc_set @ tc_Message_Omsg ) )
            | ! [SY2740: $i,SY2741: $i] :
                ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SY2740 ) @ ( c_Message_Oanalz @ SY2741 ) @ ( tc_set @ tc_Message_Omsg ) )
                | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SY2740 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SY2741 @ SY2739 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4372]) ).

thf(5651,plain,
    ! [SV1267: $i] :
      ( ( ! [SY2742: $i] :
            ( ~ ( c_in @ SV1267 @ ( c_Message_Osynth @ ( c_Message_Osynth @ SY2742 ) ) @ tc_Message_Omsg )
            | ( c_in @ SV1267 @ ( c_Message_Osynth @ SY2742 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4373]) ).

thf(5652,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[4374]) ).

thf(5653,plain,
    ! [SV1268: $i,SV1: $i] :
      ( ( ! [SY2743: $i,SY2744: $i] :
            ( ( ( c_Datatype__Universe_OLeaf @ SV1 @ SV1268 @ SY2743 )
             != ( c_Datatype__Universe_OLeaf @ SY2744 @ SV1268 @ SY2743 ) )
            | ( SV1 = SY2744 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4376]) ).

thf(5654,plain,
    ! [SV1269: $i,SV2: $i] :
      ( ( ! [SY2745: $i,SY2746: $i] :
            ( ( ( c_Datatype__Universe_ONumb @ SV2 @ SV1269 @ SY2745 )
             != ( c_Datatype__Universe_ONumb @ SY2746 @ SV1269 @ SY2745 ) )
            | ( SV2 = SY2746 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4377]) ).

thf(5655,plain,
    ! [SV1270: $i,SV3: $i] :
      ( ( ! [SY2747: $i,SY2748: $i,SY2749: $i] :
            ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1270 @ SY2747 @ SY2748 @ SY2749 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2748 @ SY2749 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2748 @ SY2749 ) ) ) )
            | ( SV3
              = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV3 @ SV1270 @ SY2747 @ SY2748 @ SY2749 ) @ ( c_Main_OdprodE__2 @ SV3 @ SV1270 @ SY2747 @ SY2748 @ SY2749 ) @ SY2748 @ SY2749 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV3 @ SV1270 @ SY2747 @ SY2748 @ SY2749 ) @ ( c_Main_OdprodE__4 @ SV3 @ SV1270 @ SY2747 @ SY2748 @ SY2749 ) @ SY2748 @ SY2749 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2748 @ SY2749 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2748 @ SY2749 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4378]) ).

thf(5656,plain,
    ! [SV1271: $i,SV4: $i] :
      ( ( ! [SY2750: $i,SY2751: $i,SY2752: $i] :
            ( ~ ( c_in @ SV4 @ ( c_Datatype__Universe_Odprod @ SV1271 @ SY2750 @ SY2751 @ SY2752 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV4 @ SV1271 @ SY2750 @ SY2751 @ SY2752 ) @ ( c_Main_OdprodE__4 @ SV4 @ SV1271 @ SY2750 @ SY2751 @ SY2752 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) ) @ SY2750 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4379]) ).

thf(5657,plain,
    ! [SV1272: $i,SV5: $i] :
      ( ( ! [SY2753: $i,SY2754: $i,SY2755: $i] :
            ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odprod @ SV1272 @ SY2753 @ SY2754 @ SY2755 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2754 @ SY2755 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2754 @ SY2755 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV5 @ SV1272 @ SY2753 @ SY2754 @ SY2755 ) @ ( c_Main_OdprodE__3 @ SV5 @ SV1272 @ SY2753 @ SY2754 @ SY2755 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2754 @ SY2755 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2754 @ SY2755 ) ) ) @ SV1272 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2754 @ SY2755 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2754 @ SY2755 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4380]) ).

thf(5658,plain,
    ! [SV1273: $i,SV6: $i] :
      ( ( ! [SY2756: $i,SY2757: $i,SY2758: $i,SY2759: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) ) @ SY2758 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) ) )
            | ! [SY2760: $i,SY2761: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY2759 @ SY2760 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) ) @ SY2761 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) ) )
                | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY2759 @ SV6 @ SY2756 @ SY2757 ) @ ( c_Datatype__Universe_OScons @ SY2760 @ SV1273 @ SY2756 @ SY2757 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY2761 @ SY2758 @ SY2756 @ SY2757 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4381]) ).

thf(5659,plain,
    ! [SV1274: $i,SV7: $i] :
      ( ( ! [SY2762: $i,SY2763: $i,SY2764: $i] :
            ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1274 @ SY2762 @ SY2763 @ SY2764 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2763 @ SY2764 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2763 @ SY2764 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1274 @ SV7 @ SY2763 @ SY2764 ) @ SY2763 @ SY2764 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1274 @ SV7 @ SY2763 @ SY2764 ) @ SY2763 @ SY2764 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2763 @ SY2764 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2763 @ SY2764 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2762 @ SV7 @ SY2763 @ SY2764 ) @ SY2763 @ SY2764 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2762 @ SV7 @ SY2763 @ SY2764 ) @ SY2763 @ SY2764 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2763 @ SY2764 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2763 @ SY2764 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4382]) ).

thf(5660,plain,
    ! [SV1275: $i,SV8: $i] :
      ( ( ! [SY2765: $i,SY2766: $i,SY2767: $i] :
            ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1275 @ SY2765 @ SY2766 @ SY2767 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) ) )
            | ( SV8
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1275 @ SV8 @ SY2766 @ SY2767 ) @ SY2766 @ SY2767 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1275 @ SV8 @ SY2766 @ SY2767 ) @ SY2766 @ SY2767 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2765 @ SV8 @ SY2766 @ SY2767 ) @ ( c_Main_OdsumE__4 @ SY2765 @ SV8 @ SY2766 @ SY2767 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) ) @ SY2765 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2766 @ SY2767 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4383]) ).

thf(5661,plain,
    ! [SV1276: $i,SV9: $i] :
      ( ( ! [SY2768: $i,SY2769: $i,SY2770: $i] :
            ( ~ ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SV1276 @ SY2768 @ SY2769 @ SY2770 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) ) )
            | ( SV9
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2768 @ SV9 @ SY2769 @ SY2770 ) @ SY2769 @ SY2770 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2768 @ SV9 @ SY2769 @ SY2770 ) @ SY2769 @ SY2770 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1276 @ SV9 @ SY2769 @ SY2770 ) @ ( c_Main_OdsumE__2 @ SV1276 @ SV9 @ SY2769 @ SY2770 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) ) @ SV1276 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2769 @ SY2770 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4384]) ).

thf(5662,plain,
    ! [SV1277: $i,SV10: $i] :
      ( ( ! [SY2771: $i,SY2772: $i,SY2773: $i] :
            ( ~ ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SV1277 @ SY2771 @ SY2772 @ SY2773 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1277 @ SV10 @ SY2772 @ SY2773 ) @ ( c_Main_OdsumE__2 @ SV1277 @ SV10 @ SY2772 @ SY2773 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) ) @ SV1277 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2771 @ SV10 @ SY2772 @ SY2773 ) @ ( c_Main_OdsumE__4 @ SY2771 @ SV10 @ SY2772 @ SY2773 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) ) @ SY2771 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2772 @ SY2773 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4385]) ).

thf(5663,plain,
    ! [SV1278: $i,SV11: $i] :
      ( ( ! [SY2774: $i,SY2775: $i,SY2776: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV11 @ SV1278 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) ) @ SY2776 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) ) )
            | ! [SY2777: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SY2774 @ SY2775 ) @ ( c_Datatype__Universe_OIn0 @ SV1278 @ SY2774 @ SY2775 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2776 @ SY2777 @ SY2774 @ SY2775 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2774 @ SY2775 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4386]) ).

thf(5664,plain,
    ! [SV1279: $i,SV12: $i] :
      ( ( ! [SY2778: $i,SY2779: $i,SY2780: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV12 @ SV1279 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) ) @ SY2780 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) ) )
            | ! [SY2781: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SY2778 @ SY2779 ) @ ( c_Datatype__Universe_OIn1 @ SV1279 @ SY2778 @ SY2779 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2781 @ SY2780 @ SY2778 @ SY2779 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2778 @ SY2779 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4387]) ).

thf(5665,plain,
    ! [SV1280: $i,SV13: $i] :
      ( ( ! [SY2782: $i,SY2783: $i,SY2784: $i] :
            ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1280 @ SY2782 @ SY2783 @ SY2784 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2783 @ SY2784 ) ) )
            | ( SV13
              = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1280 @ SY2782 @ SV13 @ SY2783 @ SY2784 ) @ ( c_Main_OuprodE__2 @ SV1280 @ SY2782 @ SV13 @ SY2783 @ SY2784 ) @ SY2783 @ SY2784 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4388]) ).

thf(5666,plain,
    ! [SV1281: $i,SV14: $i] :
      ( ( ! [SY2785: $i,SY2786: $i,SY2787: $i] :
            ( ~ ( c_in @ SV14 @ ( c_Datatype__Universe_Ouprod @ SV1281 @ SY2785 @ SY2786 @ SY2787 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2786 @ SY2787 ) ) )
            | ( c_in @ ( c_Main_OuprodE__2 @ SV1281 @ SY2785 @ SV14 @ SY2786 @ SY2787 ) @ SY2785 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2786 @ SY2787 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4389]) ).

thf(5667,plain,
    ! [SV1282: $i,SV15: $i] :
      ( ( ! [SY2788: $i,SY2789: $i,SY2790: $i] :
            ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ouprod @ SV1282 @ SY2788 @ SY2789 @ SY2790 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2789 @ SY2790 ) ) )
            | ( c_in @ ( c_Main_OuprodE__1 @ SV1282 @ SY2788 @ SV15 @ SY2789 @ SY2790 ) @ SV1282 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2789 @ SY2790 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4390]) ).

thf(5668,plain,
    ! [SV1283: $i,SV16: $i] :
      ( ( ! [SY2791: $i,SY2792: $i] :
            ( ~ ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2791 @ SY2792 ) ) )
            | ! [SY2793: $i,SY2794: $i] :
                ( ~ ( c_in @ SY2793 @ SY2794 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2791 @ SY2792 ) ) )
                | ( c_in @ ( c_Datatype__Universe_OScons @ SY2793 @ SV16 @ SY2791 @ SY2792 ) @ ( c_Datatype__Universe_Ouprod @ SY2794 @ SV1283 @ SY2791 @ SY2792 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2791 @ SY2792 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4391]) ).

thf(5669,plain,
    ! [SV1284: $i,SV17: $i] :
      ( ( ! [SY2795: $i,SY2796: $i,SY2797: $i] :
            ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1284 @ SY2795 @ SY2796 @ SY2797 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2796 @ SY2797 ) ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1284 @ SV17 @ SY2796 @ SY2797 ) @ SY2796 @ SY2797 ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2795 @ SV17 @ SY2796 @ SY2797 ) @ SY2796 @ SY2797 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4392]) ).

thf(5670,plain,
    ! [SV1285: $i,SV18: $i] :
      ( ( ! [SY2798: $i,SY2799: $i,SY2800: $i] :
            ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1285 @ SY2798 @ SY2799 @ SY2800 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2799 @ SY2800 ) ) )
            | ( SV18
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1285 @ SV18 @ SY2799 @ SY2800 ) @ SY2799 @ SY2800 ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SY2798 @ SV18 @ SY2799 @ SY2800 ) @ SY2798 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2799 @ SY2800 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4393]) ).

thf(5671,plain,
    ! [SV1286: $i,SV19: $i] :
      ( ( ! [SY2801: $i,SY2802: $i,SY2803: $i] :
            ( ~ ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SV1286 @ SY2801 @ SY2802 @ SY2803 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2802 @ SY2803 ) ) )
            | ( SV19
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2801 @ SV19 @ SY2802 @ SY2803 ) @ SY2802 @ SY2803 ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SV1286 @ SV19 @ SY2802 @ SY2803 ) @ SV1286 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2802 @ SY2803 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4394]) ).

thf(5672,plain,
    ! [SV1287: $i,SV20: $i] :
      ( ( ! [SY2804: $i,SY2805: $i,SY2806: $i] :
            ( ~ ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SV1287 @ SY2804 @ SY2805 @ SY2806 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2805 @ SY2806 ) ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SV1287 @ SV20 @ SY2805 @ SY2806 ) @ SV1287 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2805 @ SY2806 ) ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SY2804 @ SV20 @ SY2805 @ SY2806 ) @ SY2804 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2805 @ SY2806 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4395]) ).

thf(5673,plain,
    ! [SV1288: $i,SV21: $i] :
      ( ( ! [SY2807: $i,SY2808: $i] :
            ( ~ ( c_in @ SV21 @ SV1288 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2807 @ SY2808 ) ) )
            | ! [SY2809: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ SV21 @ SY2807 @ SY2808 ) @ ( c_Datatype__Universe_Ousum @ SV1288 @ SY2809 @ SY2807 @ SY2808 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2807 @ SY2808 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4396]) ).

thf(5674,plain,
    ! [SV1289: $i,SV22: $i] :
      ( ( ! [SY2810: $i,SY2811: $i] :
            ( ~ ( c_in @ SV22 @ SV1289 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2810 @ SY2811 ) ) )
            | ! [SY2812: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ SV22 @ SY2810 @ SY2811 ) @ ( c_Datatype__Universe_Ousum @ SY2812 @ SV1289 @ SY2810 @ SY2811 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2810 @ SY2811 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4397]) ).

thf(5675,plain,
    ! [SV1290: $i,SV25: $i] :
      ( ( c_Divides_Oop_Advd @ SV25 @ ( c_times @ SV25 @ SV1290 @ tc_nat ) @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4400]) ).

thf(5676,plain,
    ! [SV1291: $i,SV26: $i] :
      ( ( c_Divides_Oop_Advd @ SV26 @ ( c_times @ SV1291 @ SV26 @ tc_nat ) @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4401]) ).

thf(5677,plain,
    ! [SV1292: $i,SV27: $i] :
      ( ( ( ( c_Divides_Oop_Amod @ SV27 @ SV1292 @ tc_nat )
         != c_0 )
        | ( SV27
          = ( c_times @ SV1292 @ ( c_Main_Omod__eq__0D__dest__1 @ SV1292 @ SV27 ) @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4402]) ).

thf(5678,plain,
    ! [SV1293: $i,SV29: $i] :
      ( ( ~ ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) )
        | ! [SY2813: $i] : ( c_in @ ( c_insert @ SY2813 @ SV29 @ SV1293 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4404]) ).

thf(5679,plain,
    ! [SV1294: $i,SV30: $i] :
      ( ( ~ ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) )
        | ! [SY2814: $i] : ( c_in @ ( c_inter @ SV30 @ SY2814 @ SV1294 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4405]) ).

thf(5680,plain,
    ! [SV1295: $i,SV31: $i] :
      ( ( ~ ( c_in @ SV31 @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) )
        | ! [SY2815: $i] : ( c_in @ ( c_inter @ SY2815 @ SV31 @ SV1295 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4406]) ).

thf(5681,plain,
    ! [SV1296: $i,SV32: $i] :
      ( ( ~ ( c_in @ SV32 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1296 ) ) )
        | ( c_in @ ( c_Main_Ofinite__Union__1 @ SV32 @ SV1296 ) @ SV32 @ ( tc_set @ SV1296 ) )
        | ( c_in @ ( c_Union @ SV32 @ SV1296 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4407]) ).

thf(5682,plain,
    ! [SV1297: $i,SV33: $i] :
      ( ( ~ ( c_in @ SV33 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1297 ) ) )
        | ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) )
        | ( c_in @ ( c_Union @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4408]) ).

thf(5683,plain,
    ! [SV1298: $i,SV34: $i] :
      ( ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV34 @ SV1298 @ tc_nat @ tc_nat ) ) @ SV34 @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4409]) ).

thf(5684,plain,
    ! [SV1299: $i,SV35: $i] :
      ( ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV35 @ SV1299 @ tc_nat @ tc_nat ) ) @ SV1299 @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4410]) ).

thf(5685,plain,
    ! [SV1300: $i,SV36: $i] :
      ( ( ~ ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        | ! [SY2816: $i] :
            ( ~ ( c_in @ SY2816 @ SV36 @ SV1300 )
            | ! [SY2817: $i] :
                ( ~ ( c_in @ SY2817 @ SV36 @ SV1300 )
                | ( SY2816 = SY2817 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4411]) ).

thf(5686,plain,
    ! [SV1301: $i,SV37: $i] :
      ( ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ SV37 ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SV1301 ) @ tc_IntDef_Oint )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4412]) ).

thf(5687,plain,
    ! [SV1302: $i,SV38: $i] :
      ( ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ SV38 ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SV1302 ) @ tc_IntDef_Oint )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4413]) ).

thf(5688,plain,
    ! [SV1303: $i,SV41: $i] :
      ( ( c_Divides_Oop_Advd @ SV41 @ ( c_times @ SV41 @ SV1303 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4416]) ).

thf(5689,plain,
    ! [SV1304: $i,SV42: $i] :
      ( ( c_Divides_Oop_Advd @ SV42 @ ( c_times @ SV1304 @ SV42 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4417]) ).

thf(5690,plain,
    ! [SV1305: $i,SV43: $i] :
      ( ( ( ( c_Divides_Oop_Amod @ SV43 @ SV1305 @ tc_IntDef_Oint )
         != c_0 )
        | ( SV43
          = ( c_times @ SV1305 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SV1305 @ SV43 ) @ tc_IntDef_Oint ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4418]) ).

thf(5691,plain,
    ! [SV1306: $i,SV44: $i] :
      ( ( c_List_Odistinct @ ( c_List_Oremdups @ SV44 @ SV1306 ) @ SV1306 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4419]) ).

thf(5692,plain,
    ! [SV1307: $i,SV45: $i] :
      ( ( c_in @ ( c_List_Oset @ SV45 @ SV1307 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1307 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4420]) ).

thf(5693,plain,
    ! [SV1308: $i,SV46: $i] :
      ( ( ! [SY2818: $i] :
            ( ~ ( c_in @ SV46 @ ( c_List_Olists @ SV1308 @ SY2818 ) @ ( tc_List_Olist @ SY2818 ) )
            | ! [SY2819: $i] :
                ( ~ ( c_in @ SY2819 @ ( c_List_Oset @ SV46 @ SY2818 ) @ SY2818 )
                | ( c_in @ SY2819 @ SV1308 @ SY2818 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4421]) ).

thf(5694,plain,
    ! [SV1309: $i,SV47: $i] :
      ( ( ! [SY2820: $i] :
            ( ( c_in @ SV47 @ ( c_List_Olists @ SV1309 @ SY2820 ) @ ( tc_List_Olist @ SY2820 ) )
            | ( c_in @ ( c_Main_Oin__listsI__1 @ SV1309 @ SV47 @ SY2820 ) @ ( c_List_Oset @ SV47 @ SY2820 ) @ SY2820 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4422]) ).

thf(5695,plain,
    ! [SV1310: $i,SV48: $i] :
      ( ( ! [SY2821: $i] :
            ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV48 @ SV1310 @ SY2821 ) @ SV48 @ SY2821 )
            | ( c_in @ SV1310 @ ( c_List_Olists @ SV48 @ SY2821 ) @ ( tc_List_Olist @ SY2821 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4423]) ).

thf(5696,plain,
    ! [SV1311: $i,SV49: $i] :
      ( ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ SV49 @ SV1311 ) @ ( tc_List_Olist @ SV1311 ) ) @ ( c_Nat_Osize @ SV49 @ ( tc_List_Olist @ SV1311 ) ) @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4424]) ).

thf(5697,plain,
    ! [SV1312: $i,SV50: $i] :
      ( ( ! [SY2822: $i,SY2823: $i,SY2824: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV50 @ SV1312 @ SY2822 ) @ SY2823 @ ( tc_List_Olist @ SY2822 ) @ ( tc_List_Olist @ SY2822 ) ) @ ( c_List_Olistrel @ SY2824 @ SY2822 ) @ ( tc_prod @ ( tc_List_Olist @ SY2822 ) @ ( tc_List_Olist @ SY2822 ) ) )
            | ( SY2823
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY2824 @ SY2823 @ SV50 @ SV1312 @ SY2822 ) @ ( c_Main_Olistrel__Cons1__2 @ SY2824 @ SY2823 @ SV50 @ SV1312 @ SY2822 ) @ SY2822 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4425]) ).

thf(5698,plain,
    ! [SV1313: $i,SV51: $i] :
      ( ( ! [SY2825: $i,SY2826: $i,SY2827: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV51 @ SV1313 @ SY2825 ) @ SY2826 @ ( tc_List_Olist @ SY2825 ) @ ( tc_List_Olist @ SY2825 ) ) @ ( c_List_Olistrel @ SY2827 @ SY2825 ) @ ( tc_prod @ ( tc_List_Olist @ SY2825 ) @ ( tc_List_Olist @ SY2825 ) ) )
            | ( c_in @ ( c_Pair @ SV1313 @ ( c_Main_Olistrel__Cons1__2 @ SY2827 @ SY2826 @ SV51 @ SV1313 @ SY2825 ) @ ( tc_List_Olist @ SY2825 ) @ ( tc_List_Olist @ SY2825 ) ) @ ( c_List_Olistrel @ SY2827 @ SY2825 ) @ ( tc_prod @ ( tc_List_Olist @ SY2825 ) @ ( tc_List_Olist @ SY2825 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4426]) ).

thf(5699,plain,
    ! [SV1314: $i,SV52: $i] :
      ( ( ! [SY2828: $i,SY2829: $i,SY2830: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV52 @ SV1314 @ SY2828 ) @ SY2829 @ ( tc_List_Olist @ SY2828 ) @ ( tc_List_Olist @ SY2828 ) ) @ ( c_List_Olistrel @ SY2830 @ SY2828 ) @ ( tc_prod @ ( tc_List_Olist @ SY2828 ) @ ( tc_List_Olist @ SY2828 ) ) )
            | ( c_in @ ( c_Pair @ SV52 @ ( c_Main_Olistrel__Cons1__1 @ SY2830 @ SY2829 @ SV52 @ SV1314 @ SY2828 ) @ SY2828 @ SY2828 ) @ SY2830 @ ( tc_prod @ SY2828 @ SY2828 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4427]) ).

thf(5700,plain,
    ! [SV1315: $i,SV53: $i] :
      ( ( ! [SY2831: $i,SY2832: $i,SY2833: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV53 @ ( c_List_Olist_OCons @ SV1315 @ SY2831 @ SY2832 ) @ ( tc_List_Olist @ SY2832 ) @ ( tc_List_Olist @ SY2832 ) ) @ ( c_List_Olistrel @ SY2833 @ SY2832 ) @ ( tc_prod @ ( tc_List_Olist @ SY2832 ) @ ( tc_List_Olist @ SY2832 ) ) )
            | ( SV53
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY2833 @ SV53 @ SV1315 @ SY2831 @ SY2832 ) @ ( c_Main_Olistrel__Cons2__2 @ SY2833 @ SV53 @ SV1315 @ SY2831 @ SY2832 ) @ SY2832 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4428]) ).

thf(5701,plain,
    ! [SV1316: $i,SV54: $i] :
      ( ( ! [SY2834: $i,SY2835: $i,SY2836: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV54 @ ( c_List_Olist_OCons @ SV1316 @ SY2834 @ SY2835 ) @ ( tc_List_Olist @ SY2835 ) @ ( tc_List_Olist @ SY2835 ) ) @ ( c_List_Olistrel @ SY2836 @ SY2835 ) @ ( tc_prod @ ( tc_List_Olist @ SY2835 ) @ ( tc_List_Olist @ SY2835 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY2836 @ SV54 @ SV1316 @ SY2834 @ SY2835 ) @ SY2834 @ ( tc_List_Olist @ SY2835 ) @ ( tc_List_Olist @ SY2835 ) ) @ ( c_List_Olistrel @ SY2836 @ SY2835 ) @ ( tc_prod @ ( tc_List_Olist @ SY2835 ) @ ( tc_List_Olist @ SY2835 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4429]) ).

thf(5702,plain,
    ! [SV1317: $i,SV55: $i] :
      ( ( ! [SY2837: $i,SY2838: $i,SY2839: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV55 @ ( c_List_Olist_OCons @ SV1317 @ SY2837 @ SY2838 ) @ ( tc_List_Olist @ SY2838 ) @ ( tc_List_Olist @ SY2838 ) ) @ ( c_List_Olistrel @ SY2839 @ SY2838 ) @ ( tc_prod @ ( tc_List_Olist @ SY2838 ) @ ( tc_List_Olist @ SY2838 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY2839 @ SV55 @ SV1317 @ SY2837 @ SY2838 ) @ SV1317 @ SY2838 @ SY2838 ) @ SY2839 @ ( tc_prod @ SY2838 @ SY2838 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4430]) ).

thf(5703,plain,
    ! [SV56: $i] :
      ( ( ( ! [SY2152: $i,SY2153: $i] :
              ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV56 @ ( tc_List_Olist @ SY2152 ) @ ( tc_List_Olist @ SY2152 ) ) @ ( c_List_Olistrel @ SY2153 @ SY2152 ) @ ( tc_prod @ ( tc_List_Olist @ SY2152 ) @ ( tc_List_Olist @ SY2152 ) ) ) )
        = $true )
      | ( ( SV56 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4431]) ).

thf(5704,plain,
    ! [SV57: $i] :
      ( ( ( ! [SY2154: $i,SY2155: $i] :
              ~ ( c_in @ ( c_Pair @ SV57 @ c_List_Olist_ONil @ ( tc_List_Olist @ SY2154 ) @ ( tc_List_Olist @ SY2154 ) ) @ ( c_List_Olistrel @ SY2155 @ SY2154 ) @ ( tc_prod @ ( tc_List_Olist @ SY2154 ) @ ( tc_List_Olist @ SY2154 ) ) ) )
        = $true )
      | ( ( SV57 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4432]) ).

thf(5705,plain,
    ! [SV1318: $i,SV58: $i] :
      ( ( ! [SY2840: $i,SY2841: $i] :
            ( ~ ( c_in @ ( c_List_Olist_OCons @ SV58 @ SV1318 @ SY2840 ) @ ( c_List_Olists @ SY2841 @ SY2840 ) @ ( tc_List_Olist @ SY2840 ) )
            | ( c_in @ SV1318 @ ( c_List_Olists @ SY2841 @ SY2840 ) @ ( tc_List_Olist @ SY2840 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4433]) ).

thf(5706,plain,
    ! [SV1319: $i,SV59: $i] :
      ( ( ! [SY2842: $i,SY2843: $i] :
            ( ~ ( c_in @ ( c_List_Olist_OCons @ SV59 @ SV1319 @ SY2842 ) @ ( c_List_Olists @ SY2843 @ SY2842 ) @ ( tc_List_Olist @ SY2842 ) )
            | ( c_in @ SV59 @ SY2843 @ SY2842 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4434]) ).

thf(5707,plain,
    ! [SV1320: $i,SV60: $i] :
      ( ( ! [SY2844: $i] :
            ( ~ ( c_in @ SV60 @ SV1320 @ SY2844 )
            | ! [SY2845: $i] :
                ( ~ ( c_in @ SY2845 @ ( c_List_Olists @ SV1320 @ SY2844 ) @ ( tc_List_Olist @ SY2844 ) )
                | ( c_in @ ( c_List_Olist_OCons @ SV60 @ SY2845 @ SY2844 ) @ ( c_List_Olists @ SV1320 @ SY2844 ) @ ( tc_List_Olist @ SY2844 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4435]) ).

thf(5708,plain,
    ! [SV1321: $i,SV61: $i] :
      ( ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ SV61 @ SV1321 ) @ ( tc_List_Olist @ SV1321 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4436]) ).

thf(5709,plain,
    ! [SV1322: $i,SV62: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV62 @ SV1322 )
        | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV62 @ SV1322 ) @ ( tc_List_Olist @ SV1322 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4437]) ).

thf(5710,plain,
    ! [SV1323: $i,SV63: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV63 @ SV1323 )
        | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV63 @ SV1323 ) @ ( tc_List_Olist @ SV1323 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4438]) ).

thf(5711,plain,
    ! [SV66: $i] :
      ( ( c_less @ SV66 @ SV66 @ tc_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4441]) ).

thf(5712,plain,
    ! [SV68: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV68 ) )
        = $true )
      | ( ( ! [SY2168: $i] : ( c_lessequals @ SY2168 @ SY2168 @ SV68 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4443]) ).

thf(5713,plain,
    ! [SV1324: $i,SV69: $i] :
      ( ( ! [SY2846: $i,SY2847: $i] :
            ( ~ ( c_in @ SV69 @ ( c_Relation_ODomain @ SV1324 @ SY2846 @ SY2847 ) @ SY2846 )
            | ( c_in @ ( c_Pair @ SV69 @ ( c_Main_ODomainE__1 @ SV69 @ SV1324 @ SY2846 @ SY2847 ) @ SY2846 @ SY2847 ) @ SV1324 @ ( tc_prod @ SY2846 @ SY2847 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4444]) ).

thf(5714,plain,
    ! [SV1325: $i,SV70: $i] :
      ( ( ! [SY2848: $i,SY2849: $i,SY2850: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1325 @ SY2848 @ SY2849 ) @ SY2850 @ ( tc_prod @ SY2848 @ SY2849 ) )
            | ( c_in @ SV70 @ ( c_Relation_ODomain @ SY2850 @ SY2848 @ SY2849 ) @ SY2848 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4445]) ).

thf(5715,plain,
    ! [SV1326: $i,SV71: $i] :
      ( ( ~ ( c_in @ SV71 @ c_Relation_OId @ ( tc_prod @ SV1326 @ SV1326 ) )
        | ( SV71
          = ( c_Pair @ ( c_Main_OIdE__1 @ SV71 @ SV1326 ) @ ( c_Main_OIdE__1 @ SV71 @ SV1326 ) @ SV1326 @ SV1326 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4446]) ).

thf(5716,plain,
    ! [SV1327: $i,SV72: $i] :
      ( ( ! [SY2851: $i,SY2852: $i,SY2853: $i] :
            ( ~ ( c_in @ SV72 @ ( c_Relation_OImage @ SV1327 @ SY2851 @ SY2852 @ SY2853 ) @ SY2853 )
            | ( c_in @ ( c_Main_OImageE__1 @ SY2851 @ SV72 @ SV1327 @ SY2852 @ SY2853 ) @ SY2851 @ SY2852 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4447]) ).

thf(5717,plain,
    ! [SV1328: $i,SV73: $i] :
      ( ( ! [SY2854: $i,SY2855: $i,SY2856: $i] :
            ( ~ ( c_in @ SV73 @ ( c_Relation_OImage @ SV1328 @ SY2854 @ SY2855 @ SY2856 ) @ SY2856 )
            | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SY2854 @ SV73 @ SV1328 @ SY2855 @ SY2856 ) @ SV73 @ SY2855 @ SY2856 ) @ SV1328 @ ( tc_prod @ SY2855 @ SY2856 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4448]) ).

thf(5718,plain,
    ! [SV1329: $i,SV74: $i] :
      ( ( ! [SY2857: $i,SY2858: $i] :
            ( ~ ( c_in @ SV74 @ SV1329 @ SY2857 )
            | ! [SY2859: $i,SY2860: $i] :
                ( ~ ( c_in @ ( c_Pair @ SV74 @ SY2858 @ SY2857 @ SY2859 ) @ SY2860 @ ( tc_prod @ SY2857 @ SY2859 ) )
                | ( c_in @ SY2858 @ ( c_Relation_OImage @ SY2860 @ SV1329 @ SY2857 @ SY2859 ) @ SY2859 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4449]) ).

thf(5719,plain,
    ! [SV1330: $i,SV75: $i] :
      ( ( ! [SY2861: $i,SY2862: $i] :
            ( ~ ( c_in @ SV75 @ ( c_Relation_ORange @ SV1330 @ SY2861 @ SY2862 ) @ SY2862 )
            | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV75 @ SV1330 @ SY2862 @ SY2861 ) @ SV75 @ SY2861 @ SY2862 ) @ SV1330 @ ( tc_prod @ SY2861 @ SY2862 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4450]) ).

thf(5720,plain,
    ! [SV1331: $i,SV76: $i] :
      ( ( ! [SY2863: $i,SY2864: $i,SY2865: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV76 @ SV1331 @ SY2863 @ SY2864 ) @ SY2865 @ ( tc_prod @ SY2863 @ SY2864 ) )
            | ( c_in @ SV1331 @ ( c_Relation_ORange @ SY2865 @ SY2863 @ SY2864 ) @ SY2864 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4451]) ).

thf(5721,plain,
    ! [SV1332: $i,SV77: $i] :
      ( ( ! [SY2866: $i,SY2867: $i] :
            ( ~ ( c_in @ SV77 @ ( c_Relation_Oconverse @ SV1332 @ SY2866 @ SY2867 ) @ ( tc_prod @ SY2867 @ SY2866 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1332 @ SV77 @ SY2866 @ SY2867 ) @ ( c_Main_OconverseE__2 @ SV1332 @ SV77 @ SY2866 @ SY2867 ) @ SY2866 @ SY2867 ) @ SV1332 @ ( tc_prod @ SY2866 @ SY2867 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4452]) ).

thf(5722,plain,
    ! [SV1333: $i,SV78: $i] :
      ( ( ! [SY2868: $i,SY2869: $i] :
            ( ~ ( c_in @ SV78 @ ( c_Relation_Oconverse @ SV1333 @ SY2868 @ SY2869 ) @ ( tc_prod @ SY2869 @ SY2868 ) )
            | ( SV78
              = ( c_Pair @ ( c_Main_OconverseE__2 @ SV1333 @ SV78 @ SY2868 @ SY2869 ) @ ( c_Main_OconverseE__1 @ SV1333 @ SV78 @ SY2868 @ SY2869 ) @ SY2869 @ SY2868 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4453]) ).

thf(5723,plain,
    ! [SV1334: $i,SV79: $i] :
      ( ( ! [SY2870: $i] :
            ( ~ ( c_in @ SV79 @ ( c_Relation_Odiag @ SV1334 @ SY2870 ) @ ( tc_prod @ SY2870 @ SY2870 ) )
            | ( SV79
              = ( c_Pair @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SY2870 ) @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SY2870 ) @ SY2870 @ SY2870 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4454]) ).

thf(5724,plain,
    ! [SV1335: $i,SV80: $i] :
      ( ( ! [SY2871: $i] :
            ( ~ ( c_in @ SV80 @ ( c_Relation_Odiag @ SV1335 @ SY2871 ) @ ( tc_prod @ SY2871 @ SY2871 ) )
            | ( c_in @ ( c_Main_OdiagE__1 @ SV1335 @ SV80 @ SY2871 ) @ SV1335 @ SY2871 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4455]) ).

thf(5725,plain,
    ! [SV1336: $i,SV81: $i] :
      ( ( ! [SY2872: $i] :
            ( ~ ( c_in @ SV81 @ SV1336 @ SY2872 )
            | ( c_in @ ( c_Pair @ SV81 @ SV81 @ SY2872 @ SY2872 ) @ ( c_Relation_Odiag @ SV1336 @ SY2872 ) @ ( tc_prod @ SY2872 @ SY2872 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4456]) ).

thf(5726,plain,
    ! [SV1337: $i,SV82: $i] :
      ( ( ! [SY2873: $i,SY2874: $i,SY2875: $i,SY2876: $i] :
            ( ~ ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SV1337 @ SY2873 @ SY2874 @ SY2875 @ SY2876 ) @ ( tc_prod @ SY2876 @ SY2875 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1337 @ SY2873 @ SV82 @ SY2874 @ SY2875 @ SY2876 ) @ ( c_Main_Orel__compE__3 @ SV1337 @ SY2873 @ SV82 @ SY2874 @ SY2875 @ SY2876 ) @ SY2874 @ SY2875 ) @ SV1337 @ ( tc_prod @ SY2874 @ SY2875 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4457]) ).

thf(5727,plain,
    ! [SV1338: $i,SV83: $i] :
      ( ( ! [SY2877: $i,SY2878: $i,SY2879: $i,SY2880: $i] :
            ( ~ ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SV1338 @ SY2877 @ SY2878 @ SY2879 @ SY2880 ) @ ( tc_prod @ SY2880 @ SY2879 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1338 @ SY2877 @ SV83 @ SY2878 @ SY2879 @ SY2880 ) @ ( c_Main_Orel__compE__2 @ SV1338 @ SY2877 @ SV83 @ SY2878 @ SY2879 @ SY2880 ) @ SY2880 @ SY2878 ) @ SY2877 @ ( tc_prod @ SY2880 @ SY2878 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4458]) ).

thf(5728,plain,
    ! [SV1339: $i,SV84: $i] :
      ( ( ! [SY2881: $i,SY2882: $i,SY2883: $i,SY2884: $i] :
            ( ~ ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SV1339 @ SY2881 @ SY2882 @ SY2883 @ SY2884 ) @ ( tc_prod @ SY2884 @ SY2883 ) )
            | ( SV84
              = ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1339 @ SY2881 @ SV84 @ SY2882 @ SY2883 @ SY2884 ) @ ( c_Main_Orel__compE__3 @ SV1339 @ SY2881 @ SV84 @ SY2882 @ SY2883 @ SY2884 ) @ SY2884 @ SY2883 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4459]) ).

thf(5729,plain,
    ! [SV1340: $i,SV85: $i] :
      ( ( ! [SY2885: $i,SY2886: $i,SY2887: $i,SY2888: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SY2885 @ SY2886 ) @ SY2887 @ ( tc_prod @ SY2885 @ SY2886 ) )
            | ! [SY2889: $i,SY2890: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY2888 @ SV85 @ SY2889 @ SY2885 ) @ SY2890 @ ( tc_prod @ SY2889 @ SY2885 ) )
                | ( c_in @ ( c_Pair @ SY2888 @ SV1340 @ SY2889 @ SY2886 ) @ ( c_Relation_Orel__comp @ SY2887 @ SY2890 @ SY2885 @ SY2886 @ SY2889 ) @ ( tc_prod @ SY2889 @ SY2886 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4460]) ).

thf(5730,plain,
    ! [SV1341: $i,SV86: $i] :
      ( ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV86 @ SV1341 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4461]) ).

thf(5731,plain,
    ! [SV1342: $i,SV87: $i] :
      ( ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV87 @ SV1342 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4462]) ).

thf(5732,plain,
    ! [SV1343: $i,SV88: $i] :
      ( ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV88 @ SV1343 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4463]) ).

thf(5733,plain,
    ! [SV1344: $i,SV89: $i] :
      ( ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV89 @ SV1344 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4464]) ).

thf(5734,plain,
    ! [SV1345: $i,SV91: $i] :
      ( ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV91 @ SV1345 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4466]) ).

thf(5735,plain,
    ! [SV1346: $i,SV92: $i] :
      ( ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV92 @ SV1346 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4467]) ).

thf(5736,plain,
    ! [SV1347: $i,SV93: $i] :
      ( ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV93 @ SV1347 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4468]) ).

thf(5737,plain,
    ! [SV1348: $i,SV94: $i] :
      ( ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV94 @ SV1348 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4469]) ).

thf(5738,plain,
    ! [SV1349: $i,SV96: $i] :
      ( ( ! [SY2891: $i] :
            ( ( c_in @ SV96 @ ( c_Inter @ SV1349 @ SY2891 ) @ SY2891 )
            | ( c_in @ ( c_Main_OInterI__1 @ SV96 @ SV1349 @ SY2891 ) @ SV1349 @ ( tc_set @ SY2891 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4471]) ).

thf(5739,plain,
    ! [SV1350: $i,SV97: $i] :
      ( ( ! [SY2892: $i] :
            ( ~ ( c_in @ SV97 @ ( c_Main_OInterI__1 @ SV97 @ SV1350 @ SY2892 ) @ SY2892 )
            | ( c_in @ SV97 @ ( c_Inter @ SV1350 @ SY2892 ) @ SY2892 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4472]) ).

thf(5740,plain,
    ! [SV1351: $i,SV98: $i] :
      ( ( c_in @ SV98 @ c_UNIV @ SV1351 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4473]) ).

thf(5741,plain,
    ! [SV1352: $i,SV99: $i] :
      ( ( ! [SY2893: $i] :
            ( ~ ( c_in @ SV99 @ ( c_Union @ SV1352 @ SY2893 ) @ SY2893 )
            | ( c_in @ ( c_Main_OUnionE__1 @ SV99 @ SV1352 @ SY2893 ) @ SV1352 @ ( tc_set @ SY2893 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4474]) ).

thf(5742,plain,
    ! [SV1353: $i,SV100: $i] :
      ( ( ! [SY2894: $i] :
            ( ~ ( c_in @ SV100 @ ( c_Union @ SV1353 @ SY2894 ) @ SY2894 )
            | ( c_in @ SV100 @ ( c_Main_OUnionE__1 @ SV100 @ SV1353 @ SY2894 ) @ SY2894 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4475]) ).

thf(5743,plain,
    ! [SV1354: $i,SV101: $i] :
      ( ( c_lessequals @ c_emptyset @ SV101 @ ( tc_set @ SV1354 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4476]) ).

thf(5744,plain,
    ! [SV1355: $i,SV102: $i] :
      ( ( ! [SY2895: $i] :
            ( ~ ( c_less @ SV102 @ SV1355 @ ( tc_set @ SY2895 ) )
            | ~ ( c_lessequals @ SV1355 @ SV102 @ ( tc_set @ SY2895 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4477]) ).

thf(5745,plain,
    ! [SV1356: $i,SV103: $i] :
      ( ( ! [SY2896: $i] :
            ( ~ ( c_less @ SV103 @ SV1356 @ ( tc_set @ SY2896 ) )
            | ( c_lessequals @ SV103 @ SV1356 @ ( tc_set @ SY2896 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4478]) ).

thf(5746,plain,
    ! [SV1357: $i,SV104: $i] :
      ( ( ! [SY2897: $i] :
            ( ~ ( c_lessequals @ SV104 @ SV1357 @ ( tc_set @ SY2897 ) )
            | ( SV104 = SV1357 )
            | ( c_less @ SV104 @ SV1357 @ ( tc_set @ SY2897 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4479]) ).

thf(5747,plain,
    ! [SV1358: $i,SV105: $i] :
      ( ( ! [SY2898: $i] :
            ~ ( c_in @ SV105 @ ( c_insert @ SV1358 @ c_emptyset @ SY2898 ) @ SY2898 )
        | ( SV105 = SV1358 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4480]) ).

thf(5748,plain,
    ! [SV1359: $i,SV106: $i] :
      ( ( c_in @ SV106 @ ( c_insert @ SV106 @ c_emptyset @ SV1359 ) @ SV1359 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4481]) ).

thf(5749,plain,
    ! [SV1360: $i,SV107: $i] :
      ( ( ! [SY2899: $i] :
            ( ( ( c_insert @ SV107 @ c_emptyset @ SV1360 )
             != ( c_insert @ SY2899 @ c_emptyset @ SV1360 ) )
            | ( SV107 = SY2899 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4482]) ).

thf(5750,plain,
    ! [SV1361: $i,SV108: $i] :
      ( ( ! [SY2900: $i] :
            ( ~ ( c_in @ SV108 @ SV1361 @ SY2900 )
            | ! [SY2901: $i] :
                ( ~ ( c_lessequals @ SV1361 @ SY2901 @ ( tc_set @ SY2900 ) )
                | ( c_in @ SV108 @ SY2901 @ SY2900 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4483]) ).

thf(5751,plain,
    ! [SV1362: $i,SV109: $i] :
      ( ( ! [SY2902: $i] :
            ( ( c_in @ ( c_Main_OsubsetI__1 @ SV109 @ SV1362 @ SY2902 ) @ SV109 @ SY2902 )
            | ( c_lessequals @ SV109 @ SV1362 @ ( tc_set @ SY2902 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4484]) ).

thf(5752,plain,
    ! [SV1363: $i,SV110: $i] :
      ( ( ! [SY2903: $i] :
            ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV110 @ SV1363 @ SY2903 ) @ SV1363 @ SY2903 )
            | ( c_lessequals @ SV110 @ SV1363 @ ( tc_set @ SY2903 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4485]) ).

thf(5753,plain,
    ! [SV1364: $i,SV111: $i] :
      ( ( ! [SY2904: $i] :
            ( ~ ( c_lessequals @ SV111 @ SV1364 @ ( tc_set @ SY2904 ) )
            | ~ ( c_lessequals @ SV1364 @ SV111 @ ( tc_set @ SY2904 ) )
            | ( SV1364 = SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4486]) ).

thf(5754,plain,
    ! [SV1365: $i,SV112: $i] :
      ( ( c_lessequals @ SV112 @ SV112 @ ( tc_set @ SV1365 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4487]) ).

thf(5755,plain,
    ! [SV1366: $i,SV113: $i] :
      ( ( ! [SY2905: $i] :
            ( ~ ( c_in @ SV113 @ SV1366 @ SY2905 )
            | ! [SY2906: $i,SY2907: $i] : ( c_in @ ( c_Sum__Type_OInl @ SV113 @ SY2905 @ SY2906 ) @ ( c_Sum__Type_OPlus @ SV1366 @ SY2907 @ SY2905 @ SY2906 ) @ ( tc_sum @ SY2905 @ SY2906 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4488]) ).

thf(5756,plain,
    ! [SV1367: $i,SV114: $i] :
      ( ( ! [SY2908: $i] :
            ( ~ ( c_in @ SV114 @ SV1367 @ SY2908 )
            | ! [SY2909: $i,SY2910: $i] : ( c_in @ ( c_Sum__Type_OInr @ SV114 @ SY2908 @ SY2909 ) @ ( c_Sum__Type_OPlus @ SY2910 @ SV1367 @ SY2909 @ SY2908 ) @ ( tc_sum @ SY2909 @ SY2908 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4489]) ).

thf(5757,plain,
    ! [SV1368: $i,SV115: $i] :
      ( ( ! [SY2911: $i,SY2912: $i,SY2913: $i] :
            ( ~ ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SV1368 @ SY2911 @ SY2912 @ SY2913 ) @ ( tc_sum @ SY2912 @ SY2913 ) )
            | ( SV115
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1368 @ SV115 @ SY2912 @ SY2913 ) @ SY2912 @ SY2913 ) )
            | ( SV115
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2911 @ SV115 @ SY2913 @ SY2912 ) @ SY2913 @ SY2912 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4490]) ).

thf(5758,plain,
    ! [SV1369: $i,SV116: $i] :
      ( ( ! [SY2914: $i,SY2915: $i,SY2916: $i] :
            ( ~ ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SV1369 @ SY2914 @ SY2915 @ SY2916 ) @ ( tc_sum @ SY2915 @ SY2916 ) )
            | ( SV116
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1369 @ SV116 @ SY2915 @ SY2916 ) @ SY2915 @ SY2916 ) )
            | ( c_in @ ( c_Main_OPlusE__2 @ SY2914 @ SV116 @ SY2916 @ SY2915 ) @ SY2914 @ SY2916 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4491]) ).

thf(5759,plain,
    ! [SV1370: $i,SV117: $i] :
      ( ( ! [SY2917: $i,SY2918: $i,SY2919: $i] :
            ( ~ ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SV1370 @ SY2917 @ SY2918 @ SY2919 ) @ ( tc_sum @ SY2918 @ SY2919 ) )
            | ( SV117
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2917 @ SV117 @ SY2919 @ SY2918 ) @ SY2919 @ SY2918 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SV1370 @ SV117 @ SY2918 @ SY2919 ) @ SV1370 @ SY2918 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4492]) ).

thf(5760,plain,
    ! [SV1371: $i,SV118: $i] :
      ( ( ! [SY2920: $i,SY2921: $i,SY2922: $i] :
            ( ~ ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SV1371 @ SY2920 @ SY2921 @ SY2922 ) @ ( tc_sum @ SY2921 @ SY2922 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SV1371 @ SV118 @ SY2921 @ SY2922 ) @ SV1371 @ SY2921 )
            | ( c_in @ ( c_Main_OPlusE__2 @ SY2920 @ SV118 @ SY2922 @ SY2921 ) @ SY2920 @ SY2922 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4493]) ).

thf(5761,plain,
    ! [SV1372: $i,SV119: $i] :
      ( ( ! [SY2923: $i] :
            ( ~ ( c_in @ SV119 @ SV1372 @ ( tc_prod @ SY2923 @ SY2923 ) )
            | ( c_in @ SV119 @ ( c_Transitive__Closure_Ortrancl @ SV1372 @ SY2923 ) @ ( tc_prod @ SY2923 @ SY2923 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4494]) ).

thf(5762,plain,
    ! [SV1373: $i,SV120: $i] :
      ( ( ! [SY2924: $i] : ( c_in @ ( c_Pair @ SV120 @ SV120 @ SV1373 @ SV1373 ) @ ( c_Transitive__Closure_Ortrancl @ SY2924 @ SV1373 ) @ ( tc_prod @ SV1373 @ SV1373 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4495]) ).

thf(5763,plain,
    ! [SV1374: $i,SV121: $i] :
      ( ( ! [SY2925: $i,SY2926: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SY2925 @ SY2925 ) @ SY2926 @ ( tc_prod @ SY2925 @ SY2925 ) )
            | ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SY2925 @ SY2925 ) @ ( c_Transitive__Closure_Otrancl @ SY2926 @ SY2925 ) @ ( tc_prod @ SY2925 @ SY2925 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4496]) ).

thf(5764,plain,
    ! [SV1375: $i,SV122: $i] :
      ( ( ! [SY2927: $i,SY2928: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SY2927 @ SY2927 ) @ ( c_Transitive__Closure_Otrancl @ SY2928 @ SY2927 ) @ ( tc_prod @ SY2927 @ SY2927 ) )
            | ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SY2927 @ SY2927 ) @ ( c_Transitive__Closure_Ortrancl @ SY2928 @ SY2927 ) @ ( tc_prod @ SY2927 @ SY2927 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4497]) ).

thf(5765,plain,
    ! [SV1376: $i,SV124: $i] :
      ( ( ~ ( c_Relation_Otrans @ SV124 @ SV1376 )
        | ! [SY2929: $i,SY2930: $i] :
            ( ~ ( c_Relation_Otrans @ SY2929 @ SY2930 )
            | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SY2929 @ SV124 @ SY2930 @ SV1376 ) @ ( tc_prod @ SY2930 @ SV1376 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4499]) ).

thf(5766,plain,
    ! [SV1377: $i,SV125: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV125 @ SV1377 )
        | ! [SY2931: $i,SY2932: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ SY2931 @ SY2932 )
            | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SY2931 @ SV125 @ SY2932 @ SV1377 ) @ ( tc_prod @ SY2932 @ SV1377 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4500]) ).

thf(5767,plain,
    ! [SV126: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ SV126 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV126 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4501]) ).

thf(5768,plain,
    ! [SV1378: $i,SV127: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV127 @ SV1378 ) )
        | ~ ( class_Finite__Set_Ofinite @ SV1378 )
        | ~ ( class_Finite__Set_Ofinite @ SV127 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4502]) ).

thf(5769,plain,
    ! [SV1379: $i,SV128: $i] :
      ( ( class_Nat_Opower @ ( tc_fun @ SV128 @ SV1379 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4503]) ).

thf(5770,plain,
    ! [SV1380: $i,SV129: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV129 @ SV1380 ) )
        | ~ ( class_Finite__Set_Ofinite @ SV1380 )
        | ~ ( class_Finite__Set_Ofinite @ SV129 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4504]) ).

thf(5771,plain,
    ! [SV133: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_set @ SV133 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV133 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4508]) ).

thf(5772,plain,
    ! [SV1381: $i,SV135: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV135 @ SV1381 ) )
        | ~ ( class_Finite__Set_Ofinite @ SV1381 )
        | ~ ( class_Finite__Set_Ofinite @ SV135 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4510]) ).

thf(5773,plain,
    ! [SV136: $i] :
      ( ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV136 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV136 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4511]) ).

thf(5774,plain,
    ! [SV137: $i] :
      ( ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV137 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV137 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4512]) ).

thf(5775,plain,
    ! [SV138: $i] :
      ( ( ( ~ ( class_LOrder_Olorder @ SV138 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV138 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4513]) ).

thf(5776,plain,
    ! [SV139: $i] :
      ( ( ( ~ ( class_LOrder_Olorder @ SV139 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV139 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4514]) ).

thf(5777,plain,
    ! [SV140: $i] :
      ( ( ( ~ ( class_LOrder_Olorder @ SV140 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV140 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4515]) ).

thf(5778,plain,
    ! [SV141: $i] :
      ( ( ( ~ ( class_LOrder_Olorder @ SV141 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV141 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4516]) ).

thf(5779,plain,
    ! [SV142: $i] :
      ( ( ( ~ ( class_LOrder_Omeet__semilorder @ SV142 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV142 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4517]) ).

thf(5780,plain,
    ! [SV143: $i] :
      ( ( ( ~ ( class_LOrder_Omeet__semilorder @ SV143 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV143 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4518]) ).

thf(5781,plain,
    ! [SV144: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV144 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV144 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4519]) ).

thf(5782,plain,
    ! [SV145: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV145 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV145 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4520]) ).

thf(5783,plain,
    ! [SV146: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV146 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV146 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4521]) ).

thf(5784,plain,
    ! [SV147: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV147 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV147 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4522]) ).

thf(5785,plain,
    ! [SV148: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV148 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV148 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4523]) ).

thf(5786,plain,
    ! [SV149: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV149 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV149 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4524]) ).

thf(5787,plain,
    ! [SV150: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV150 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV150 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4525]) ).

thf(5788,plain,
    ! [SV151: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV151 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV151 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4526]) ).

thf(5789,plain,
    ! [SV152: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV152 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV152 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4527]) ).

thf(5790,plain,
    ! [SV153: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV153 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV153 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4528]) ).

thf(5791,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV154 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV154 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4529]) ).

thf(5792,plain,
    ! [SV155: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV155 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV155 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4530]) ).

thf(5793,plain,
    ! [SV156: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV156 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV156 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4531]) ).

thf(5794,plain,
    ! [SV157: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV157 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV157 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4532]) ).

thf(5795,plain,
    ! [SV158: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV158 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV158 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4533]) ).

thf(5796,plain,
    ! [SV159: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV159 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV159 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4534]) ).

thf(5797,plain,
    ! [SV160: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV160 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV160 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4535]) ).

thf(5798,plain,
    ! [SV161: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV161 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV161 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4536]) ).

thf(5799,plain,
    ! [SV162: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV162 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4537]) ).

thf(5800,plain,
    ! [SV163: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV163 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV163 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4538]) ).

thf(5801,plain,
    ! [SV164: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV164 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring__1 @ SV164 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4539]) ).

thf(5802,plain,
    ! [SV165: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV165 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV165 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4540]) ).

thf(5803,plain,
    ! [SV166: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV166 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV166 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4541]) ).

thf(5804,plain,
    ! [SV167: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV167 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV167 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4542]) ).

thf(5805,plain,
    ! [SV168: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV168 ) )
        = $true )
      | ( ( class_Numeral_Onumber @ SV168 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4543]) ).

thf(5806,plain,
    ! [SV169: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV169 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV169 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4544]) ).

thf(5807,plain,
    ! [SV170: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV170 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV170 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4545]) ).

thf(5808,plain,
    ! [SV171: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV171 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV171 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4546]) ).

thf(5809,plain,
    ! [SV172: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV172 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV172 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4547]) ).

thf(5810,plain,
    ! [SV173: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV173 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV173 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4548]) ).

thf(5811,plain,
    ! [SV174: $i] :
      ( ( ( ~ ( class_Numeral_Onumber__ring @ SV174 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV174 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4549]) ).

thf(5812,plain,
    ! [SV175: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV175 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV175 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4550]) ).

thf(5813,plain,
    ! [SV176: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV176 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV176 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4551]) ).

thf(5814,plain,
    ! [SV177: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV177 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV177 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4552]) ).

thf(5815,plain,
    ! [SV178: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV178 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV178 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4553]) ).

thf(5816,plain,
    ! [SV179: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV179 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV179 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4554]) ).

thf(5817,plain,
    ! [SV180: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV180 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV180 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4555]) ).

thf(5818,plain,
    ! [SV181: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV181 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV181 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4556]) ).

thf(5819,plain,
    ! [SV182: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV182 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV182 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4557]) ).

thf(5820,plain,
    ! [SV183: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV183 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV183 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4558]) ).

thf(5821,plain,
    ! [SV184: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV184 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV184 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4559]) ).

thf(5822,plain,
    ! [SV185: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV185 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV185 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4560]) ).

thf(5823,plain,
    ! [SV186: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV186 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV186 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4561]) ).

thf(5824,plain,
    ! [SV187: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV187 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV187 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4562]) ).

thf(5825,plain,
    ! [SV188: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV188 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV188 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4563]) ).

thf(5826,plain,
    ! [SV189: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV189 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV189 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4564]) ).

thf(5827,plain,
    ! [SV190: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV190 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV190 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4565]) ).

thf(5828,plain,
    ! [SV191: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV191 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV191 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4566]) ).

thf(5829,plain,
    ! [SV192: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV192 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV192 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4567]) ).

thf(5830,plain,
    ! [SV193: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV193 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV193 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4568]) ).

thf(5831,plain,
    ! [SV194: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV194 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV194 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4569]) ).

thf(5832,plain,
    ! [SV195: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV195 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV195 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4570]) ).

thf(5833,plain,
    ! [SV196: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV196 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV196 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4571]) ).

thf(5834,plain,
    ! [SV197: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV197 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV197 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4572]) ).

thf(5835,plain,
    ! [SV198: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV198 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV198 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4573]) ).

thf(5836,plain,
    ! [SV199: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV199 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV199 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4574]) ).

thf(5837,plain,
    ! [SV200: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV200 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV200 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4575]) ).

thf(5838,plain,
    ! [SV201: $i] :
      ( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV201 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV201 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4576]) ).

thf(5839,plain,
    ! [SV202: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV202 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV202 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4577]) ).

thf(5840,plain,
    ! [SV203: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV203 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV203 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4578]) ).

thf(5841,plain,
    ! [SV204: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV204 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV204 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4579]) ).

thf(5842,plain,
    ! [SV205: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV205 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV205 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4580]) ).

thf(5843,plain,
    ! [SV206: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV206 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV206 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4581]) ).

thf(5844,plain,
    ! [SV207: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV207 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV207 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4582]) ).

thf(5845,plain,
    ! [SV208: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV208 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV208 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4583]) ).

thf(5846,plain,
    ! [SV209: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV209 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV209 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4584]) ).

thf(5847,plain,
    ! [SV210: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV210 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV210 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4585]) ).

thf(5848,plain,
    ! [SV211: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV211 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV211 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4586]) ).

thf(5849,plain,
    ! [SV212: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV212 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV212 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4587]) ).

thf(5850,plain,
    ! [SV213: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV213 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV213 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4588]) ).

thf(5851,plain,
    ! [SV214: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV214 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV214 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4589]) ).

thf(5852,plain,
    ! [SV215: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV215 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV215 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4590]) ).

thf(5853,plain,
    ! [SV216: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV216 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV216 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4591]) ).

thf(5854,plain,
    ! [SV217: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV217 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV217 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4592]) ).

thf(5855,plain,
    ! [SV218: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV218 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV218 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4593]) ).

thf(5856,plain,
    ! [SV219: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV219 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV219 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4594]) ).

thf(5857,plain,
    ! [SV220: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV220 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV220 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4595]) ).

thf(5858,plain,
    ! [SV221: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV221 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV221 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4596]) ).

thf(5859,plain,
    ! [SV222: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV222 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV222 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4597]) ).

thf(5860,plain,
    ! [SV223: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV223 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV223 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4598]) ).

thf(5861,plain,
    ! [SV224: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV224 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV224 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4599]) ).

thf(5862,plain,
    ! [SV225: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV225 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV225 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4600]) ).

thf(5863,plain,
    ! [SV226: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV226 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV226 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4601]) ).

thf(5864,plain,
    ! [SV227: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV227 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV227 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4602]) ).

thf(5865,plain,
    ! [SV228: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV228 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV228 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4603]) ).

thf(5866,plain,
    ! [SV229: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV229 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV229 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4604]) ).

thf(5867,plain,
    ! [SV230: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV230 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV230 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4605]) ).

thf(5868,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV231 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV231 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4606]) ).

thf(5869,plain,
    ! [SV232: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV232 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV232 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4607]) ).

thf(5870,plain,
    ! [SV233: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV233 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV233 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4608]) ).

thf(5871,plain,
    ! [SV234: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV234 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV234 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4609]) ).

thf(5872,plain,
    ! [SV235: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV235 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV235 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4610]) ).

thf(5873,plain,
    ! [SV236: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV236 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV236 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4611]) ).

thf(5874,plain,
    ! [SV237: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV237 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV237 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4612]) ).

thf(5875,plain,
    ! [SV238: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV238 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV238 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4613]) ).

thf(5876,plain,
    ! [SV239: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV239 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV239 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4614]) ).

thf(5877,plain,
    ! [SV240: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV240 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV240 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4615]) ).

thf(5878,plain,
    ! [SV241: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV241 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV241 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4616]) ).

thf(5879,plain,
    ! [SV242: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV242 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV242 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4617]) ).

thf(5880,plain,
    ! [SV243: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV243 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV243 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4618]) ).

thf(5881,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV244 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV244 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4619]) ).

thf(5882,plain,
    ! [SV245: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV245 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV245 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4620]) ).

thf(5883,plain,
    ! [SV246: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV246 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV246 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4621]) ).

thf(5884,plain,
    ! [SV247: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV247 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV247 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4622]) ).

thf(5885,plain,
    ! [SV248: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV248 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV248 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4623]) ).

thf(5886,plain,
    ! [SV249: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV249 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV249 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4624]) ).

thf(5887,plain,
    ! [SV250: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV250 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV250 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4625]) ).

thf(5888,plain,
    ! [SV251: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV251 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV251 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4626]) ).

thf(5889,plain,
    ! [SV252: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV252 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV252 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4627]) ).

thf(5890,plain,
    ! [SV253: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV253 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV253 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4628]) ).

thf(5891,plain,
    ! [SV254: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV254 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV254 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4629]) ).

thf(5892,plain,
    ! [SV255: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV255 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV255 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4630]) ).

thf(5893,plain,
    ! [SV256: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV256 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV256 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4631]) ).

thf(5894,plain,
    ! [SV257: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV257 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV257 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4632]) ).

thf(5895,plain,
    ! [SV258: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV258 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV258 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4633]) ).

thf(5896,plain,
    ! [SV259: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV259 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV259 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4634]) ).

thf(5897,plain,
    ! [SV260: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV260 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV260 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4635]) ).

thf(5898,plain,
    ! [SV261: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV261 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV261 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4636]) ).

thf(5899,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV262 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV262 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4637]) ).

thf(5900,plain,
    ! [SV263: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV263 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV263 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4638]) ).

thf(5901,plain,
    ! [SV264: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV264 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV264 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4639]) ).

thf(5902,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV265 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV265 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4640]) ).

thf(5903,plain,
    ! [SV266: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV266 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV266 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4641]) ).

thf(5904,plain,
    ! [SV267: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV267 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV267 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4642]) ).

thf(5905,plain,
    ! [SV268: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV268 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV268 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4643]) ).

thf(5906,plain,
    ! [SV269: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV269 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV269 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4644]) ).

thf(5907,plain,
    ! [SV270: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV270 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV270 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4645]) ).

thf(5908,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV271 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV271 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4646]) ).

thf(5909,plain,
    ! [SV272: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV272 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV272 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4647]) ).

thf(5910,plain,
    ! [SV273: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV273 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV273 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4648]) ).

thf(5911,plain,
    ! [SV274: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV274 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV274 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4649]) ).

thf(5912,plain,
    ! [SV275: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV275 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV275 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4650]) ).

thf(5913,plain,
    ! [SV276: $i] :
      ( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV276 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV276 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4651]) ).

thf(5914,plain,
    ! [SV277: $i] :
      ( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV277 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV277 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4652]) ).

thf(5915,plain,
    ! [SV278: $i] :
      ( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV278 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV278 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4653]) ).

thf(5916,plain,
    ! [SV279: $i] :
      ( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV279 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV279 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4654]) ).

thf(5917,plain,
    ! [SV280: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV280 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV280 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4655]) ).

thf(5918,plain,
    ! [SV281: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV281 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV281 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4656]) ).

thf(5919,plain,
    ! [SV282: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV282 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV282 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4657]) ).

thf(5920,plain,
    ! [SV283: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV283 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV283 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4658]) ).

thf(5921,plain,
    ! [SV284: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV284 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV284 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4659]) ).

thf(5922,plain,
    ! [SV285: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV285 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV285 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4660]) ).

thf(5923,plain,
    ! [SV286: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV286 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV286 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4661]) ).

thf(5924,plain,
    ! [SV287: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV287 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV287 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4662]) ).

thf(5925,plain,
    ! [SV288: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV288 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV288 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4663]) ).

thf(5926,plain,
    ! [SV289: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV289 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV289 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4664]) ).

thf(5927,plain,
    ! [SV290: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV290 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV290 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4665]) ).

thf(5928,plain,
    ! [SV291: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV291 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV291 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4666]) ).

thf(5929,plain,
    ! [SV292: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV292 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV292 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4667]) ).

thf(5930,plain,
    ! [SV293: $i] :
      ( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV293 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV293 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4668]) ).

thf(5931,plain,
    ! [SV294: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV294 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV294 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4669]) ).

thf(5932,plain,
    ! [SV295: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV295 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV295 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4670]) ).

thf(5933,plain,
    ! [SV296: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV296 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV296 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4671]) ).

thf(5934,plain,
    ! [SV297: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV297 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV297 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4672]) ).

thf(5935,plain,
    ! [SV298: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV298 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV298 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4673]) ).

thf(5936,plain,
    ! [SV299: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV299 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV299 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4674]) ).

thf(5937,plain,
    ! [SV300: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV300 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV300 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4675]) ).

thf(5938,plain,
    ! [SV301: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV301 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV301 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4676]) ).

thf(5939,plain,
    ! [SV302: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV302 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV302 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4677]) ).

thf(5940,plain,
    ! [SV303: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV303 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV303 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4678]) ).

thf(5941,plain,
    ! [SV304: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV304 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV304 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4679]) ).

thf(5942,plain,
    ! [SV305: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV305 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV305 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4680]) ).

thf(5943,plain,
    ! [SV306: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV306 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV306 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4681]) ).

thf(5944,plain,
    ! [SV307: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV307 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4682]) ).

thf(5945,plain,
    ! [SV308: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV308 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV308 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4683]) ).

thf(5946,plain,
    ! [SV309: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV309 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV309 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4684]) ).

thf(5947,plain,
    ! [SV310: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV310 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV310 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4685]) ).

thf(5948,plain,
    ! [SV311: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV311 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV311 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4686]) ).

thf(5949,plain,
    ! [SV312: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV312 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV312 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4687]) ).

thf(5950,plain,
    ! [SV313: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV313 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV313 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4688]) ).

thf(5951,plain,
    ! [SV314: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV314 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV314 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4689]) ).

thf(5952,plain,
    ! [SV315: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV315 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV315 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4690]) ).

thf(5953,plain,
    ! [SV316: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV316 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV316 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4691]) ).

thf(5954,plain,
    ! [SV317: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV317 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV317 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4692]) ).

thf(5955,plain,
    ! [SV318: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV318 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV318 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4693]) ).

thf(5956,plain,
    ! [SV319: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV319 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV319 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4694]) ).

thf(5957,plain,
    ! [SV320: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV320 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV320 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4695]) ).

thf(5958,plain,
    ! [SV321: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV321 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV321 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4696]) ).

thf(5959,plain,
    ! [SV322: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV322 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV322 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4697]) ).

thf(5960,plain,
    ! [SV323: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV323 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV323 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4698]) ).

thf(5961,plain,
    ! [SV324: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV324 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV324 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4699]) ).

thf(5962,plain,
    ! [SV325: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV325 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV325 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4700]) ).

thf(5963,plain,
    ! [SV326: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV326 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV326 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4701]) ).

thf(5964,plain,
    ! [SV327: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV327 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV327 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4702]) ).

thf(5965,plain,
    ! [SV328: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV328 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV328 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4703]) ).

thf(5966,plain,
    ! [SV329: $i] :
      ( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV329 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV329 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4704]) ).

thf(5967,plain,
    ! [SV330: $i] :
      ( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV330 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV330 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4705]) ).

thf(5968,plain,
    ! [SV331: $i] :
      ( ( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV331 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV331 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4706]) ).

thf(5969,plain,
    ! [SV332: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV332 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV332 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4707]) ).

thf(5970,plain,
    ! [SV333: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV333 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV333 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4708]) ).

thf(5971,plain,
    ! [SV334: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV334 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV334 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4709]) ).

thf(5972,plain,
    ! [SV335: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV335 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV335 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4710]) ).

thf(5973,plain,
    ! [SV336: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV336 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV336 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4711]) ).

thf(5974,plain,
    ! [SV337: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV337 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV337 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4712]) ).

thf(5975,plain,
    ! [SV338: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV338 ) )
        = $true )
      | ( ( class_Nat_Opower @ SV338 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4713]) ).

thf(5976,plain,
    ! [SV339: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV339 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV339 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4714]) ).

thf(5977,plain,
    ! [SV340: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV340 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV340 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4715]) ).

thf(5978,plain,
    ! [SV341: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV341 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV341 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4716]) ).

thf(5979,plain,
    ! [SV342: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV342 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV342 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4717]) ).

thf(5980,plain,
    ! [SV343: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV343 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV343 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4718]) ).

thf(5981,plain,
    ! [SV344: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV344 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV344 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4719]) ).

thf(5982,plain,
    ! [SV345: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV345 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV345 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4720]) ).

thf(5983,plain,
    ! [SV346: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV346 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV346 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4721]) ).

thf(5984,plain,
    ! [SV347: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV347 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV347 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4722]) ).

thf(5985,plain,
    ! [SV348: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV348 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV348 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4723]) ).

thf(5986,plain,
    ! [SV349: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV349 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV349 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4724]) ).

thf(5987,plain,
    ! [SV350: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV350 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV350 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4725]) ).

thf(5988,plain,
    ! [SV351: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV351 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV351 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4726]) ).

thf(5989,plain,
    ! [SV352: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV352 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV352 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4727]) ).

thf(5990,plain,
    ! [SV353: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV353 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV353 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4728]) ).

thf(5991,plain,
    ! [SV354: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV354 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV354 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4729]) ).

thf(5992,plain,
    ! [SV355: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV355 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV355 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4730]) ).

thf(5993,plain,
    ! [SV356: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV356 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV356 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4731]) ).

thf(5994,plain,
    ! [SV357: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV357 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV357 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4732]) ).

thf(5995,plain,
    ! [SV358: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV358 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV358 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4733]) ).

thf(5996,plain,
    ! [SV359: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV359 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV359 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4734]) ).

thf(5997,plain,
    ! [SV360: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV360 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV360 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4735]) ).

thf(5998,plain,
    ! [SV361: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV361 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV361 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4736]) ).

thf(5999,plain,
    ! [SV362: $i] :
      ( ( ( ~ ( class_Power_Orecpower @ SV362 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV362 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4737]) ).

thf(6000,plain,
    ! [SV363: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV363 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV363 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4738]) ).

thf(6001,plain,
    ! [SV364: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV364 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV364 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4739]) ).

thf(6002,plain,
    ! [SV365: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV365 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV365 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4740]) ).

thf(6003,plain,
    ! [SV366: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV366 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV366 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4741]) ).

thf(6004,plain,
    ! [SV367: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV367 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV367 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4742]) ).

thf(6005,plain,
    ! [SV368: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV368 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV368 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4743]) ).

thf(6006,plain,
    ! [SV369: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV369 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV369 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4744]) ).

thf(6007,plain,
    ! [SV370: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV370 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV370 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4745]) ).

thf(6008,plain,
    ! [SV371: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV371 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV371 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4746]) ).

thf(6009,plain,
    ! [SV372: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV372 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV372 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4747]) ).

thf(6010,plain,
    ! [SV373: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV373 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV373 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4748]) ).

thf(6011,plain,
    ! [SV374: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV374 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV374 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4749]) ).

thf(6012,plain,
    ! [SV375: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV375 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV375 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4750]) ).

thf(6013,plain,
    ! [SV376: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV376 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV376 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4751]) ).

thf(6014,plain,
    ! [SV377: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV377 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV377 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4752]) ).

thf(6015,plain,
    ! [SV378: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV378 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV378 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4753]) ).

thf(6016,plain,
    ! [SV379: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV379 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV379 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4754]) ).

thf(6017,plain,
    ! [SV380: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV380 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV380 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4755]) ).

thf(6018,plain,
    ! [SV381: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV381 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV381 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4756]) ).

thf(6019,plain,
    ! [SV382: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV382 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV382 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4757]) ).

thf(6020,plain,
    ! [SV383: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV383 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV383 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4758]) ).

thf(6021,plain,
    ! [SV384: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV384 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV384 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4759]) ).

thf(6022,plain,
    ! [SV385: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV385 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV385 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4760]) ).

thf(6023,plain,
    ! [SV386: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV386 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV386 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4761]) ).

thf(6024,plain,
    ! [SV387: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV387 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV387 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4762]) ).

thf(6025,plain,
    ! [SV388: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV388 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV388 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4763]) ).

thf(6026,plain,
    ! [SV389: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV389 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV389 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4764]) ).

thf(6027,plain,
    ! [SV390: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV390 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV390 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4765]) ).

thf(6028,plain,
    ! [SV391: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV391 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV391 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4766]) ).

thf(6029,plain,
    ! [SV392: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV392 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV392 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4767]) ).

thf(6030,plain,
    ! [SV393: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV393 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV393 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4768]) ).

thf(6031,plain,
    ! [SV394: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV394 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV394 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4769]) ).

thf(6032,plain,
    ! [SV395: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV395 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV395 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4770]) ).

thf(6033,plain,
    ! [SV396: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV396 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV396 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4771]) ).

thf(6034,plain,
    ! [SV397: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV397 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV397 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4772]) ).

thf(6035,plain,
    ! [SV398: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV398 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV398 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4773]) ).

thf(6036,plain,
    ! [SV399: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV399 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV399 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4774]) ).

thf(6037,plain,
    ! [SV400: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV400 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV400 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4775]) ).

thf(6038,plain,
    ! [SV401: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV401 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV401 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4776]) ).

thf(6039,plain,
    ! [SV402: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV402 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4777]) ).

thf(6040,plain,
    ! [SV403: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV403 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV403 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4778]) ).

thf(6041,plain,
    ! [SV404: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV404 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV404 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4779]) ).

thf(6042,plain,
    ! [SV405: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV405 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV405 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4780]) ).

thf(6043,plain,
    ! [SV406: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV406 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV406 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4781]) ).

thf(6044,plain,
    ! [SV407: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV407 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV407 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4782]) ).

thf(6045,plain,
    ! [SV408: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV408 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring__1 @ SV408 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4783]) ).

thf(6046,plain,
    ! [SV409: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV409 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV409 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4784]) ).

thf(6047,plain,
    ! [SV410: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV410 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV410 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4785]) ).

thf(6048,plain,
    ! [SV411: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV411 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV411 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4786]) ).

thf(6049,plain,
    ! [SV412: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV412 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV412 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4787]) ).

thf(6050,plain,
    ! [SV413: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV413 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV413 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4788]) ).

thf(6051,plain,
    ! [SV414: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV414 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV414 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4789]) ).

thf(6052,plain,
    ! [SV415: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV415 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV415 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4790]) ).

thf(6053,plain,
    ! [SV416: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV416 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV416 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4791]) ).

thf(6054,plain,
    ! [SV417: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV417 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV417 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4792]) ).

thf(6055,plain,
    ! [SV418: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV418 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV418 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4793]) ).

thf(6056,plain,
    ! [SV419: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV419 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV419 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4794]) ).

thf(6057,plain,
    ! [SV420: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV420 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV420 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4795]) ).

thf(6058,plain,
    ! [SV421: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV421 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV421 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4796]) ).

thf(6059,plain,
    ! [SV422: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV422 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV422 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4797]) ).

thf(6060,plain,
    ! [SV423: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV423 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV423 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4798]) ).

thf(6061,plain,
    ! [SV424: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV424 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV424 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4799]) ).

thf(6062,plain,
    ! [SV425: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV425 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV425 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4800]) ).

thf(6063,plain,
    ! [SV426: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV426 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV426 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4801]) ).

thf(6064,plain,
    ! [SV427: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV427 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV427 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4802]) ).

thf(6065,plain,
    ! [SV428: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV428 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV428 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4803]) ).

thf(6066,plain,
    ! [SV429: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV429 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV429 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4804]) ).

thf(6067,plain,
    ! [SV430: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV430 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV430 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4805]) ).

thf(6068,plain,
    ! [SV431: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV431 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV431 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4806]) ).

thf(6069,plain,
    ! [SV432: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV432 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV432 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4807]) ).

thf(6070,plain,
    ! [SV433: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV433 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV433 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4808]) ).

thf(6071,plain,
    ! [SV434: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV434 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV434 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4809]) ).

thf(6072,plain,
    ! [SV435: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV435 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV435 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4810]) ).

thf(6073,plain,
    ! [SV436: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV436 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV436 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4811]) ).

thf(6074,plain,
    ! [SV437: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV437 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV437 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4812]) ).

thf(6075,plain,
    ! [SV438: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV438 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV438 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4813]) ).

thf(6076,plain,
    ! [SV439: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV439 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV439 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4814]) ).

thf(6077,plain,
    ! [SV440: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV440 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV440 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4815]) ).

thf(6078,plain,
    ! [SV441: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV441 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV441 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4816]) ).

thf(6079,plain,
    ! [SV442: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV442 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV442 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4817]) ).

thf(6080,plain,
    ! [SV443: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV443 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV443 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4818]) ).

thf(6081,plain,
    ! [SV444: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV444 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV444 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4819]) ).

thf(6082,plain,
    ! [SV445: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV445 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV445 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4820]) ).

thf(6083,plain,
    ! [SV446: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV446 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV446 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4821]) ).

thf(6084,plain,
    ! [SV447: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV447 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV447 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4822]) ).

thf(6085,plain,
    ! [SV448: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV448 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV448 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4823]) ).

thf(6086,plain,
    ! [SV449: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV449 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV449 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4824]) ).

thf(6087,plain,
    ! [SV450: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV450 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV450 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4825]) ).

thf(6088,plain,
    ! [SV451: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV451 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV451 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4826]) ).

thf(6089,plain,
    ! [SV452: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV452 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV452 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4827]) ).

thf(6090,plain,
    ! [SV453: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV453 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV453 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4828]) ).

thf(6091,plain,
    ! [SV454: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV454 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV454 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4829]) ).

thf(6092,plain,
    ! [SV455: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV455 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV455 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4830]) ).

thf(6093,plain,
    ! [SV456: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV456 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV456 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4831]) ).

thf(6094,plain,
    ! [SV457: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV457 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV457 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4832]) ).

thf(6095,plain,
    ! [SV458: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV458 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV458 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4833]) ).

thf(6096,plain,
    ! [SV459: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV459 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV459 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4834]) ).

thf(6097,plain,
    ! [SV460: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV460 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV460 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4835]) ).

thf(6098,plain,
    ! [SV461: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV461 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV461 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4836]) ).

thf(6099,plain,
    ! [SV462: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV462 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV462 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4837]) ).

thf(6100,plain,
    ! [SV463: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV463 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV463 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4838]) ).

thf(6101,plain,
    ! [SV464: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV464 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV464 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4839]) ).

thf(6102,plain,
    ! [SV465: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV465 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV465 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4840]) ).

thf(6103,plain,
    ! [SV466: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV466 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV466 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4841]) ).

thf(6104,plain,
    ! [SV467: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV467 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV467 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4842]) ).

thf(6105,plain,
    ! [SV468: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV468 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV468 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4843]) ).

thf(6106,plain,
    ! [SV469: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV469 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV469 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4844]) ).

thf(6107,plain,
    ! [SV470: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV470 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV470 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4845]) ).

thf(6108,plain,
    ! [SV471: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV471 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV471 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4846]) ).

thf(6109,plain,
    ! [SV472: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV472 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV472 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4847]) ).

thf(6110,plain,
    ! [SV473: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV473 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV473 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4848]) ).

thf(6111,plain,
    ! [SV474: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV474 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV474 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4849]) ).

thf(6112,plain,
    ! [SV475: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV475 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV475 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4850]) ).

thf(6113,plain,
    ! [SV476: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV476 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV476 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4851]) ).

thf(6114,plain,
    ! [SV477: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV477 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV477 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4852]) ).

thf(6115,plain,
    ! [SV478: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV478 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV478 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4853]) ).

thf(6116,plain,
    ! [SV479: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV479 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV479 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4854]) ).

thf(6117,plain,
    ! [SV480: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV480 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV480 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4855]) ).

thf(6118,plain,
    ! [SV481: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV481 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV481 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4856]) ).

thf(6119,plain,
    ! [SV482: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV482 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV482 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4857]) ).

thf(6120,plain,
    ! [SV483: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV483 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV483 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4858]) ).

thf(6121,plain,
    ! [SV484: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV484 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV484 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4859]) ).

thf(6122,plain,
    ! [SV485: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV485 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV485 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4860]) ).

thf(6123,plain,
    ! [SV486: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV486 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV486 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4861]) ).

thf(6124,plain,
    ! [SV487: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV487 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV487 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4862]) ).

thf(6125,plain,
    ! [SV488: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV488 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV488 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4863]) ).

thf(6126,plain,
    ! [SV489: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV489 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV489 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4864]) ).

thf(6127,plain,
    ! [SV490: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV490 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV490 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4865]) ).

thf(6128,plain,
    ! [SV491: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV491 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV491 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4866]) ).

thf(6129,plain,
    ! [SV492: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV492 ) )
        = $true )
      | ( ( class_HOL_Oinverse @ SV492 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4867]) ).

thf(6130,plain,
    ! [SV493: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV493 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV493 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4868]) ).

thf(6131,plain,
    ! [SV494: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV494 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV494 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4869]) ).

thf(6132,plain,
    ! [SV495: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV495 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV495 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4870]) ).

thf(6133,plain,
    ! [SV496: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV496 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV496 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4871]) ).

thf(6134,plain,
    ! [SV497: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV497 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV497 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4872]) ).

thf(6135,plain,
    ! [SV498: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV498 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV498 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4873]) ).

thf(6136,plain,
    ! [SV499: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV499 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV499 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4874]) ).

thf(6137,plain,
    ! [SV500: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV500 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV500 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4875]) ).

thf(6138,plain,
    ! [SV501: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV501 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV501 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4876]) ).

thf(6139,plain,
    ! [SV502: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV502 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV502 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4877]) ).

thf(6140,plain,
    ! [SV503: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV503 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV503 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4878]) ).

thf(6141,plain,
    ! [SV504: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV504 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV504 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4879]) ).

thf(6142,plain,
    ! [SV505: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV505 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring__1 @ SV505 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4880]) ).

thf(6143,plain,
    ! [SV506: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV506 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV506 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4881]) ).

thf(6144,plain,
    ! [SV507: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV507 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV507 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4882]) ).

thf(6145,plain,
    ! [SV508: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV508 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV508 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4883]) ).

thf(6146,plain,
    ! [SV509: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV509 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV509 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4884]) ).

thf(6147,plain,
    ! [SV510: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV510 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV510 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4885]) ).

thf(6148,plain,
    ! [SV511: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV511 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV511 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4886]) ).

thf(6149,plain,
    ! [SV512: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV512 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV512 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4887]) ).

thf(6150,plain,
    ! [SV513: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV513 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV513 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4888]) ).

thf(6151,plain,
    ! [SV514: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV514 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV514 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4889]) ).

thf(6152,plain,
    ! [SV515: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV515 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV515 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4890]) ).

thf(6153,plain,
    ! [SV516: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV516 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV516 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4891]) ).

thf(6154,plain,
    ! [SV517: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV517 ) )
        = $true )
      | ( ( class_HOL_Oinverse @ SV517 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4892]) ).

thf(6155,plain,
    ! [SV518: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV518 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oidom @ SV518 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4893]) ).

thf(6156,plain,
    ! [SV519: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV519 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV519 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4894]) ).

thf(6157,plain,
    ! [SV520: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV520 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV520 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4895]) ).

thf(6158,plain,
    ! [SV521: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV521 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV521 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4896]) ).

thf(6159,plain,
    ! [SV522: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV522 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV522 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4897]) ).

thf(6160,plain,
    ! [SV523: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV523 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV523 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4898]) ).

thf(6161,plain,
    ! [SV524: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV524 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV524 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4899]) ).

thf(6162,plain,
    ! [SV525: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Ofield @ SV525 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV525 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4900]) ).

thf(6163,plain,
    ! [SV526: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV526 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV526 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4901]) ).

thf(6164,plain,
    ! [SV527: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV527 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV527 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4902]) ).

thf(6165,plain,
    ! [SV528: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV528 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV528 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4903]) ).

thf(6166,plain,
    ! [SV529: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV529 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV529 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4904]) ).

thf(6167,plain,
    ! [SV530: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV530 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV530 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4905]) ).

thf(6168,plain,
    ! [SV531: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV531 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV531 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4906]) ).

thf(6169,plain,
    ! [SV532: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV532 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV532 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4907]) ).

thf(6170,plain,
    ! [SV533: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV533 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV533 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4908]) ).

thf(6171,plain,
    ! [SV534: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV534 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV534 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4909]) ).

thf(6172,plain,
    ! [SV535: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV535 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV535 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4910]) ).

thf(6173,plain,
    ! [SV536: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV536 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV536 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4911]) ).

thf(6174,plain,
    ! [SV537: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV537 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV537 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4912]) ).

thf(6175,plain,
    ! [SV538: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV538 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring__1 @ SV538 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4913]) ).

thf(6176,plain,
    ! [SV539: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV539 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV539 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4914]) ).

thf(6177,plain,
    ! [SV540: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV540 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV540 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4915]) ).

thf(6178,plain,
    ! [SV541: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV541 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV541 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4916]) ).

thf(6179,plain,
    ! [SV542: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV542 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV542 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4917]) ).

thf(6180,plain,
    ! [SV543: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV543 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV543 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4918]) ).

thf(6181,plain,
    ! [SV544: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV544 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV544 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4919]) ).

thf(6182,plain,
    ! [SV545: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV545 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV545 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4920]) ).

thf(6183,plain,
    ! [SV546: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV546 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV546 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4921]) ).

thf(6184,plain,
    ! [SV547: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV547 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV547 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4922]) ).

thf(6185,plain,
    ! [SV548: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV548 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV548 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4923]) ).

thf(6186,plain,
    ! [SV549: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV549 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV549 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4924]) ).

thf(6187,plain,
    ! [SV550: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV550 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV550 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4925]) ).

thf(6188,plain,
    ! [SV551: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV551 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV551 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4926]) ).

thf(6189,plain,
    ! [SV552: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV552 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV552 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4927]) ).

thf(6190,plain,
    ! [SV553: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV553 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV553 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4928]) ).

thf(6191,plain,
    ! [SV554: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV554 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV554 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4929]) ).

thf(6192,plain,
    ! [SV555: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV555 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV555 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4930]) ).

thf(6193,plain,
    ! [SV556: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oidom @ SV556 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV556 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4931]) ).

thf(6194,plain,
    ! [SV557: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV557 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV557 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4932]) ).

thf(6195,plain,
    ! [SV558: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV558 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV558 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4933]) ).

thf(6196,plain,
    ! [SV559: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV559 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV559 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4934]) ).

thf(6197,plain,
    ! [SV560: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV560 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV560 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4935]) ).

thf(6198,plain,
    ! [SV561: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV561 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV561 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4936]) ).

thf(6199,plain,
    ! [SV562: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV562 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV562 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4937]) ).

thf(6200,plain,
    ! [SV563: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV563 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV563 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4938]) ).

thf(6201,plain,
    ! [SV564: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV564 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV564 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4939]) ).

thf(6202,plain,
    ! [SV565: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV565 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV565 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4940]) ).

thf(6203,plain,
    ! [SV566: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV566 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV566 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4941]) ).

thf(6204,plain,
    ! [SV567: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV567 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV567 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4942]) ).

thf(6205,plain,
    ! [SV568: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV568 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV568 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4943]) ).

thf(6206,plain,
    ! [SV569: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV569 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV569 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4944]) ).

thf(6207,plain,
    ! [SV570: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV570 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV570 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4945]) ).

thf(6208,plain,
    ! [SV571: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV571 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV571 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4946]) ).

thf(6209,plain,
    ! [SV572: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV572 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV572 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4947]) ).

thf(6210,plain,
    ! [SV573: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV573 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV573 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4948]) ).

thf(6211,plain,
    ! [SV574: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV574 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV574 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4949]) ).

thf(6212,plain,
    ! [SV575: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV575 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV575 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4950]) ).

thf(6213,plain,
    ! [SV576: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV576 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV576 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4951]) ).

thf(6214,plain,
    ! [SV577: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV577 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV577 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4952]) ).

thf(6215,plain,
    ! [SV578: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV578 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV578 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4953]) ).

thf(6216,plain,
    ! [SV579: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV579 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV579 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4954]) ).

thf(6217,plain,
    ! [SV580: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV580 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV580 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4955]) ).

thf(6218,plain,
    ! [SV581: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV581 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV581 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4956]) ).

thf(6219,plain,
    ! [SV582: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV582 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV582 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4957]) ).

thf(6220,plain,
    ! [SV583: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV583 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV583 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4958]) ).

thf(6221,plain,
    ! [SV584: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV584 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV584 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4959]) ).

thf(6222,plain,
    ! [SV585: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV585 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV585 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4960]) ).

thf(6223,plain,
    ! [SV586: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV586 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV586 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4961]) ).

thf(6224,plain,
    ! [SV587: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV587 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV587 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4962]) ).

thf(6225,plain,
    ! [SV588: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV588 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV588 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4963]) ).

thf(6226,plain,
    ! [SV589: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV589 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV589 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4964]) ).

thf(6227,plain,
    ! [SV590: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV590 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV590 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4965]) ).

thf(6228,plain,
    ! [SV591: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV591 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV591 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4966]) ).

thf(6229,plain,
    ! [SV592: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV592 ) )
        = $true )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV592 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4967]) ).

thf(6230,plain,
    ! [SV593: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV593 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV593 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4968]) ).

thf(6231,plain,
    ! [SV594: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV594 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV594 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4969]) ).

thf(6232,plain,
    ! [SV595: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV595 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV595 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4970]) ).

thf(6233,plain,
    ! [SV596: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV596 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV596 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4971]) ).

thf(6234,plain,
    ! [SV597: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV597 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV597 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4972]) ).

thf(6235,plain,
    ! [SV598: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV598 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV598 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4973]) ).

thf(6236,plain,
    ! [SV599: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV599 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV599 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4974]) ).

thf(6237,plain,
    ! [SV600: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV600 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV600 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4975]) ).

thf(6238,plain,
    ! [SV601: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV601 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV601 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4976]) ).

thf(6239,plain,
    ! [SV602: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV602 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV602 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4977]) ).

thf(6240,plain,
    ! [SV603: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV603 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV603 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4978]) ).

thf(6241,plain,
    ! [SV604: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV604 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV604 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4979]) ).

thf(6242,plain,
    ! [SV605: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV605 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV605 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4980]) ).

thf(6243,plain,
    ! [SV606: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV606 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV606 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4981]) ).

thf(6244,plain,
    ! [SV607: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV607 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV607 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4982]) ).

thf(6245,plain,
    ! [SV608: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV608 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV608 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4983]) ).

thf(6246,plain,
    ! [SV609: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV609 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV609 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4984]) ).

thf(6247,plain,
    ! [SV610: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV610 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV610 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4985]) ).

thf(6248,plain,
    ! [SV611: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV611 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV611 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4986]) ).

thf(6249,plain,
    ! [SV612: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV612 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV612 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4987]) ).

thf(6250,plain,
    ! [SV613: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV613 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV613 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4988]) ).

thf(6251,plain,
    ! [SV614: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV614 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV614 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4989]) ).

thf(6252,plain,
    ! [SV615: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV615 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV615 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4990]) ).

thf(6253,plain,
    ! [SV616: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV616 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV616 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4991]) ).

thf(6254,plain,
    ! [SV617: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV617 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV617 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4992]) ).

thf(6255,plain,
    ! [SV618: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV618 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ofield @ SV618 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4993]) ).

thf(6256,plain,
    ! [SV619: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV619 ) )
        = $true )
      | ( ( class_HOL_Oinverse @ SV619 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4994]) ).

thf(6257,plain,
    ! [SV620: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV620 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV620 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4995]) ).

thf(6258,plain,
    ! [SV621: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV621 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV621 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4996]) ).

thf(6259,plain,
    ! [SV622: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV622 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV622 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4997]) ).

thf(6260,plain,
    ! [SV623: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV623 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV623 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4998]) ).

thf(6261,plain,
    ! [SV624: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV624 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV624 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4999]) ).

thf(6262,plain,
    ! [SV625: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV625 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV625 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5000]) ).

thf(6263,plain,
    ! [SV626: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV626 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV626 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5001]) ).

thf(6264,plain,
    ! [SV627: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV627 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV627 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5002]) ).

thf(6265,plain,
    ! [SV628: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV628 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV628 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5003]) ).

thf(6266,plain,
    ! [SV629: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV629 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV629 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5004]) ).

thf(6267,plain,
    ! [SV630: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV630 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oidom @ SV630 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5005]) ).

thf(6268,plain,
    ! [SV631: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV631 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV631 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5006]) ).

thf(6269,plain,
    ! [SV632: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV632 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV632 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5007]) ).

thf(6270,plain,
    ! [SV633: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV633 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV633 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5008]) ).

thf(6271,plain,
    ! [SV634: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV634 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV634 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5009]) ).

thf(6272,plain,
    ! [SV635: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV635 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV635 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5010]) ).

thf(6273,plain,
    ! [SV636: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV636 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV636 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5011]) ).

thf(6274,plain,
    ! [SV637: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV637 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV637 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5012]) ).

thf(6275,plain,
    ! [SV638: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV638 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV638 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5013]) ).

thf(6276,plain,
    ! [SV639: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV639 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV639 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5014]) ).

thf(6277,plain,
    ! [SV640: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV640 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV640 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5015]) ).

thf(6278,plain,
    ! [SV641: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV641 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV641 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5016]) ).

thf(6279,plain,
    ! [SV642: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV642 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV642 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5017]) ).

thf(6280,plain,
    ! [SV643: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV643 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV643 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5018]) ).

thf(6281,plain,
    ! [SV644: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV644 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV644 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5019]) ).

thf(6282,plain,
    ! [SV645: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV645 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV645 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5020]) ).

thf(6283,plain,
    ! [SV646: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV646 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV646 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5021]) ).

thf(6284,plain,
    ! [SV647: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV647 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV647 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5022]) ).

thf(6285,plain,
    ! [SV648: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV648 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV648 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5023]) ).

thf(6286,plain,
    ! [SV649: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV649 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV649 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5024]) ).

thf(6287,plain,
    ! [SV650: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV650 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__ring__strict @ SV650 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5025]) ).

thf(6288,plain,
    ! [SV651: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV651 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV651 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5026]) ).

thf(6289,plain,
    ! [SV652: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV652 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV652 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5027]) ).

thf(6290,plain,
    ! [SV653: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV653 ) )
        = $true )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV653 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5028]) ).

thf(6291,plain,
    ! [SV654: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV654 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV654 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5029]) ).

thf(6292,plain,
    ! [SV655: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV655 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV655 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5030]) ).

thf(6293,plain,
    ! [SV656: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV656 ) )
        = $true )
      | ( ( class_Ring__and__Field_Olordered__ring @ SV656 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5031]) ).

thf(6294,plain,
    ! [SV657: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV657 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV657 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5032]) ).

thf(6295,plain,
    ! [SV658: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV658 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV658 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5033]) ).

thf(6296,plain,
    ! [SV659: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV659 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV659 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5034]) ).

thf(6297,plain,
    ! [SV660: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV660 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV660 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5035]) ).

thf(6298,plain,
    ! [SV661: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV661 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV661 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5036]) ).

thf(6299,plain,
    ! [SV662: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV662 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV662 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5037]) ).

thf(6300,plain,
    ! [SV663: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV663 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring__1 @ SV663 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5038]) ).

thf(6301,plain,
    ! [SV664: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV664 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV664 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5039]) ).

thf(6302,plain,
    ! [SV665: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV665 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV665 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5040]) ).

thf(6303,plain,
    ! [SV666: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV666 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV666 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5041]) ).

thf(6304,plain,
    ! [SV667: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV667 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV667 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5042]) ).

thf(6305,plain,
    ! [SV668: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV668 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV668 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5043]) ).

thf(6306,plain,
    ! [SV669: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV669 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV669 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5044]) ).

thf(6307,plain,
    ! [SV670: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV670 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV670 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5045]) ).

thf(6308,plain,
    ! [SV671: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV671 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV671 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5046]) ).

thf(6309,plain,
    ! [SV672: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV672 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV672 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5047]) ).

thf(6310,plain,
    ! [SV673: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV673 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV673 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5048]) ).

thf(6311,plain,
    ! [SV674: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV674 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV674 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5049]) ).

thf(6312,plain,
    ! [SV675: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV675 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__semidom @ SV675 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5050]) ).

thf(6313,plain,
    ! [SV676: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV676 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV676 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5051]) ).

thf(6314,plain,
    ! [SV677: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV677 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV677 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5052]) ).

thf(6315,plain,
    ! [SV678: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV678 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV678 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5053]) ).

thf(6316,plain,
    ! [SV679: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV679 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV679 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5054]) ).

thf(6317,plain,
    ! [SV680: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV680 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV680 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5055]) ).

thf(6318,plain,
    ! [SV681: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV681 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV681 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5056]) ).

thf(6319,plain,
    ! [SV682: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV682 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV682 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5057]) ).

thf(6320,plain,
    ! [SV683: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV683 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV683 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5058]) ).

thf(6321,plain,
    ! [SV684: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV684 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5059]) ).

thf(6322,plain,
    ! [SV685: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV685 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV685 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5060]) ).

thf(6323,plain,
    ! [SV686: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV686 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV686 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5061]) ).

thf(6324,plain,
    ! [SV687: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV687 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV687 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5062]) ).

thf(6325,plain,
    ! [SV688: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV688 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV688 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5063]) ).

thf(6326,plain,
    ! [SV689: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV689 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV689 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5064]) ).

thf(6327,plain,
    ! [SV690: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV690 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV690 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5065]) ).

thf(6328,plain,
    ! [SV691: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV691 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring__1 @ SV691 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5066]) ).

thf(6329,plain,
    ! [SV692: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV692 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV692 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5067]) ).

thf(6330,plain,
    ! [SV693: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV693 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV693 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5068]) ).

thf(6331,plain,
    ! [SV694: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV694 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV694 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5069]) ).

thf(6332,plain,
    ! [SV695: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV695 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV695 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5070]) ).

thf(6333,plain,
    ! [SV696: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV696 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV696 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5071]) ).

thf(6334,plain,
    ! [SV697: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV697 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV697 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5072]) ).

thf(6335,plain,
    ! [SV698: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV698 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV698 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5073]) ).

thf(6336,plain,
    ! [SV699: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV699 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV699 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5074]) ).

thf(6337,plain,
    ! [SV700: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV700 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV700 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5075]) ).

thf(6338,plain,
    ! [SV701: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV701 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV701 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5076]) ).

thf(6339,plain,
    ! [SV702: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV702 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV702 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5077]) ).

thf(6340,plain,
    ! [SV703: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV703 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV703 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5078]) ).

thf(6341,plain,
    ! [SV704: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV704 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV704 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5079]) ).

thf(6342,plain,
    ! [SV705: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV705 ) )
        = $true )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV705 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5080]) ).

thf(6343,plain,
    ! [SV706: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV706 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV706 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5081]) ).

thf(6344,plain,
    ! [SV707: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV707 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV707 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5082]) ).

thf(6345,plain,
    ! [SV708: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV708 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV708 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5083]) ).

thf(6346,plain,
    ! [SV709: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV709 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV709 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5084]) ).

thf(6347,plain,
    ! [SV710: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV710 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV710 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5085]) ).

thf(6348,plain,
    ! [SV711: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV711 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV711 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5086]) ).

thf(6349,plain,
    ! [SV712: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV712 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV712 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5087]) ).

thf(6350,plain,
    ! [SV713: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV713 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV713 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5088]) ).

thf(6351,plain,
    ! [SV714: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV714 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV714 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5089]) ).

thf(6352,plain,
    ! [SV715: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV715 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV715 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5090]) ).

thf(6353,plain,
    ! [SV716: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV716 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV716 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5091]) ).

thf(6354,plain,
    ! [SV717: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV717 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV717 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5092]) ).

thf(6355,plain,
    ! [SV718: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV718 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV718 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5093]) ).

thf(6356,plain,
    ! [SV719: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV719 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV719 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5094]) ).

thf(6357,plain,
    ! [SV720: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV720 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV720 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5095]) ).

thf(6358,plain,
    ! [SV721: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV721 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__ring__strict @ SV721 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5096]) ).

thf(6359,plain,
    ! [SV722: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV722 ) )
        = $true )
      | ( ( class_Ring__and__Field_Olordered__ring @ SV722 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5097]) ).

thf(6360,plain,
    ! [SV723: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV723 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV723 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5098]) ).

thf(6361,plain,
    ! [SV724: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV724 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV724 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5099]) ).

thf(6362,plain,
    ! [SV725: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV725 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV725 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5100]) ).

thf(6363,plain,
    ! [SV726: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV726 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV726 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5101]) ).

thf(6364,plain,
    ! [SV727: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV727 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV727 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5102]) ).

thf(6365,plain,
    ! [SV728: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV728 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV728 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5103]) ).

thf(6366,plain,
    ! [SV729: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV729 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV729 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5104]) ).

thf(6367,plain,
    ! [SV730: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV730 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__semidom @ SV730 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5105]) ).

thf(6368,plain,
    ! [SV731: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV731 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV731 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5106]) ).

thf(6369,plain,
    ! [SV732: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV732 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oidom @ SV732 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5107]) ).

thf(6370,plain,
    ! [SV733: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV733 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV733 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5108]) ).

thf(6371,plain,
    ! [SV734: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV734 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV734 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5109]) ).

thf(6372,plain,
    ! [SV735: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV735 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV735 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5110]) ).

thf(6373,plain,
    ! [SV736: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV736 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV736 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5111]) ).

thf(6374,plain,
    ! [SV737: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV737 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV737 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5112]) ).

thf(6375,plain,
    ! [SV738: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV738 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV738 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5113]) ).

thf(6376,plain,
    ! [SV739: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV739 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV739 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5114]) ).

thf(6377,plain,
    ! [SV740: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV740 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV740 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5115]) ).

thf(6378,plain,
    ! [SV741: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV741 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV741 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5116]) ).

thf(6379,plain,
    ! [SV742: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV742 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV742 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5117]) ).

thf(6380,plain,
    ! [SV743: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV743 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV743 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5118]) ).

thf(6381,plain,
    ! [SV744: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV744 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV744 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5119]) ).

thf(6382,plain,
    ! [SV745: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV745 ) )
        = $true )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV745 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5120]) ).

thf(6383,plain,
    ! [SV746: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV746 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV746 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5121]) ).

thf(6384,plain,
    ! [SV747: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV747 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5122]) ).

thf(6385,plain,
    ! [SV748: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV748 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV748 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5123]) ).

thf(6386,plain,
    ! [SV749: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV749 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV749 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5124]) ).

thf(6387,plain,
    ! [SV750: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV750 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV750 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5125]) ).

thf(6388,plain,
    ! [SV751: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV751 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV751 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5126]) ).

thf(6389,plain,
    ! [SV752: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV752 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV752 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5127]) ).

thf(6390,plain,
    ! [SV753: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV753 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV753 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5128]) ).

thf(6391,plain,
    ! [SV754: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV754 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV754 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5129]) ).

thf(6392,plain,
    ! [SV755: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV755 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV755 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5130]) ).

thf(6393,plain,
    ! [SV756: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV756 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV756 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5131]) ).

thf(6394,plain,
    ! [SV757: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV757 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV757 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5132]) ).

thf(6395,plain,
    ! [SV758: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV758 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV758 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5133]) ).

thf(6396,plain,
    ! [SV759: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV759 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV759 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5134]) ).

thf(6397,plain,
    ! [SV760: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV760 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV760 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5135]) ).

thf(6398,plain,
    ! [SV761: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV761 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV761 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5136]) ).

thf(6399,plain,
    ! [SV762: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV762 ) )
        = $true )
      | ( ( class_Ring__and__Field_Olordered__ring @ SV762 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5137]) ).

thf(6400,plain,
    ! [SV763: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV763 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV763 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5138]) ).

thf(6401,plain,
    ! [SV764: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV764 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV764 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5139]) ).

thf(6402,plain,
    ! [SV765: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV765 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV765 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5140]) ).

thf(6403,plain,
    ! [SV766: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV766 ) )
        = $true )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV766 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5141]) ).

thf(6404,plain,
    ! [SV767: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV767 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV767 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5142]) ).

thf(6405,plain,
    ! [SV768: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV768 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV768 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5143]) ).

thf(6406,plain,
    ! [SV769: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV769 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV769 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5144]) ).

thf(6407,plain,
    ! [SV770: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV770 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV770 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5145]) ).

thf(6408,plain,
    ! [SV771: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV771 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV771 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5146]) ).

thf(6409,plain,
    ! [SV772: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV772 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV772 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5147]) ).

thf(6410,plain,
    ! [SV773: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV773 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV773 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5148]) ).

thf(6411,plain,
    ! [SV774: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV774 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV774 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5149]) ).

thf(6412,plain,
    ! [SV775: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV775 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV775 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5150]) ).

thf(6413,plain,
    ! [SV776: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV776 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV776 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5151]) ).

thf(6414,plain,
    ! [SV777: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV777 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV777 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5152]) ).

thf(6415,plain,
    ! [SV778: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV778 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV778 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5153]) ).

thf(6416,plain,
    ! [SV779: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV779 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV779 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5154]) ).

thf(6417,plain,
    ! [SV780: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV780 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV780 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5155]) ).

thf(6418,plain,
    ! [SV781: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV781 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV781 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5156]) ).

thf(6419,plain,
    ! [SV782: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV782 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV782 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5157]) ).

thf(6420,plain,
    ! [SV783: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV783 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV783 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5158]) ).

thf(6421,plain,
    ! [SV784: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV784 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV784 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5159]) ).

thf(6422,plain,
    ! [SV785: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV785 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV785 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5160]) ).

thf(6423,plain,
    ! [SV786: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV786 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV786 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5161]) ).

thf(6424,plain,
    ! [SV787: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV787 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV787 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5162]) ).

thf(6425,plain,
    ! [SV788: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV788 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV788 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5163]) ).

thf(6426,plain,
    ! [SV789: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV789 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV789 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5164]) ).

thf(6427,plain,
    ! [SV790: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV790 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV790 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5165]) ).

thf(6428,plain,
    ! [SV791: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV791 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV791 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5166]) ).

thf(6429,plain,
    ! [SV792: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV792 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV792 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5167]) ).

thf(6430,plain,
    ! [SV793: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV793 ) )
        = $true )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV793 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5168]) ).

thf(6431,plain,
    ! [SV794: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV794 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV794 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5169]) ).

thf(6432,plain,
    ! [SV795: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV795 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV795 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5170]) ).

thf(6433,plain,
    ! [SV796: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV796 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV796 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5171]) ).

thf(6434,plain,
    ! [SV797: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV797 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV797 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5172]) ).

thf(6435,plain,
    ! [SV798: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV798 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV798 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5173]) ).

thf(6436,plain,
    ! [SV799: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV799 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV799 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5174]) ).

thf(6437,plain,
    ! [SV800: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV800 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV800 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5175]) ).

thf(6438,plain,
    ! [SV801: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV801 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV801 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5176]) ).

thf(6439,plain,
    ! [SV802: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV802 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV802 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5177]) ).

thf(6440,plain,
    ! [SV803: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV803 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV803 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5178]) ).

thf(6441,plain,
    ! [SV804: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV804 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV804 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5179]) ).

thf(6442,plain,
    ! [SV805: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV805 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV805 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5180]) ).

thf(6443,plain,
    ! [SV806: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV806 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV806 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5181]) ).

thf(6444,plain,
    ! [SV807: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV807 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV807 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5182]) ).

thf(6445,plain,
    ! [SV808: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV808 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV808 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5183]) ).

thf(6446,plain,
    ! [SV809: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV809 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV809 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5184]) ).

thf(6447,plain,
    ! [SV810: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV810 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV810 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5185]) ).

thf(6448,plain,
    ! [SV811: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV811 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV811 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5186]) ).

thf(6449,plain,
    ! [SV812: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV812 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV812 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5187]) ).

thf(6450,plain,
    ! [SV813: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV813 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV813 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5188]) ).

thf(6451,plain,
    ! [SV814: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV814 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV814 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5189]) ).

thf(6452,plain,
    ! [SV815: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV815 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV815 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5190]) ).

thf(6453,plain,
    ! [SV816: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV816 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV816 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5191]) ).

thf(6454,plain,
    ! [SV817: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV817 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV817 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5192]) ).

thf(6455,plain,
    ! [SV818: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV818 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV818 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5193]) ).

thf(6456,plain,
    ! [SV819: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV819 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV819 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5194]) ).

thf(6457,plain,
    ! [SV820: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV820 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV820 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5195]) ).

thf(6458,plain,
    ! [SV821: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV821 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV821 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5196]) ).

thf(6459,plain,
    ! [SV822: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV822 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV822 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5197]) ).

thf(6460,plain,
    ! [SV823: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV823 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV823 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5198]) ).

thf(6461,plain,
    ! [SV824: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV824 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV824 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5199]) ).

thf(6462,plain,
    ! [SV825: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV825 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV825 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5200]) ).

thf(6463,plain,
    ! [SV826: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV826 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV826 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5201]) ).

thf(6464,plain,
    ! [SV827: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV827 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV827 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5202]) ).

thf(6465,plain,
    ! [SV828: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV828 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV828 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5203]) ).

thf(6466,plain,
    ! [SV829: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV829 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV829 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5204]) ).

thf(6467,plain,
    ! [SV830: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV830 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV830 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5205]) ).

thf(6468,plain,
    ! [SV831: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV831 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV831 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5206]) ).

thf(6469,plain,
    ! [SV832: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV832 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV832 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5207]) ).

thf(6470,plain,
    ! [SV833: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV833 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV833 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5208]) ).

thf(6471,plain,
    ! [SV834: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV834 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV834 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5209]) ).

thf(6472,plain,
    ! [SV835: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV835 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV835 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5210]) ).

thf(6473,plain,
    ! [SV836: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV836 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV836 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5211]) ).

thf(6474,plain,
    ! [SV837: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV837 ) )
        = $true )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV837 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5212]) ).

thf(6475,plain,
    ! [SV838: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV838 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV838 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5213]) ).

thf(6476,plain,
    ! [SV839: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV839 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV839 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5214]) ).

thf(6477,plain,
    ! [SV840: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV840 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV840 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5215]) ).

thf(6478,plain,
    ! [SV841: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV841 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV841 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5216]) ).

thf(6479,plain,
    ! [SV842: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV842 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV842 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5217]) ).

thf(6480,plain,
    ! [SV843: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV843 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV843 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5218]) ).

thf(6481,plain,
    ! [SV844: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV844 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV844 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5219]) ).

thf(6482,plain,
    ! [SV845: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV845 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV845 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5220]) ).

thf(6483,plain,
    ! [SV846: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV846 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV846 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5221]) ).

thf(6484,plain,
    ! [SV847: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV847 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV847 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5222]) ).

thf(6485,plain,
    ! [SV848: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV848 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV848 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5223]) ).

thf(6486,plain,
    ! [SV849: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV849 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV849 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5224]) ).

thf(6487,plain,
    ! [SV850: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV850 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV850 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5225]) ).

thf(6488,plain,
    ! [SV851: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV851 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV851 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5226]) ).

thf(6489,plain,
    ! [SV852: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV852 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV852 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5227]) ).

thf(6490,plain,
    ! [SV853: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV853 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV853 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5228]) ).

thf(6491,plain,
    ! [SV854: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV854 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV854 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5229]) ).

thf(6492,plain,
    ! [SV855: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV855 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV855 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5230]) ).

thf(6493,plain,
    ! [SV856: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV856 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV856 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5231]) ).

thf(6494,plain,
    ! [SV857: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV857 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV857 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5232]) ).

thf(6495,plain,
    ! [SV858: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV858 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV858 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5233]) ).

thf(6496,plain,
    ! [SV859: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV859 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV859 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5234]) ).

thf(6497,plain,
    ! [SV860: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV860 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV860 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5235]) ).

thf(6498,plain,
    ! [SV861: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV861 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV861 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5236]) ).

thf(6499,plain,
    ! [SV862: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV862 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV862 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5237]) ).

thf(6500,plain,
    ! [SV863: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV863 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV863 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5238]) ).

thf(6501,plain,
    ! [SV864: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV864 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV864 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5239]) ).

thf(6502,plain,
    ! [SV865: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV865 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV865 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5240]) ).

thf(6503,plain,
    ! [SV866: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV866 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV866 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5241]) ).

thf(6504,plain,
    ! [SV867: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV867 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV867 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5242]) ).

thf(6505,plain,
    ! [SV868: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV868 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV868 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5243]) ).

thf(6506,plain,
    ! [SV869: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV869 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV869 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5244]) ).

thf(6507,plain,
    ! [SV870: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV870 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV870 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5245]) ).

thf(6508,plain,
    ! [SV871: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV871 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV871 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5246]) ).

thf(6509,plain,
    ! [SV872: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV872 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV872 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5247]) ).

thf(6510,plain,
    ! [SV873: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV873 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV873 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5248]) ).

thf(6511,plain,
    ! [SV874: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV874 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV874 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5249]) ).

thf(6512,plain,
    ! [SV875: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV875 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV875 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5250]) ).

thf(6513,plain,
    ! [SV876: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV876 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV876 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5251]) ).

thf(6514,plain,
    ! [SV877: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV877 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV877 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5252]) ).

thf(6515,plain,
    ! [SV878: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV878 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV878 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5253]) ).

thf(6516,plain,
    ! [SV879: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV879 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV879 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5254]) ).

thf(6517,plain,
    ! [SV880: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV880 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV880 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5255]) ).

thf(6518,plain,
    ! [SV881: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV881 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV881 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5256]) ).

thf(6519,plain,
    ! [SV882: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV882 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV882 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5257]) ).

thf(6520,plain,
    ! [SV883: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV883 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV883 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5258]) ).

thf(6521,plain,
    ! [SV884: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV884 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV884 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5259]) ).

thf(6522,plain,
    ! [SV885: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV885 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV885 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5260]) ).

thf(6523,plain,
    ! [SV886: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV886 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV886 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5261]) ).

thf(6524,plain,
    ! [SV887: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV887 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV887 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5262]) ).

thf(6525,plain,
    ! [SV888: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV888 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV888 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5263]) ).

thf(6526,plain,
    ! [SV889: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV889 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV889 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5264]) ).

thf(6527,plain,
    ! [SV890: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV890 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV890 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5265]) ).

thf(6528,plain,
    ! [SV891: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV891 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV891 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5266]) ).

thf(6529,plain,
    ! [SV892: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV892 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV892 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5267]) ).

thf(6530,plain,
    ! [SV893: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV893 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV893 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5268]) ).

thf(6531,plain,
    ! [SV894: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV894 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV894 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5269]) ).

thf(6532,plain,
    ! [SV895: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV895 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV895 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5270]) ).

thf(6533,plain,
    ! [SV896: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV896 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV896 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5271]) ).

thf(6534,plain,
    ! [SV897: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV897 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV897 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5272]) ).

thf(6535,plain,
    ! [SV898: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV898 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV898 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5273]) ).

thf(6536,plain,
    ! [SV899: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV899 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV899 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5274]) ).

thf(6537,plain,
    ! [SV900: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV900 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV900 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5275]) ).

thf(6538,plain,
    ! [SV901: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV901 ) )
        = $true )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV901 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5276]) ).

thf(6539,plain,
    ! [SV902: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV902 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV902 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5277]) ).

thf(6540,plain,
    ! [SV903: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV903 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV903 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5278]) ).

thf(6541,plain,
    ! [SV904: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV904 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV904 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5279]) ).

thf(6542,plain,
    ! [SV905: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV905 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV905 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5280]) ).

thf(6543,plain,
    ! [SV906: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV906 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV906 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5281]) ).

thf(6544,plain,
    ! [SV907: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV907 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV907 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5282]) ).

thf(6545,plain,
    ! [SV908: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV908 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV908 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5283]) ).

thf(6546,plain,
    ! [SV909: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV909 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV909 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5284]) ).

thf(6547,plain,
    ! [SV910: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV910 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV910 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5285]) ).

thf(6548,plain,
    ! [SV911: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV911 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV911 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5286]) ).

thf(6549,plain,
    ! [SV912: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV912 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV912 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5287]) ).

thf(6550,plain,
    ! [SV913: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV913 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV913 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5288]) ).

thf(6551,plain,
    ! [SV914: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV914 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV914 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5289]) ).

thf(6552,plain,
    ! [SV915: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV915 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV915 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5290]) ).

thf(6553,plain,
    ! [SV916: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV916 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV916 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5291]) ).

thf(6554,plain,
    ! [SV917: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV917 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV917 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5292]) ).

thf(6555,plain,
    ! [SV918: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV918 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV918 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5293]) ).

thf(6556,plain,
    ! [SV919: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV919 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV919 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5294]) ).

thf(6557,plain,
    ! [SV920: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV920 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV920 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5295]) ).

thf(6558,plain,
    ! [SV921: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV921 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV921 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5296]) ).

thf(6559,plain,
    ! [SV922: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV922 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV922 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5297]) ).

thf(6560,plain,
    ! [SV923: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV923 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV923 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5298]) ).

thf(6561,plain,
    ! [SV924: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV924 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV924 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5299]) ).

thf(6562,plain,
    ! [SV925: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV925 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV925 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5300]) ).

thf(6563,plain,
    ! [SV926: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV926 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV926 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5301]) ).

thf(6564,plain,
    ! [SV927: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV927 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV927 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5302]) ).

thf(6565,plain,
    ! [SV928: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV928 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV928 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5303]) ).

thf(6566,plain,
    ! [SV929: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV929 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV929 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5304]) ).

thf(6567,plain,
    ! [SV930: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV930 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV930 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5305]) ).

thf(6568,plain,
    ! [SV931: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV931 ) )
        = $true )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV931 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5306]) ).

thf(6569,plain,
    ! [SV932: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV932 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV932 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5307]) ).

thf(6570,plain,
    ! [SV933: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV933 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV933 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5308]) ).

thf(6571,plain,
    ! [SV934: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV934 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV934 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5309]) ).

thf(6572,plain,
    ! [SV935: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV935 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV935 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5310]) ).

thf(6573,plain,
    ! [SV936: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV936 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV936 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5311]) ).

thf(6574,plain,
    ! [SV937: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV937 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV937 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5312]) ).

thf(6575,plain,
    ! [SV938: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV938 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV938 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5313]) ).

thf(6576,plain,
    ! [SV939: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV939 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV939 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5314]) ).

thf(6577,plain,
    ! [SV940: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV940 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV940 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5315]) ).

thf(6578,plain,
    ! [SV941: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV941 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV941 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5316]) ).

thf(6579,plain,
    ! [SV942: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV942 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV942 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5317]) ).

thf(6580,plain,
    ! [SV943: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV943 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV943 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5318]) ).

thf(6581,plain,
    ! [SV944: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV944 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV944 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5319]) ).

thf(6582,plain,
    ! [SV945: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV945 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV945 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5320]) ).

thf(6583,plain,
    ! [SV946: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV946 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV946 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5321]) ).

thf(6584,plain,
    ! [SV947: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV947 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV947 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5322]) ).

thf(6585,plain,
    ! [SV948: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV948 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV948 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5323]) ).

thf(6586,plain,
    ! [SV949: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV949 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV949 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5324]) ).

thf(6587,plain,
    ! [SV950: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV950 ) )
        = $true )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV950 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5325]) ).

thf(6588,plain,
    ! [SV951: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV951 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV951 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5326]) ).

thf(6589,plain,
    ! [SV952: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV952 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV952 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5327]) ).

thf(6590,plain,
    ! [SV953: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV953 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV953 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5328]) ).

thf(6591,plain,
    ! [SV954: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV954 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV954 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5329]) ).

thf(6592,plain,
    ! [SV955: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV955 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV955 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5330]) ).

thf(6593,plain,
    ! [SV956: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV956 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV956 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5331]) ).

thf(6594,plain,
    ! [SV957: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV957 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV957 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5332]) ).

thf(6595,plain,
    ! [SV958: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV958 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV958 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5333]) ).

thf(6596,plain,
    ! [SV959: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV959 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV959 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5334]) ).

thf(6597,plain,
    ! [SV960: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV960 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV960 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5335]) ).

thf(6598,plain,
    ! [SV961: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV961 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV961 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5336]) ).

thf(6599,plain,
    ! [SV962: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV962 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV962 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5337]) ).

thf(6600,plain,
    ! [SV963: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV963 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV963 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5338]) ).

thf(6601,plain,
    ! [SV964: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring @ SV964 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV964 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5339]) ).

thf(6602,plain,
    ! [SV965: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV965 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oring @ SV965 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5340]) ).

thf(6603,plain,
    ! [SV966: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV966 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__group__add @ SV966 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5341]) ).

thf(6604,plain,
    ! [SV967: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV967 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV967 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5342]) ).

thf(6605,plain,
    ! [SV968: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV968 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV968 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5343]) ).

thf(6606,plain,
    ! [SV969: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV969 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV969 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5344]) ).

thf(6607,plain,
    ! [SV970: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV970 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV970 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5345]) ).

thf(6608,plain,
    ! [SV971: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV971 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV971 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5346]) ).

thf(6609,plain,
    ! [SV972: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV972 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV972 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5347]) ).

thf(6610,plain,
    ! [SV973: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV973 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV973 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5348]) ).

thf(6611,plain,
    ! [SV974: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV974 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV974 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5349]) ).

thf(6612,plain,
    ! [SV975: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV975 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV975 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5350]) ).

thf(6613,plain,
    ! [SV976: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV976 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV976 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5351]) ).

thf(6614,plain,
    ! [SV977: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV977 ) )
        = $true )
      | ( ( class_HOL_Ominus @ SV977 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5352]) ).

thf(6615,plain,
    ! [SV978: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV978 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV978 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5353]) ).

thf(6616,plain,
    ! [SV979: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV979 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV979 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5354]) ).

thf(6617,plain,
    ! [SV980: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV980 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV980 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5355]) ).

thf(6618,plain,
    ! [SV981: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV981 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV981 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5356]) ).

thf(6619,plain,
    ! [SV982: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV982 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV982 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5357]) ).

thf(6620,plain,
    ! [SV983: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV983 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV983 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5358]) ).

thf(6621,plain,
    ! [SV984: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV984 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV984 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5359]) ).

thf(6622,plain,
    ! [SV985: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV985 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV985 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5360]) ).

thf(6623,plain,
    ! [SV986: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV986 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV986 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5361]) ).

thf(6624,plain,
    ! [SV987: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV987 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV987 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5362]) ).

thf(6625,plain,
    ! [SV988: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV988 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV988 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5363]) ).

thf(6626,plain,
    ! [SV989: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV989 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV989 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5364]) ).

thf(6627,plain,
    ! [SV990: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV990 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV990 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5365]) ).

thf(6628,plain,
    ! [SV991: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV991 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV991 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5366]) ).

thf(6629,plain,
    ! [SV992: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV992 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV992 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5367]) ).

thf(6630,plain,
    ! [SV993: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV993 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV993 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5368]) ).

thf(6631,plain,
    ! [SV994: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV994 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV994 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5369]) ).

thf(6632,plain,
    ! [SV995: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV995 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV995 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5370]) ).

thf(6633,plain,
    ! [SV996: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV996 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV996 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5371]) ).

thf(6634,plain,
    ! [SV997: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV997 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV997 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5372]) ).

thf(6635,plain,
    ! [SV998: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV998 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV998 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5373]) ).

thf(6636,plain,
    ! [SV999: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV999 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV999 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5374]) ).

thf(6637,plain,
    ! [SV1000: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1000 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV1000 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5375]) ).

thf(6638,plain,
    ! [SV1001: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1001 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV1001 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5376]) ).

thf(6639,plain,
    ! [SV1002: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1002 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV1002 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5377]) ).

thf(6640,plain,
    ! [SV1003: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1003 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1003 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5378]) ).

thf(6641,plain,
    ! [SV1004: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1004 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV1004 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5379]) ).

thf(6642,plain,
    ! [SV1005: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1005 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV1005 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5380]) ).

thf(6643,plain,
    ! [SV1006: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1006 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV1006 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5381]) ).

thf(6644,plain,
    ! [SV1007: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1007 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV1007 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5382]) ).

thf(6645,plain,
    ! [SV1008: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1008 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1008 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5383]) ).

thf(6646,plain,
    ! [SV1009: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1009 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1009 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5384]) ).

thf(6647,plain,
    ! [SV1010: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1010 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV1010 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5385]) ).

thf(6648,plain,
    ! [SV1011: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1011 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV1011 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5386]) ).

thf(6649,plain,
    ! [SV1012: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1012 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV1012 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5387]) ).

thf(6650,plain,
    ! [SV1013: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1013 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV1013 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5388]) ).

thf(6651,plain,
    ! [SV1014: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1014 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV1014 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5389]) ).

thf(6652,plain,
    ! [SV1015: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1015 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV1015 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5390]) ).

thf(6653,plain,
    ! [SV1016: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1016 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV1016 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5391]) ).

thf(6654,plain,
    ! [SV1017: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1017 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV1017 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5392]) ).

thf(6655,plain,
    ! [SV1018: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1018 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1018 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5393]) ).

thf(6656,plain,
    ! [SV1019: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1019 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV1019 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5394]) ).

thf(6657,plain,
    ! [SV1020: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1020 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV1020 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5395]) ).

thf(6658,plain,
    ! [SV1021: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1021 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV1021 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5396]) ).

thf(6659,plain,
    ! [SV1022: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1022 ) )
        = $true )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1022 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5397]) ).

thf(6660,plain,
    ! [SV1023: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1023 ) )
        = $true )
      | ( ( class_HOL_Oone @ SV1023 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5398]) ).

thf(6661,plain,
    ! [SV1024: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1024 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV1024 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5399]) ).

thf(6662,plain,
    ! [SV1025: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1025 ) )
        = $true )
      | ( ( class_HOL_Otimes @ SV1025 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5400]) ).

thf(6663,plain,
    ! [SV1026: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1026 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1026 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5401]) ).

thf(6664,plain,
    ! [SV1027: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1027 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV1027 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5402]) ).

thf(6665,plain,
    ! [SV1028: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1028 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1028 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5403]) ).

thf(6666,plain,
    ! [SV1029: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1029 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV1029 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5404]) ).

thf(6667,plain,
    ! [SV1030: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1030 ) )
        = $true )
      | ( ( class_Ring__and__Field_Osemiring @ SV1030 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5405]) ).

thf(6668,plain,
    ! [SV1031: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1031 ) )
        = $true )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1031 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5406]) ).

thf(6669,plain,
    ! [SV1032: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1032 ) )
        = $true )
      | ( ( class_HOL_Ozero @ SV1032 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5407]) ).

thf(6670,plain,
    ! [SV1033: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1033 ) )
        = $true )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV1033 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5408]) ).

thf(6671,plain,
    ! [SV1034: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1034 ) )
        = $true )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV1034 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5409]) ).

thf(6672,plain,
    ! [SV1035: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1035 ) )
        = $true )
      | ( ( class_HOL_Oplus @ SV1035 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5410]) ).

thf(6673,plain,
    ! [SV1036: $i] :
      ( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1036 ) )
        = $true )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV1036 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5411]) ).

thf(6674,plain,
    ! [SV1037: $i] :
      ( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1037 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1037 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5412]) ).

thf(6675,plain,
    ! [SV1038: $i] :
      ( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1038 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1038 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5413]) ).

thf(6676,plain,
    ! [SV1039: $i] :
      ( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1039 ) )
        = $true )
      | ( ( class_LOrder_Omeet__semilorder @ SV1039 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5414]) ).

thf(6677,plain,
    ! [SV1040: $i] :
      ( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1040 ) )
        = $true )
      | ( ( class_LOrder_Ojoin__semilorder @ SV1040 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5415]) ).

thf(6678,plain,
    ! [SV1041: $i] :
      ( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1041 ) )
        = $true )
      | ( ( class_LOrder_Olorder @ SV1041 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5416]) ).

thf(6679,plain,
    ! [SV1042: $i] :
      ( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1042 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1042 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5417]) ).

thf(6680,plain,
    ! [SV1382: $i,SV1043: $i] :
      ( ( ! [SY2933: $i] :
            ( ~ ( c_in @ SV1043 @ ( c_Datatype_Oo2s @ SV1382 @ SY2933 ) @ SY2933 )
            | ( SV1382
              = ( c_Datatype_Ooption_OSome @ SV1043 @ SY2933 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5418]) ).

thf(6681,plain,
    ! [SV1383: $i,SV1044: $i] :
      ( ( c_in @ SV1044 @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ SV1044 @ SV1383 ) @ SV1383 ) @ SV1383 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5419]) ).

thf(6682,plain,
    ! [SV1045: $i] :
      ( ( ( SV1045 = c_Datatype_Ooption_ONone )
        = $true )
      | ( ( ! [SY2317: $i] :
              ( SV1045
              = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ SV1045 @ SY2317 ) @ SY2317 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5420]) ).

thf(6683,plain,
    ! [SV1046: $i] :
      ( ( ( SV1046 = c_Datatype_Ooption_ONone )
        = $true )
      | ( ( ! [SY2318: $i] :
              ( SV1046
              = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ SV1046 @ SY2318 ) @ SY2318 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5421]) ).

thf(6684,plain,
    ! [SV1384: $i,SV1047: $i] :
      ( ( c_Datatype_Ooption_ONone
       != ( c_Datatype_Ooption_OSome @ SV1047 @ SV1384 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5422]) ).

thf(6685,plain,
    ! [SV1385: $i,SV1048: $i] :
      ( ( ( c_Datatype_Ooption_OSome @ SV1048 @ SV1385 )
       != c_Datatype_Ooption_ONone )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5423]) ).

thf(6686,plain,
    ! [SV1386: $i,SV1049: $i] :
      ( ( ! [SY2934: $i] :
            ( ( ( c_Datatype_Ooption_OSome @ SV1049 @ SV1386 )
             != ( c_Datatype_Ooption_OSome @ SY2934 @ SV1386 ) )
            | ( SV1049 = SY2934 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5424]) ).

thf(6687,plain,
    ! [SV1387: $i,SV1050: $i] :
      ( ( ! [SY2935: $i,SY2936: $i] :
            ( ( ( c_Datatype__Universe_OAtom @ SV1050 @ SV1387 @ SY2935 )
             != ( c_Datatype__Universe_OAtom @ SY2936 @ SV1387 @ SY2935 ) )
            | ( SV1050 = SY2936 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5425]) ).

thf(6688,plain,
    ! [SV1388: $i,SV1051: $i] :
      ( ( ! [SY2937: $i,SY2938: $i,SY2939: $i] :
            ( ( c_Datatype__Universe_OAtom @ SV1051 @ SV1388 @ SY2937 )
           != ( c_Datatype__Universe_OScons @ SY2938 @ SY2939 @ SV1388 @ SY2937 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5426]) ).

thf(6689,plain,
    ! [SV1389: $i,SV1052: $i] :
      ( ( ! [SY2940: $i,SY2941: $i] :
            ( ( ( c_Datatype__Universe_OIn0 @ SV1052 @ SV1389 @ SY2940 )
             != ( c_Datatype__Universe_OIn0 @ SY2941 @ SV1389 @ SY2940 ) )
            | ( SV1052 = SY2941 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5427]) ).

thf(6690,plain,
    ! [SV1390: $i,SV1053: $i] :
      ( ( ! [SY2942: $i,SY2943: $i] :
            ( ( c_Datatype__Universe_OIn0 @ SV1053 @ SV1390 @ SY2942 )
           != ( c_Datatype__Universe_OIn1 @ SY2943 @ SV1390 @ SY2942 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5428]) ).

thf(6691,plain,
    ! [SV1391: $i,SV1054: $i] :
      ( ( ! [SY2944: $i,SY2945: $i] :
            ( ( ( c_Datatype__Universe_OIn1 @ SV1054 @ SV1391 @ SY2944 )
             != ( c_Datatype__Universe_OIn1 @ SY2945 @ SV1391 @ SY2944 ) )
            | ( SV1054 = SY2945 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5429]) ).

thf(6692,plain,
    ! [SV1392: $i,SV1055: $i] :
      ( ( ! [SY2946: $i,SY2947: $i] :
            ( ( c_Datatype__Universe_OIn1 @ SV1055 @ SV1392 @ SY2946 )
           != ( c_Datatype__Universe_OIn0 @ SY2947 @ SV1392 @ SY2946 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5430]) ).

thf(6693,plain,
    ! [SV1393: $i,SV1056: $i] :
      ( ( ! [SY2948: $i,SY2949: $i] :
            ( ( c_Datatype__Universe_OLeaf @ SV1056 @ SV1393 @ SY2948 )
           != ( c_Datatype__Universe_ONumb @ SY2949 @ SV1393 @ SY2948 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5431]) ).

thf(6694,plain,
    ! [SV1394: $i,SV1057: $i] :
      ( ( ! [SY2950: $i,SY2951: $i,SY2952: $i] :
            ( ( c_Datatype__Universe_OLeaf @ SV1057 @ SV1394 @ SY2950 )
           != ( c_Datatype__Universe_OScons @ SY2951 @ SY2952 @ SV1394 @ SY2950 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5432]) ).

thf(6695,plain,
    ! [SV1395: $i,SV1058: $i] :
      ( ( ! [SY2953: $i,SY2954: $i] :
            ( ( c_Datatype__Universe_ONumb @ SV1058 @ SV1395 @ SY2953 )
           != ( c_Datatype__Universe_OLeaf @ SY2954 @ SV1395 @ SY2953 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5433]) ).

thf(6696,plain,
    ! [SV1396: $i,SV1059: $i] :
      ( ( ! [SY2955: $i,SY2956: $i,SY2957: $i] :
            ( ( c_Datatype__Universe_ONumb @ SV1059 @ SV1396 @ SY2955 )
           != ( c_Datatype__Universe_OScons @ SY2956 @ SY2957 @ SV1396 @ SY2955 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5434]) ).

thf(6697,plain,
    ! [SV1397: $i,SV1060: $i] :
      ( ( ! [SY2958: $i,SY2959: $i,SY2960: $i] :
            ( ! [SY2961: $i] :
                ( ( c_Datatype__Universe_OScons @ SV1060 @ SV1397 @ SY2958 @ SY2959 )
               != ( c_Datatype__Universe_OScons @ SY2960 @ SY2961 @ SY2958 @ SY2959 ) )
            | ( SV1060 = SY2960 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5435]) ).

thf(6698,plain,
    ! [SV1398: $i,SV1061: $i] :
      ( ( ! [SY2962: $i,SY2963: $i,SY2964: $i,SY2965: $i] :
            ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SV1398 @ SY2962 @ SY2963 )
             != ( c_Datatype__Universe_OScons @ SY2964 @ SY2965 @ SY2962 @ SY2963 ) )
            | ( SV1398 = SY2965 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5436]) ).

thf(6699,plain,
    ! [SV1399: $i,SV1062: $i] :
      ( ( ! [SY2966: $i,SY2967: $i,SY2968: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1062 @ SV1399 @ SY2966 @ SY2967 )
           != ( c_Datatype__Universe_OAtom @ SY2968 @ SY2966 @ SY2967 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5437]) ).

thf(6700,plain,
    ! [SV1400: $i,SV1063: $i] :
      ( ( ! [SY2969: $i,SY2970: $i,SY2971: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1063 @ SV1400 @ SY2969 @ SY2970 )
           != ( c_Datatype__Universe_OLeaf @ SY2971 @ SY2969 @ SY2970 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5438]) ).

thf(6701,plain,
    ! [SV1401: $i,SV1064: $i] :
      ( ( ! [SY2972: $i,SY2973: $i,SY2974: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1064 @ SV1401 @ SY2972 @ SY2973 )
           != ( c_Datatype__Universe_ONumb @ SY2974 @ SY2972 @ SY2973 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5439]) ).

thf(6702,plain,
    ! [SV1065: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1065 @ tc_nat ) )
        = $true )
      | ( ( SV1065 = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5440]) ).

thf(6703,plain,
    ! [SV1066: $i] :
      ( ( ( ! [SY2378: $i,SY2379: $i] :
              ( c_emptyset
             != ( c_Equiv__Relations_Oquotient @ SV1066 @ SY2378 @ SY2379 ) ) )
        = $true )
      | ( ( SV1066 = c_emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5441]) ).

thf(6704,plain,
    ! [SV1402: $i,SV1067: $i] :
      ( ( c_emptyset
        = ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1067 @ SV1402 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5442]) ).

thf(6705,plain,
    ! [SV1068: $i] :
      ( ( ( ! [SY2381: $i,SY2382: $i] :
              ( ( c_Equiv__Relations_Oquotient @ SV1068 @ SY2381 @ SY2382 )
             != c_emptyset ) )
        = $true )
      | ( ( SV1068 = c_emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5443]) ).

thf(6706,plain,
    ! [SV1403: $i,SV1069: $i] :
      ( ( ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1069 @ SV1403 )
        = c_emptyset )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5444]) ).

thf(6707,plain,
    ! [SV1404: $i,SV1070: $i] :
      ( ( ! [SY2975: $i,SY2976: $i] :
            ( ~ ( c_in @ ( c_minus @ SV1070 @ ( c_insert @ SV1404 @ SY2975 @ SY2976 ) @ ( tc_set @ SY2976 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2976 ) )
            | ( c_in @ ( c_minus @ SV1070 @ SY2975 @ ( tc_set @ SY2976 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2976 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5447]) ).

thf(6708,plain,
    ! [SV1405: $i,SV1071: $i] :
      ( ( ! [SY2977: $i] :
            ( ~ ( c_in @ ( c_minus @ SV1071 @ SV1405 @ ( tc_set @ SY2977 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2977 ) )
            | ! [SY2978: $i] : ( c_in @ ( c_minus @ SV1071 @ ( c_insert @ SY2978 @ SV1405 @ SY2977 ) @ ( tc_set @ SY2977 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2977 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5448]) ).

thf(6709,plain,
    ! [SV1406: $i,SV1072: $i] :
      ( ( ~ ( c_in @ ( c_Pow @ SV1072 @ SV1406 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1406 ) ) )
        | ( c_in @ SV1072 @ c_Finite__Set_OFinites @ ( tc_set @ SV1406 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5449]) ).

thf(6710,plain,
    ! [SV1407: $i,SV1073: $i] :
      ( ( ~ ( c_in @ SV1073 @ c_Finite__Set_OFinites @ ( tc_set @ SV1407 ) )
        | ( c_in @ ( c_Pow @ SV1073 @ SV1407 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1407 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5450]) ).

thf(6711,plain,
    ! [SV1408: $i,SV1074: $i] :
      ( ( ! [SY2979: $i] :
            ( ~ ( c_in @ ( c_union @ SV1074 @ SV1408 @ SY2979 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2979 ) )
            | ( c_in @ SV1074 @ c_Finite__Set_OFinites @ ( tc_set @ SY2979 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5451]) ).

thf(6712,plain,
    ! [SV1409: $i,SV1075: $i] :
      ( ( ! [SY2980: $i] :
            ( ~ ( c_in @ ( c_union @ SV1075 @ SV1409 @ SY2980 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2980 ) )
            | ( c_in @ SV1409 @ c_Finite__Set_OFinites @ ( tc_set @ SY2980 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5452]) ).

thf(6713,plain,
    ! [SV1410: $i,SV1076: $i] :
      ( ( ~ ( c_in @ SV1076 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        | ! [SY2981: $i] :
            ( ~ ( c_in @ SY2981 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
            | ( c_in @ ( c_union @ SY2981 @ SV1076 @ SV1410 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5453]) ).

thf(6714,plain,
    ! [SV1411: $i,SV1077: $i] :
      ( ( ! [SY2982: $i] :
            ( ~ ( c_in @ ( c_Relation_Oconverse @ SV1077 @ SV1411 @ SY2982 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2982 @ SV1411 ) ) )
            | ( c_in @ SV1077 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1411 @ SY2982 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5454]) ).

thf(6715,plain,
    ! [SV1412: $i,SV1078: $i] :
      ( ( ! [SY2983: $i] :
            ( ~ ( c_in @ SV1078 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1412 @ SY2983 ) ) )
            | ( c_in @ ( c_Relation_Oconverse @ SV1078 @ SV1412 @ SY2983 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2983 @ SV1412 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5455]) ).

thf(6716,plain,
    ! [SV1413: $i,SV1079: $i] :
      ( ( ! [SY2984: $i] :
            ~ ( c_Divides_Oop_Advd @ SV1079 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1413 @ SY2984 @ tc_nat @ tc_nat ) ) @ tc_nat )
        | ( c_Divides_Oop_Advd @ SV1079 @ SV1413 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5456]) ).

thf(6717,plain,
    ! [SV1414: $i,SV1080: $i] :
      ( ( ! [SY2985: $i] :
            ( ~ ( c_Divides_Oop_Advd @ SV1080 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1414 @ SY2985 @ tc_nat @ tc_nat ) ) @ tc_nat )
            | ( c_Divides_Oop_Advd @ SV1080 @ SY2985 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5457]) ).

thf(6718,plain,
    ! [SV1415: $i,SV1081: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SV1415 @ tc_nat )
        | ! [SY2986: $i] :
            ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SY2986 @ tc_nat )
            | ( c_Divides_Oop_Advd @ SV1081 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2986 @ SV1415 @ tc_nat @ tc_nat ) ) @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5458]) ).

thf(6719,plain,
    ! [SV1416: $i,SV1082: $i] :
      ( ( ( ( c_IntDef_Oint @ SV1082 )
         != ( c_IntDef_Oint @ SV1416 ) )
        | ( SV1082 = SV1416 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5460]) ).

thf(6720,plain,
    ! [SV1417: $i,SV1083: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ SV1083 @ ( c_uminus @ SV1417 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        | ( c_Divides_Oop_Advd @ SV1083 @ SV1417 @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5461]) ).

thf(6721,plain,
    ! [SV1418: $i,SV1084: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ SV1084 @ SV1418 @ tc_IntDef_Oint )
        | ( c_Divides_Oop_Advd @ SV1084 @ ( c_uminus @ SV1418 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5462]) ).

thf(6722,plain,
    ! [SV1085: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1085 @ tc_IntDef_Oint ) )
        = $true )
      | ( ( SV1085 = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5463]) ).

thf(6723,plain,
    ! [SV1419: $i,SV1086: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ SV1086 @ tc_IntDef_Oint ) @ SV1419 @ tc_IntDef_Oint )
        | ( c_Divides_Oop_Advd @ SV1086 @ SV1419 @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5464]) ).

thf(6724,plain,
    ! [SV1420: $i,SV1087: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ SV1087 @ SV1420 @ tc_IntDef_Oint )
        | ( c_Divides_Oop_Advd @ ( c_uminus @ SV1087 @ tc_IntDef_Oint ) @ SV1420 @ tc_IntDef_Oint ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5465]) ).

thf(6725,plain,
    ! [SV1421: $i,SV1088: $i] :
      ( ( ! [SY2987: $i] :
            ~ ( c_in @ ( c_Pair @ SV1088 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1421 ) @ ( tc_List_Olist @ SV1421 ) ) @ ( c_List_Olex @ SY2987 @ SV1421 ) @ ( tc_prod @ ( tc_List_Olist @ SV1421 ) @ ( tc_List_Olist @ SV1421 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5466]) ).

thf(6726,plain,
    ! [SV1089: $i] :
      ( ( ( ! [SY2415: $i,SY2416: $i] :
              ( c_List_Olist_ONil
             != ( c_append @ SV1089 @ SY2415 @ SY2416 ) ) )
        = $true )
      | ( ( SV1089 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5467]) ).

thf(6727,plain,
    ! [SV1422: $i,SV1090: $i] :
      ( ( ! [SY2988: $i] :
            ( c_List_Olist_ONil
           != ( c_append @ SV1090 @ SV1422 @ SY2988 ) )
        | ( SV1422 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5468]) ).

thf(6728,plain,
    ! [SV1092: $i] :
      ( ( ( ! [SY2419: $i] :
              ( c_List_Olist_ONil
             != ( c_List_Orev @ SV1092 @ SY2419 ) ) )
        = $true )
      | ( ( SV1092 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5470]) ).

thf(6729,plain,
    ! [SV1423: $i,SV1094: $i] :
      ( ( ! [SY2989: $i] :
            ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1094 @ ( tc_List_Olist @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) @ ( c_List_Olex @ SY2989 @ SV1423 ) @ ( tc_prod @ ( tc_List_Olist @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5472]) ).

thf(6730,plain,
    ! [SV1424: $i,SV1095: $i] :
      ( ( ! [SY2990: $i,SY2991: $i] :
            ( ! [SY2992: $i] :
                ( ( c_append @ SV1095 @ ( c_List_Olist_OCons @ SV1424 @ c_List_Olist_ONil @ SY2990 ) @ SY2990 )
               != ( c_append @ SY2991 @ ( c_List_Olist_OCons @ SY2992 @ c_List_Olist_ONil @ SY2990 ) @ SY2990 ) )
            | ( SV1095 = SY2991 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5473]) ).

thf(6731,plain,
    ! [SV1425: $i,SV1096: $i] :
      ( ( ! [SY2993: $i,SY2994: $i,SY2995: $i] :
            ( ( ( c_append @ SV1096 @ ( c_List_Olist_OCons @ SV1425 @ c_List_Olist_ONil @ SY2993 ) @ SY2993 )
             != ( c_append @ SY2994 @ ( c_List_Olist_OCons @ SY2995 @ c_List_Olist_ONil @ SY2993 ) @ SY2993 ) )
            | ( SV1425 = SY2995 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5474]) ).

thf(6732,plain,
    ! [SV1426: $i,SV1097: $i] :
      ( ( ! [SY2996: $i,SY2997: $i] :
            ( ~ ( c_in @ ( c_append @ SV1097 @ SV1426 @ SY2996 ) @ ( c_List_Olists @ SY2997 @ SY2996 ) @ ( tc_List_Olist @ SY2996 ) )
            | ( c_in @ SV1097 @ ( c_List_Olists @ SY2997 @ SY2996 ) @ ( tc_List_Olist @ SY2996 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5475]) ).

thf(6733,plain,
    ! [SV1427: $i,SV1098: $i] :
      ( ( ! [SY2998: $i,SY2999: $i] :
            ( ~ ( c_in @ ( c_append @ SV1098 @ SV1427 @ SY2998 ) @ ( c_List_Olists @ SY2999 @ SY2998 ) @ ( tc_List_Olist @ SY2998 ) )
            | ( c_in @ SV1427 @ ( c_List_Olists @ SY2999 @ SY2998 ) @ ( tc_List_Olist @ SY2998 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5476]) ).

thf(6734,plain,
    ! [SV1428: $i,SV1099: $i] :
      ( ( ! [SY3000: $i] :
            ( ~ ( c_in @ SV1099 @ ( c_List_Olists @ SV1428 @ SY3000 ) @ ( tc_List_Olist @ SY3000 ) )
            | ! [SY3001: $i] :
                ( ~ ( c_in @ SY3001 @ ( c_List_Olists @ SV1428 @ SY3000 ) @ ( tc_List_Olist @ SY3000 ) )
                | ( c_in @ ( c_append @ SY3001 @ SV1099 @ SY3000 ) @ ( c_List_Olists @ SV1428 @ SY3000 ) @ ( tc_List_Olist @ SY3000 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5477]) ).

thf(6735,plain,
    ! [SV1100: $i] :
      ( ( ( ! [SY2439: $i,SY2440: $i] :
              ( ( c_append @ SV1100 @ SY2439 @ SY2440 )
             != c_List_Olist_ONil ) )
        = $true )
      | ( ( SV1100 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5478]) ).

thf(6736,plain,
    ! [SV1429: $i,SV1101: $i] :
      ( ( ! [SY3002: $i] :
            ( ( c_append @ SV1101 @ SV1429 @ SY3002 )
           != c_List_Olist_ONil )
        | ( SV1429 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5479]) ).

thf(6737,plain,
    ! [SV1430: $i,SV1103: $i] :
      ( ( ! [SY3003: $i,SY3004: $i] :
            ( ( ( c_append @ SV1103 @ SV1430 @ SY3003 )
             != ( c_append @ SY3004 @ SV1430 @ SY3003 ) )
            | ( SV1103 = SY3004 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5481]) ).

thf(6738,plain,
    ! [SV1104: $i] :
      ( ( ( ! [SY2446: $i,SY2447: $i] :
              ( ( c_append @ SV1104 @ SY2446 @ SY2447 )
             != SY2446 ) )
        = $true )
      | ( ( SV1104 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5482]) ).

thf(6739,plain,
    ! [SV1431: $i,SV1105: $i] :
      ( ( ( c_append @ c_List_Olist_ONil @ SV1105 @ SV1431 )
        = SV1105 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5483]) ).

thf(6740,plain,
    ! [SV1432: $i,SV1106: $i] :
      ( ( ! [SY3005: $i] :
            ( ( c_append @ SV1106 @ SV1432 @ SY3005 )
           != SV1106 )
        | ( SV1432 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5484]) ).

thf(6741,plain,
    ! [SV1433: $i,SV1107: $i] :
      ( ( ( c_append @ SV1107 @ c_List_Olist_ONil @ SV1433 )
        = SV1107 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5485]) ).

thf(6742,plain,
    ! [SV1434: $i,SV1108: $i] :
      ( ( ! [SY3006: $i] :
            ( ! [SY3007: $i] :
                ( ( c_List_Ochar_OChar @ SV1108 @ SV1434 )
               != ( c_List_Ochar_OChar @ SY3006 @ SY3007 ) )
            | ( SV1108 = SY3006 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5486]) ).

thf(6743,plain,
    ! [SV1435: $i,SV1109: $i] :
      ( ( ! [SY3008: $i,SY3009: $i] :
            ( ( ( c_List_Ochar_OChar @ SV1109 @ SV1435 )
             != ( c_List_Ochar_OChar @ SY3008 @ SY3009 ) )
            | ( SV1435 = SY3009 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5487]) ).

thf(6744,plain,
    ! [SV1110: $i] :
      ( ( ( ! [SY2458: $i] :
              ( ( c_Nat_Osize @ SV1110 @ ( tc_List_Olist @ SY2458 ) )
             != c_0 ) )
        = $true )
      | ( ( SV1110 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5488]) ).

thf(6745,plain,
    ! [SV1112: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1112 ) ) @ tc_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5490]) ).

thf(6746,plain,
    ! [SV1113: $i] :
      ( ( ( SV1113 = c_List_Olist_ONil )
        = $true )
      | ( ( ! [SY2459: $i] : ( c_less @ c_0 @ ( c_Nat_Osize @ SV1113 @ ( tc_List_Olist @ SY2459 ) ) @ tc_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5491]) ).

thf(6747,plain,
    ! [SV1436: $i,SV1114: $i] :
      ( ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1114 @ SV1436 ) @ ( tc_List_Olist @ SV1436 ) )
         != ( c_Nat_Osize @ SV1114 @ ( tc_List_Olist @ SV1436 ) ) )
        | ( ( c_List_Oremdups @ SV1114 @ SV1436 )
          = SV1114 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5492]) ).

thf(6748,plain,
    ! [SV1437: $i,SV1115: $i] :
      ( ( ( ( c_List_Oremdups @ SV1115 @ SV1437 )
         != SV1115 )
        | ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1115 @ SV1437 ) @ ( tc_List_Olist @ SV1437 ) )
          = ( c_Nat_Osize @ SV1115 @ ( tc_List_Olist @ SV1437 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5493]) ).

thf(6749,plain,
    ! [SV1438: $i,SV1116: $i] :
      ( ( ! [SY3010: $i] :
            ( c_List_Olist_ONil
           != ( c_List_Olist_OCons @ SV1116 @ SV1438 @ SY3010 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5494]) ).

thf(6750,plain,
    ! [SV1439: $i,SV1117: $i] :
      ( ( ! [SY3011: $i] :
            ( ( c_List_Olist_OCons @ SV1117 @ SV1439 @ SY3011 )
           != c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5495]) ).

thf(6751,plain,
    ! [SV1440: $i,SV1118: $i] :
      ( ( ! [SY3012: $i,SY3013: $i] :
            ( ! [SY3014: $i] :
                ( ( c_List_Olist_OCons @ SV1118 @ SV1440 @ SY3012 )
               != ( c_List_Olist_OCons @ SY3013 @ SY3014 @ SY3012 ) )
            | ( SV1118 = SY3013 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5496]) ).

thf(6752,plain,
    ! [SV1441: $i,SV1119: $i] :
      ( ( ! [SY3015: $i,SY3016: $i,SY3017: $i] :
            ( ( ( c_List_Olist_OCons @ SV1119 @ SV1441 @ SY3015 )
             != ( c_List_Olist_OCons @ SY3016 @ SY3017 @ SY3015 ) )
            | ( SV1441 = SY3017 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5497]) ).

thf(6753,plain,
    ! [SV1442: $i,SV1120: $i] :
      ( ( ! [SY3018: $i,SY3019: $i] :
            ( ( ( c_List_Orev @ SV1120 @ SV1442 )
             != ( c_List_Olist_OCons @ SY3018 @ SY3019 @ SV1442 ) )
            | ( SV1120
              = ( c_append @ ( c_List_Orev @ SY3019 @ SV1442 ) @ ( c_List_Olist_OCons @ SY3018 @ c_List_Olist_ONil @ SV1442 ) @ SV1442 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5498]) ).

thf(6754,plain,
    ! [SV1443: $i,SV1121: $i] :
      ( ( ! [SY3020: $i] :
            ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ SV1121 @ SV1443 ) @ ( c_List_Olist_OCons @ SY3020 @ c_List_Olist_ONil @ SV1443 ) @ SV1443 ) @ SV1443 )
            = ( c_List_Olist_OCons @ SY3020 @ SV1121 @ SV1443 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5499]) ).

thf(6755,plain,
    ! [SV1122: $i] :
      ( ( ( ! [SY2479: $i] :
              ( ( c_List_Orev @ SV1122 @ SY2479 )
             != c_List_Olist_ONil ) )
        = $true )
      | ( ( SV1122 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5500]) ).

thf(6756,plain,
    ! [SV1444: $i,SV1124: $i] :
      ( ( ! [SY3021: $i] :
            ( ( ( c_List_Orev @ SV1124 @ SV1444 )
             != ( c_List_Orev @ SY3021 @ SV1444 ) )
            | ( SV1124 = SY3021 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5502]) ).

thf(6757,plain,
    ! [SV1445: $i,SV1125: $i] :
      ( ( ! [SY3022: $i,SY3023: $i] :
            ( ( ( c_append @ SV1125 @ SV1445 @ SY3022 )
             != ( c_append @ SV1125 @ SY3023 @ SY3022 ) )
            | ( SV1445 = SY3023 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5503]) ).

thf(6758,plain,
    ! [SV1446: $i,SV1126: $i] :
      ( ( ! [SY3024: $i] :
            ( SV1126
           != ( c_append @ SV1446 @ SV1126 @ SY3024 ) )
        | ( SV1446 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5504]) ).

thf(6759,plain,
    ! [SV1447: $i,SV1127: $i] :
      ( ( SV1127
        = ( c_append @ c_List_Olist_ONil @ SV1127 @ SV1447 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5505]) ).

thf(6760,plain,
    ! [SV1448: $i,SV1128: $i] :
      ( ( ! [SY3025: $i] :
            ( SV1128
           != ( c_append @ SV1128 @ SV1448 @ SY3025 ) )
        | ( SV1448 = c_List_Olist_ONil ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5506]) ).

thf(6761,plain,
    ! [SV1449: $i,SV1129: $i] :
      ( ( SV1129
        = ( c_append @ SV1129 @ c_List_Olist_ONil @ SV1449 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5507]) ).

thf(6762,plain,
    ! [SV1130: $i] :
      ( ( ( ! [SY2491: $i] :
              ( c_emptyset
             != ( c_List_Oset @ SV1130 @ SY2491 ) ) )
        = $true )
      | ( ( SV1130 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5508]) ).

thf(6763,plain,
    ! [SV1132: $i] :
      ( ( ( ! [SY2492: $i] :
              ( ( c_List_Oset @ SV1132 @ SY2492 )
             != c_emptyset ) )
        = $true )
      | ( ( SV1132 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5510]) ).

thf(6764,plain,
    ! [SV1450: $i,SV1134: $i] :
      ( ( ( ( c_Suc @ SV1134 )
         != ( c_Suc @ SV1450 ) )
        | ( SV1134 = SV1450 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5512]) ).

thf(6765,plain,
    ! [SV1451: $i,SV1135: $i] :
      ( ( ~ ( c_lessequals @ ( c_Suc @ SV1135 ) @ ( c_Suc @ SV1451 ) @ tc_nat )
        | ( c_lessequals @ SV1135 @ SV1451 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5513]) ).

thf(6766,plain,
    ! [SV1452: $i,SV1136: $i] :
      ( ( ~ ( c_lessequals @ SV1136 @ SV1452 @ tc_nat )
        | ( c_lessequals @ ( c_Suc @ SV1136 ) @ ( c_Suc @ SV1452 ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5514]) ).

thf(6767,plain,
    ! [SV1453: $i,SV1137: $i] :
      ( ( ~ ( c_less @ ( c_Suc @ SV1137 ) @ ( c_Suc @ SV1453 ) @ tc_nat )
        | ( c_less @ SV1137 @ SV1453 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5515]) ).

thf(6768,plain,
    ! [SV1454: $i,SV1138: $i] :
      ( ( ~ ( c_less @ SV1138 @ SV1454 @ tc_nat )
        | ( c_less @ ( c_Suc @ SV1138 ) @ ( c_Suc @ SV1454 ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5516]) ).

thf(6769,plain,
    ! [SV1139: $i] :
      ( ( ( c_Suc @ SV1139 )
        = c_0 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5517]) ).

thf(6770,plain,
    ! [SV1140: $i] :
      ( ( c_0
        = ( c_Suc @ SV1140 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5518]) ).

thf(6771,plain,
    ! [SV1455: $i,SV1141: $i] :
      ( ( ~ ( c_less @ c_0 @ ( c_plus @ SV1141 @ SV1455 @ tc_nat ) @ tc_nat )
        | ( c_less @ c_0 @ SV1455 @ tc_nat )
        | ( c_less @ c_0 @ SV1141 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5519]) ).

thf(6772,plain,
    ! [SV1142: $i] :
      ( ( ( ~ ( c_less @ c_0 @ SV1142 @ tc_nat ) )
        = $true )
      | ( ( ! [SY2499: $i] : ( c_less @ c_0 @ ( c_plus @ SV1142 @ SY2499 @ tc_nat ) @ tc_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5520]) ).

thf(6773,plain,
    ! [SV1143: $i] :
      ( ( ( ~ ( c_less @ c_0 @ SV1143 @ tc_nat ) )
        = $true )
      | ( ( ! [SY2500: $i] : ( c_less @ c_0 @ ( c_plus @ SY2500 @ SV1143 @ tc_nat ) @ tc_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5521]) ).

thf(6774,plain,
    ! [SV1144: $i] :
      ( ( ( ! [SY2501: $i] :
              ( ( c_plus @ SV1144 @ SY2501 @ tc_nat )
             != c_0 ) )
        = $true )
      | ( ( SV1144 = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5522]) ).

thf(6775,plain,
    ! [SV1456: $i,SV1145: $i] :
      ( ( ( ( c_plus @ SV1145 @ SV1456 @ tc_nat )
         != c_0 )
        | ( SV1456 = c_0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5523]) ).

thf(6776,plain,
    ! [SV1146: $i] :
      ( ( ( ~ ( c_lessequals @ SV1146 @ c_0 @ tc_nat ) )
        = $true )
      | ( ( SV1146 = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5524]) ).

thf(6777,plain,
    ! [SV1147: $i] :
      ( ( ( ~ ( c_less @ SV1147 @ ( c_Suc @ c_0 ) @ tc_nat ) )
        = $true )
      | ( ( SV1147 = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5525]) ).

thf(6778,plain,
    ! [SV1148: $i] :
      ( ( ( ~ ( c_less @ SV1148 @ c_1 @ tc_nat ) )
        = $true )
      | ( ( SV1148 = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5526]) ).

thf(6779,plain,
    ! [SV1149: $i] :
      ( ( ( SV1149 = c_0 )
        = $true )
      | ( ( c_less @ c_0 @ SV1149 @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5527]) ).

thf(6780,plain,
    ! [SV1457: $i,SV1150: $i] :
      ( ( ~ ( c_less @ ( c_plus @ SV1150 @ SV1457 @ tc_nat ) @ SV1150 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5529]) ).

thf(6781,plain,
    ! [SV1458: $i,SV1151: $i] :
      ( ( ~ ( c_less @ ( c_plus @ SV1151 @ SV1458 @ tc_nat ) @ SV1458 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5530]) ).

thf(6782,plain,
    ! [SV1152: $i] :
      ( ( c_less @ SV1152 @ c_0 @ tc_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5531]) ).

thf(6783,plain,
    ! [SV1153: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV1153 ) )
        = $true )
      | ( ( ! [SY2505: $i] :
              ~ ( c_less @ SY2505 @ SY2505 @ SV1153 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5534]) ).

thf(6784,plain,
    ! [SV1459: $i,SV1154: $i] :
      ( ( ! [SY3026: $i,SY3027: $i,SY3028: $i] :
            ( ! [SY3029: $i] :
                ( ( c_Pair @ SV1154 @ SV1459 @ SY3026 @ SY3027 )
               != ( c_Pair @ SY3028 @ SY3029 @ SY3026 @ SY3027 ) )
            | ( SV1154 = SY3028 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5535]) ).

thf(6785,plain,
    ! [SV1460: $i,SV1155: $i] :
      ( ( ! [SY3030: $i,SY3031: $i,SY3032: $i,SY3033: $i] :
            ( ( ( c_Pair @ SV1155 @ SV1460 @ SY3030 @ SY3031 )
             != ( c_Pair @ SY3032 @ SY3033 @ SY3030 @ SY3031 ) )
            | ( SV1460 = SY3033 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5536]) ).

thf(6786,plain,
    ! [SV1461: $i,SV1156: $i] :
      ( ( c_in @ ( c_Pair @ SV1156 @ SV1156 @ SV1461 @ SV1461 ) @ c_Relation_OId @ ( tc_prod @ SV1461 @ SV1461 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5537]) ).

thf(6787,plain,
    ! [SV1462: $i,SV1157: $i] :
      ( ( ! [SY3034: $i,SY3035: $i,SY3036: $i] :
            ( ~ ( c_in @ SV1157 @ ( c_Relation_OImage @ SV1462 @ ( c_insert @ SY3034 @ c_emptyset @ SY3035 ) @ SY3035 @ SY3036 ) @ SY3036 )
            | ( c_in @ ( c_Pair @ SY3034 @ SV1157 @ SY3035 @ SY3036 ) @ SV1462 @ ( tc_prod @ SY3035 @ SY3036 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5538]) ).

thf(6788,plain,
    ! [SV1463: $i,SV1158: $i] :
      ( ( ! [SY3037: $i,SY3038: $i,SY3039: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1158 @ SV1463 @ SY3037 @ SY3038 ) @ SY3039 @ ( tc_prod @ SY3037 @ SY3038 ) )
            | ( c_in @ SV1463 @ ( c_Relation_OImage @ SY3039 @ ( c_insert @ SV1158 @ c_emptyset @ SY3037 ) @ SY3037 @ SY3038 ) @ SY3038 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5539]) ).

thf(6789,plain,
    ! [SV1464: $i,SV1159: $i] :
      ( ( ! [SY3040: $i,SY3041: $i,SY3042: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1159 @ SV1464 @ SY3040 @ SY3041 ) @ ( c_Relation_Oconverse @ SY3042 @ SY3041 @ SY3040 ) @ ( tc_prod @ SY3040 @ SY3041 ) )
            | ( c_in @ ( c_Pair @ SV1464 @ SV1159 @ SY3041 @ SY3040 ) @ SY3042 @ ( tc_prod @ SY3041 @ SY3040 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5540]) ).

thf(6790,plain,
    ! [SV1465: $i,SV1160: $i] :
      ( ( ! [SY3043: $i,SY3044: $i,SY3045: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1160 @ SV1465 @ SY3043 @ SY3044 ) @ SY3045 @ ( tc_prod @ SY3043 @ SY3044 ) )
            | ( c_in @ ( c_Pair @ SV1465 @ SV1160 @ SY3044 @ SY3043 ) @ ( c_Relation_Oconverse @ SY3045 @ SY3043 @ SY3044 ) @ ( tc_prod @ SY3044 @ SY3043 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5541]) ).

thf(6791,plain,
    ! [SV1466: $i,SV1161: $i] :
      ( ( ! [SY3046: $i] :
            ~ ( c_in @ ( c_Pair @ SV1161 @ SV1466 @ SY3046 @ SY3046 ) @ c_Relation_OId @ ( tc_prod @ SY3046 @ SY3046 ) )
        | ( SV1161 = SV1466 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5542]) ).

thf(6792,plain,
    ! [SV1162: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1162 ) )
        = $true )
      | ( ( ! [SY2535: $i,SY2536: $i] :
              ( ( ( c_SetInterval_OatLeast @ SY2535 @ SV1162 )
               != ( c_SetInterval_OatLeast @ SY2536 @ SV1162 ) )
              | ( SY2535 = SY2536 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5543]) ).

thf(6793,plain,
    ! [SV1163: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1163 ) )
        = $true )
      | ( ( ! [SY2537: $i,SY2538: $i] :
              ( ~ ( c_in @ SY2537 @ ( c_SetInterval_OatLeast @ SY2538 @ SV1163 ) @ SV1163 )
              | ( c_lessequals @ SY2538 @ SY2537 @ SV1163 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5544]) ).

thf(6794,plain,
    ! [SV1164: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1164 ) )
        = $true )
      | ( ( ! [SY2539: $i,SY2540: $i] :
              ( ~ ( c_lessequals @ SY2539 @ SY2540 @ SV1164 )
              | ( c_in @ SY2540 @ ( c_SetInterval_OatLeast @ SY2539 @ SV1164 ) @ SV1164 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5545]) ).

thf(6795,plain,
    ! [SV1165: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV1165 ) )
        = $true )
      | ( ( ! [SY2541: $i,SY2542: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2541 @ SV1165 ) @ ( c_SetInterval_OatLeast @ SY2542 @ SV1165 ) @ ( tc_set @ SV1165 ) )
              | ( c_lessequals @ SY2542 @ SY2541 @ SV1165 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5546]) ).

thf(6796,plain,
    ! [SV1166: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV1166 ) )
        = $true )
      | ( ( ! [SY2543: $i,SY2544: $i] :
              ( ~ ( c_lessequals @ SY2543 @ SY2544 @ SV1166 )
              | ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2544 @ SV1166 ) @ ( c_SetInterval_OatLeast @ SY2543 @ SV1166 ) @ ( tc_set @ SV1166 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5547]) ).

thf(6797,plain,
    ! [SV1167: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1167 ) )
        = $true )
      | ( ( ! [SY2545: $i,SY2546: $i] :
              ( ( ( c_SetInterval_OatMost @ SY2545 @ SV1167 )
               != ( c_SetInterval_OatMost @ SY2546 @ SV1167 ) )
              | ( SY2545 = SY2546 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5548]) ).

thf(6798,plain,
    ! [SV1168: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1168 ) )
        = $true )
      | ( ( ! [SY2547: $i,SY2548: $i] :
              ( ~ ( c_in @ SY2547 @ ( c_SetInterval_OatMost @ SY2548 @ SV1168 ) @ SV1168 )
              | ( c_lessequals @ SY2547 @ SY2548 @ SV1168 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5549]) ).

thf(6799,plain,
    ! [SV1169: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1169 ) )
        = $true )
      | ( ( ! [SY2549: $i,SY2550: $i] :
              ( ~ ( c_lessequals @ SY2549 @ SY2550 @ SV1169 )
              | ( c_in @ SY2549 @ ( c_SetInterval_OatMost @ SY2550 @ SV1169 ) @ SV1169 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5550]) ).

thf(6800,plain,
    ! [SV1170: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV1170 ) )
        = $true )
      | ( ( ! [SY2551: $i,SY2552: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SY2551 @ SV1170 ) @ ( c_SetInterval_OatMost @ SY2552 @ SV1170 ) @ ( tc_set @ SV1170 ) )
              | ( c_lessequals @ SY2551 @ SY2552 @ SV1170 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5551]) ).

thf(6801,plain,
    ! [SV1171: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV1171 ) )
        = $true )
      | ( ( ! [SY2553: $i,SY2554: $i] :
              ( ~ ( c_lessequals @ SY2553 @ SY2554 @ SV1171 )
              | ( c_lessequals @ ( c_SetInterval_OatMost @ SY2553 @ SV1171 ) @ ( c_SetInterval_OatMost @ SY2554 @ SV1171 ) @ ( tc_set @ SV1171 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5552]) ).

thf(6802,plain,
    ! [SV1172: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1172 ) )
        = $true )
      | ( ( ! [SY2555: $i,SY2556: $i] :
              ( ( ( c_SetInterval_OgreaterThan @ SY2555 @ SV1172 )
               != ( c_SetInterval_OgreaterThan @ SY2556 @ SV1172 ) )
              | ( SY2555 = SY2556 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5553]) ).

thf(6803,plain,
    ! [SV1173: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1173 ) )
        = $true )
      | ( ( ! [SY2557: $i,SY2558: $i] :
              ( ~ ( c_in @ SY2557 @ ( c_SetInterval_OgreaterThan @ SY2558 @ SV1173 ) @ SV1173 )
              | ( c_less @ SY2558 @ SY2557 @ SV1173 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5554]) ).

thf(6804,plain,
    ! [SV1174: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1174 ) )
        = $true )
      | ( ( ! [SY2559: $i,SY2560: $i] :
              ( ~ ( c_less @ SY2559 @ SY2560 @ SV1174 )
              | ( c_in @ SY2560 @ ( c_SetInterval_OgreaterThan @ SY2559 @ SV1174 ) @ SV1174 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5555]) ).

thf(6805,plain,
    ! [SV1175: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1175 ) )
        = $true )
      | ( ( ! [SY2561: $i,SY2562: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2561 @ SV1175 ) @ ( c_SetInterval_OgreaterThan @ SY2562 @ SV1175 ) @ ( tc_set @ SV1175 ) )
              | ( c_lessequals @ SY2562 @ SY2561 @ SV1175 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5556]) ).

thf(6806,plain,
    ! [SV1176: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1176 ) )
        = $true )
      | ( ( ! [SY2563: $i,SY2564: $i] :
              ( ~ ( c_lessequals @ SY2563 @ SY2564 @ SV1176 )
              | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2564 @ SV1176 ) @ ( c_SetInterval_OgreaterThan @ SY2563 @ SV1176 ) @ ( tc_set @ SV1176 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5557]) ).

thf(6807,plain,
    ! [SV1177: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1177 ) )
        = $true )
      | ( ( ! [SY2565: $i,SY2566: $i] :
              ( ( ( c_SetInterval_OlessThan @ SY2565 @ SV1177 )
               != ( c_SetInterval_OlessThan @ SY2566 @ SV1177 ) )
              | ( SY2565 = SY2566 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5558]) ).

thf(6808,plain,
    ! [SV1178: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1178 ) )
        = $true )
      | ( ( ! [SY2567: $i,SY2568: $i] :
              ( ~ ( c_in @ SY2567 @ ( c_SetInterval_OlessThan @ SY2568 @ SV1178 ) @ SV1178 )
              | ( c_less @ SY2567 @ SY2568 @ SV1178 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5559]) ).

thf(6809,plain,
    ! [SV1179: $i] :
      ( ( ( ~ ( class_Orderings_Oord @ SV1179 ) )
        = $true )
      | ( ( ! [SY2569: $i,SY2570: $i] :
              ( ~ ( c_less @ SY2569 @ SY2570 @ SV1179 )
              | ( c_in @ SY2569 @ ( c_SetInterval_OlessThan @ SY2570 @ SV1179 ) @ SV1179 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5560]) ).

thf(6810,plain,
    ! [SV1180: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1180 ) )
        = $true )
      | ( ( ! [SY2571: $i,SY2572: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2571 @ SV1180 ) @ ( c_SetInterval_OlessThan @ SY2572 @ SV1180 ) @ ( tc_set @ SV1180 ) )
              | ( c_lessequals @ SY2571 @ SY2572 @ SV1180 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5561]) ).

thf(6811,plain,
    ! [SV1181: $i] :
      ( ( ( ~ ( class_Orderings_Olinorder @ SV1181 ) )
        = $true )
      | ( ( ! [SY2573: $i,SY2574: $i] :
              ( ~ ( c_lessequals @ SY2573 @ SY2574 @ SV1181 )
              | ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2573 @ SV1181 ) @ ( c_SetInterval_OlessThan @ SY2574 @ SV1181 ) @ ( tc_set @ SV1181 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5562]) ).

thf(6812,plain,
    ! [SV1467: $i,SV1182: $i] :
      ( ( ! [SY3047: $i] :
            ( ~ ( c_in @ SV1182 @ SV1467 @ SY3047 )
            | ~ ( c_in @ SV1182 @ ( c_uminus @ SV1467 @ ( tc_set @ SY3047 ) ) @ SY3047 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5563]) ).

thf(6813,plain,
    ! [SV1468: $i,SV1183: $i] :
      ( ( ! [SY3048: $i] :
            ( ( c_in @ SV1183 @ SV1468 @ SY3048 )
            | ( c_in @ SV1183 @ ( c_uminus @ SV1468 @ ( tc_set @ SY3048 ) ) @ SY3048 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5564]) ).

thf(6814,plain,
    ! [SV1469: $i,SV1184: $i] :
      ( ( ! [SY3049: $i] :
            ( ( ( c_uminus @ SV1184 @ ( tc_set @ SV1469 ) )
             != ( c_uminus @ SY3049 @ ( tc_set @ SV1469 ) ) )
            | ( SV1184 = SY3049 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5565]) ).

thf(6815,plain,
    ! [SV1470: $i,SV1185: $i] :
      ( ( ! [SY3050: $i] :
            ( ~ ( c_lessequals @ ( c_uminus @ SV1185 @ ( tc_set @ SV1470 ) ) @ ( c_uminus @ SY3050 @ ( tc_set @ SV1470 ) ) @ ( tc_set @ SV1470 ) )
            | ( c_lessequals @ SY3050 @ SV1185 @ ( tc_set @ SV1470 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5566]) ).

thf(6816,plain,
    ! [SV1471: $i,SV1186: $i] :
      ( ( ! [SY3051: $i] :
            ( ~ ( c_lessequals @ SV1186 @ SV1471 @ ( tc_set @ SY3051 ) )
            | ( c_lessequals @ ( c_uminus @ SV1471 @ ( tc_set @ SY3051 ) ) @ ( c_uminus @ SV1186 @ ( tc_set @ SY3051 ) ) @ ( tc_set @ SY3051 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5567]) ).

thf(6817,plain,
    ! [SV1472: $i,SV1187: $i] :
      ( ( ! [SY3052: $i] :
            ( ~ ( c_in @ SV1187 @ SV1472 @ SY3052 )
            | ! [SY3053: $i] :
                ~ ( c_in @ SV1187 @ ( c_minus @ SY3053 @ SV1472 @ ( tc_set @ SY3052 ) ) @ SY3052 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5568]) ).

thf(6818,plain,
    ! [SV1473: $i,SV1188: $i] :
      ( ( ! [SY3054: $i,SY3055: $i] :
            ( ~ ( c_in @ SV1188 @ ( c_minus @ SV1473 @ SY3054 @ ( tc_set @ SY3055 ) ) @ SY3055 )
            | ( c_in @ SV1188 @ SV1473 @ SY3055 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5569]) ).

thf(6819,plain,
    ! [SV1474: $i,SV1189: $i] :
      ( ( ! [SY3056: $i] :
            ( ~ ( c_in @ SV1189 @ SV1474 @ SY3056 )
            | ! [SY3057: $i] :
                ( ( c_in @ SV1189 @ SY3057 @ SY3056 )
                | ( c_in @ SV1189 @ ( c_minus @ SV1474 @ SY3057 @ ( tc_set @ SY3056 ) ) @ SY3056 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5570]) ).

thf(6820,plain,
    ! [SV1475: $i,SV1190: $i] :
      ( ( ! [SY3058: $i,SY3059: $i] :
            ( ~ ( c_in @ SV1190 @ ( c_inter @ SV1475 @ SY3058 @ SY3059 ) @ SY3059 )
            | ( c_in @ SV1190 @ SY3058 @ SY3059 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5571]) ).

thf(6821,plain,
    ! [SV1476: $i,SV1191: $i] :
      ( ( ! [SY3060: $i,SY3061: $i] :
            ( ~ ( c_in @ SV1191 @ ( c_inter @ SV1476 @ SY3060 @ SY3061 ) @ SY3061 )
            | ( c_in @ SV1191 @ SV1476 @ SY3061 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5572]) ).

thf(6822,plain,
    ! [SV1477: $i,SV1192: $i] :
      ( ( ! [SY3062: $i] :
            ( ~ ( c_in @ SV1192 @ SV1477 @ SY3062 )
            | ! [SY3063: $i] :
                ( ~ ( c_in @ SV1192 @ SY3063 @ SY3062 )
                | ( c_in @ SV1192 @ ( c_inter @ SY3063 @ SV1477 @ SY3062 ) @ SY3062 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5573]) ).

thf(6823,plain,
    ! [SV1478: $i,SV1193: $i] :
      ( ( ! [SY3064: $i] :
            ( ~ ( c_in @ SV1193 @ SV1478 @ ( tc_set @ SY3064 ) )
            | ! [SY3065: $i] :
                ( ~ ( c_in @ SY3065 @ ( c_Inter @ SV1478 @ SY3064 ) @ SY3064 )
                | ( c_in @ SY3065 @ SV1193 @ SY3064 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5574]) ).

thf(6824,plain,
    ! [SV1479: $i,SV1194: $i] :
      ( ( ! [SY3066: $i] :
            ( ~ ( c_in @ SV1194 @ ( c_Pow @ SV1479 @ SY3066 ) @ ( tc_set @ SY3066 ) )
            | ( c_lessequals @ SV1194 @ SV1479 @ ( tc_set @ SY3066 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5575]) ).

thf(6825,plain,
    ! [SV1480: $i,SV1195: $i] :
      ( ( ! [SY3067: $i] :
            ( ~ ( c_lessequals @ SV1195 @ SV1480 @ ( tc_set @ SY3067 ) )
            | ( c_in @ SV1195 @ ( c_Pow @ SV1480 @ SY3067 ) @ ( tc_set @ SY3067 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5576]) ).

thf(6826,plain,
    ! [SV1481: $i,SV1196: $i] :
      ( ( ! [SY3068: $i] :
            ( ~ ( c_in @ SV1196 @ SV1481 @ SY3068 )
            | ! [SY3069: $i] : ( c_in @ SV1196 @ ( c_union @ SY3069 @ SV1481 @ SY3068 ) @ SY3068 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5578]) ).

thf(6827,plain,
    ! [SV1482: $i,SV1197: $i] :
      ( ( ! [SY3070: $i] :
            ( ~ ( c_in @ SV1197 @ SV1482 @ SY3070 )
            | ! [SY3071: $i] : ( c_in @ SV1197 @ ( c_union @ SV1482 @ SY3071 @ SY3070 ) @ SY3070 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5579]) ).

thf(6828,plain,
    ! [SV1483: $i,SV1198: $i] :
      ( ( ! [SY3072: $i,SY3073: $i] :
            ( ~ ( c_in @ SV1198 @ ( c_union @ SV1483 @ SY3072 @ SY3073 ) @ SY3073 )
            | ( c_in @ SV1198 @ SY3072 @ SY3073 )
            | ( c_in @ SV1198 @ SV1483 @ SY3073 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5580]) ).

thf(6829,plain,
    ! [SV1199: $i] :
      ( ( ( ! [SY2619: $i,SY2620: $i] :
              ( ( c_union @ SV1199 @ SY2619 @ SY2620 )
             != c_emptyset ) )
        = $true )
      | ( ( SV1199 = c_emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5581]) ).

thf(6830,plain,
    ! [SV1484: $i,SV1200: $i] :
      ( ( ! [SY3074: $i] :
            ( ( c_union @ SV1200 @ SV1484 @ SY3074 )
           != c_emptyset )
        | ( SV1484 = c_emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5582]) ).

thf(6831,plain,
    ! [SV1485: $i,SV1202: $i] :
      ( ( ! [SY3075: $i] :
            ( ~ ( c_in @ SV1202 @ SV1485 @ SY3075 )
            | ! [SY3076: $i] :
                ( ~ ( c_in @ SV1485 @ SY3076 @ ( tc_set @ SY3075 ) )
                | ( c_in @ SV1202 @ ( c_Union @ SY3076 @ SY3075 ) @ SY3075 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5584]) ).

thf(6832,plain,
    ! [SV1486: $i,SV1203: $i] :
      ( ( ~ ( c_in @ SV1203 @ c_emptyset @ SV1486 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5585]) ).

thf(6833,plain,
    ! [SV1487: $i,SV1204: $i] :
      ( ( ! [SY3077: $i] :
            ( ~ ( c_in @ SV1204 @ SV1487 @ SY3077 )
            | ! [SY3078: $i] : ( c_in @ SV1204 @ ( c_insert @ SY3078 @ SV1487 @ SY3077 ) @ SY3077 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5586]) ).

thf(6834,plain,
    ! [SV1488: $i,SV1205: $i] :
      ( ( ! [SY3079: $i] : ( c_in @ SV1205 @ ( c_insert @ SV1205 @ SV1488 @ SY3079 ) @ SY3079 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5587]) ).

thf(6835,plain,
    ! [SV1489: $i,SV1206: $i] :
      ( ( ! [SY3080: $i,SY3081: $i] :
            ( ~ ( c_in @ SV1206 @ ( c_insert @ SV1489 @ SY3080 @ SY3081 ) @ SY3081 )
            | ( SV1206 = SV1489 )
            | ( c_in @ SV1206 @ SY3080 @ SY3081 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5588]) ).

thf(6836,plain,
    ! [SV1490: $i,SV1207: $i] :
      ( ( ~ ( c_less @ SV1207 @ c_emptyset @ ( tc_set @ SV1490 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5589]) ).

thf(6837,plain,
    ! [SV1491: $i,SV1208: $i] :
      ( ( ! [SY3082: $i,SY3083: $i] :
            ( ( ( c_insert @ SV1208 @ SV1491 @ SY3082 )
             != ( c_insert @ SY3083 @ c_emptyset @ SY3082 ) )
            | ( SV1208 = SY3083 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5590]) ).

thf(6838,plain,
    ! [SV1492: $i,SV1209: $i] :
      ( ( ! [SY3084: $i,SY3085: $i] :
            ( ( ( c_insert @ SV1209 @ SV1492 @ SY3084 )
             != ( c_insert @ SY3085 @ c_emptyset @ SY3084 ) )
            | ( c_lessequals @ SV1492 @ ( c_insert @ SY3085 @ c_emptyset @ SY3084 ) @ ( tc_set @ SY3084 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5591]) ).

thf(6839,plain,
    ! [SV1493: $i,SV1210: $i] :
      ( ( ! [SY3086: $i] :
            ( ~ ( c_lessequals @ SV1210 @ ( c_insert @ SV1493 @ c_emptyset @ SY3086 ) @ ( tc_set @ SY3086 ) )
            | ( ( c_insert @ SV1493 @ SV1210 @ SY3086 )
              = ( c_insert @ SV1493 @ c_emptyset @ SY3086 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5592]) ).

thf(6840,plain,
    ! [SV1494: $i,SV1211: $i] :
      ( ( ! [SY3087: $i] :
            ( ! [SY3088: $i] :
                ( ( c_insert @ SV1211 @ c_emptyset @ SV1494 )
               != ( c_insert @ SY3087 @ SY3088 @ SV1494 ) )
            | ( SY3087 = SV1211 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5593]) ).

thf(6841,plain,
    ! [SV1495: $i,SV1212: $i] :
      ( ( ! [SY3089: $i,SY3090: $i] :
            ( ( ( c_insert @ SV1212 @ c_emptyset @ SV1495 )
             != ( c_insert @ SY3089 @ SY3090 @ SV1495 ) )
            | ( c_lessequals @ SY3090 @ ( c_insert @ SV1212 @ c_emptyset @ SV1495 ) @ ( tc_set @ SV1495 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5594]) ).

thf(6842,plain,
    ! [SV1496: $i,SV1213: $i] :
      ( ( ! [SY3091: $i] :
            ( ~ ( c_lessequals @ SV1213 @ ( c_insert @ SV1496 @ c_emptyset @ SY3091 ) @ ( tc_set @ SY3091 ) )
            | ( ( c_insert @ SV1496 @ c_emptyset @ SY3091 )
              = ( c_insert @ SV1496 @ SV1213 @ SY3091 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5595]) ).

thf(6843,plain,
    ! [SV1497: $i,SV1214: $i] :
      ( ( ! [SY3092: $i,SY3093: $i] :
            ( ( ( c_Sum__Type_OInl @ SV1214 @ SV1497 @ SY3092 )
             != ( c_Sum__Type_OInl @ SY3093 @ SV1497 @ SY3092 ) )
            | ( SV1214 = SY3093 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5596]) ).

thf(6844,plain,
    ! [SV1498: $i,SV1215: $i] :
      ( ( ! [SY3094: $i,SY3095: $i] :
            ( ( c_Sum__Type_OInl @ SV1215 @ SV1498 @ SY3094 )
           != ( c_Sum__Type_OInr @ SY3095 @ SY3094 @ SV1498 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5597]) ).

thf(6845,plain,
    ! [SV1499: $i,SV1216: $i] :
      ( ( ! [SY3096: $i,SY3097: $i] :
            ( ( ( c_Sum__Type_OInr @ SV1216 @ SV1499 @ SY3096 )
             != ( c_Sum__Type_OInr @ SY3097 @ SV1499 @ SY3096 ) )
            | ( SV1216 = SY3097 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5598]) ).

thf(6846,plain,
    ! [SV1500: $i,SV1217: $i] :
      ( ( ! [SY3098: $i,SY3099: $i] :
            ( ( c_Sum__Type_OInr @ SV1217 @ SV1500 @ SY3098 )
           != ( c_Sum__Type_OInl @ SY3099 @ SY3098 @ SV1500 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5599]) ).

thf(6847,plain,
    ! [SV1501: $i,SV1218: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1218 @ SV1501 @ SV1501 ) @ SV1501 )
        | ( c_Wellfounded__Recursion_Oacyclic @ SV1218 @ SV1501 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5600]) ).

thf(6848,plain,
    ! [SV1502: $i,SV1219: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1219 @ SV1502 )
        | ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1219 @ SV1502 @ SV1502 ) @ SV1502 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5601]) ).

thf(6849,plain,
    ! [SV1503: $i,SV1220: $i] :
      ( ( ! [SY3100: $i,SY3101: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1220 @ SV1503 @ SY3100 @ SY3100 ) @ SY3101 @ ( tc_prod @ SY3100 @ SY3100 ) ) @ SY3100 )
            | ( c_Wellfounded__Recursion_Oacyclic @ SY3101 @ SY3100 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5602]) ).

thf(6850,plain,
    ! [SV1504: $i,SV1221: $i] :
      ( ( ! [SY3102: $i,SY3103: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1221 @ SV1504 @ SY3102 @ SY3102 ) @ SY3103 @ ( tc_prod @ SY3102 @ SY3102 ) ) @ SY3102 )
            | ~ ( c_in @ ( c_Pair @ SV1504 @ SV1221 @ SY3102 @ SY3102 ) @ ( c_Transitive__Closure_Ortrancl @ SY3103 @ SY3102 ) @ ( tc_prod @ SY3102 @ SY3102 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5603]) ).

thf(6851,plain,
    ! [SV1505: $i,SV1222: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1222 @ SV1505 )
        | ! [SY3104: $i,SY3105: $i] :
            ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SY3104 @ SY3105 @ SV1505 @ SV1505 ) @ SV1222 @ ( tc_prod @ SV1505 @ SV1505 ) ) @ SV1505 )
            | ( c_in @ ( c_Pair @ SY3105 @ SY3104 @ SV1505 @ SV1505 ) @ ( c_Transitive__Closure_Ortrancl @ SV1222 @ SV1505 ) @ ( tc_prod @ SV1505 @ SV1505 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5604]) ).

thf(6852,plain,
    ! [SV1506: $i,SV1223: $i] :
      ( ( ! [SY3106: $i,SY3107: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1223 @ SV1506 @ SY3106 @ SY3106 ) @ SY3107 @ ( tc_prod @ SY3106 @ SY3106 ) ) @ SY3106 )
            | ( c_Wellfounded__Recursion_Owf @ SY3107 @ SY3106 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5605]) ).

thf(6853,plain,
    ! [SV1507: $i,SV1224: $i] :
      ( ( ! [SY3108: $i,SY3109: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1224 @ SV1507 @ SY3108 @ SY3108 ) @ SY3109 @ ( tc_prod @ SY3108 @ SY3108 ) ) @ SY3108 )
            | ~ ( c_in @ ( c_Pair @ SV1507 @ SV1224 @ SY3108 @ SY3108 ) @ ( c_Transitive__Closure_Ortrancl @ SY3109 @ SY3108 ) @ ( tc_prod @ SY3108 @ SY3108 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5606]) ).

thf(6854,plain,
    ! [SV1508: $i,SV1225: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1225 @ SV1508 )
        | ! [SY3110: $i,SY3111: $i] :
            ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SY3110 @ SY3111 @ SV1508 @ SV1508 ) @ SV1225 @ ( tc_prod @ SV1508 @ SV1508 ) ) @ SV1508 )
            | ( c_in @ ( c_Pair @ SY3111 @ SY3110 @ SV1508 @ SV1508 ) @ ( c_Transitive__Closure_Ortrancl @ SV1225 @ SV1508 ) @ ( tc_prod @ SV1508 @ SV1508 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5607]) ).

thf(6855,plain,
    ! [SV1509: $i,SV1226: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV1226 @ SV1509 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
        | ( c_less @ SV1226 @ SV1509 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5608]) ).

thf(6856,plain,
    ! [SV1510: $i,SV1227: $i] :
      ( ( ~ ( c_less @ SV1227 @ SV1510 @ tc_nat )
        | ( c_in @ ( c_Pair @ SV1227 @ SV1510 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5609]) ).

thf(6857,plain,
    ! [SV1511: $i,SV1228: $i] :
      ( ( ! [SY3112: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ ( c_Message_Osynth @ SY3112 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ SY3112 @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OKey @ SV1228 ) @ SY3112 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5610]) ).

thf(6858,plain,
    ! [SV1512: $i,SV1229: $i] :
      ( ( ! [SY3113: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ ( c_Message_Osynth @ SY3113 ) @ tc_Message_Omsg )
            | ( c_in @ SV1512 @ ( c_Message_Osynth @ SY3113 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ SY3113 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5611]) ).

thf(6859,plain,
    ! [SV1513: $i,SV1230: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg )
        | ( c_in @ SV1230 @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ SV1513 @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5612]) ).

thf(6860,plain,
    ! [SV1514: $i,SV1231: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ ( c_Message_Osynth @ SV1514 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ SV1514 @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5613]) ).

thf(6861,plain,
    ! [SV1515: $i,SV1232: $i] :
      ( ( ! [SY3114: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1232 @ SV1515 ) @ ( c_Message_Oanalz @ SY3114 ) @ tc_Message_Omsg )
            | ( c_in @ SV1515 @ ( c_Message_Oanalz @ SY3114 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5614]) ).

thf(6862,plain,
    ! [SV1516: $i,SV1233: $i] :
      ( ( ! [SY3115: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1233 @ SV1516 ) @ ( c_Message_Oanalz @ SY3115 ) @ tc_Message_Omsg )
            | ( c_in @ SV1233 @ ( c_Message_Oanalz @ SY3115 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5615]) ).

thf(6863,plain,
    ! [SV1517: $i,SV1234: $i] :
      ( ( ! [SY3116: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1234 @ SV1517 ) @ ( c_Message_Oparts @ SY3116 ) @ tc_Message_Omsg )
            | ( c_in @ SV1517 @ ( c_Message_Oparts @ SY3116 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5616]) ).

thf(6864,plain,
    ! [SV1518: $i,SV1235: $i] :
      ( ( ! [SY3117: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1235 @ SV1518 ) @ ( c_Message_Oparts @ SY3117 ) @ tc_Message_Omsg )
            | ( c_in @ SV1235 @ ( c_Message_Oparts @ SY3117 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5617]) ).

thf(6865,plain,
    ! [SV1519: $i,SV1236: $i] :
      ( ( ! [SY3118: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ ( c_Message_Osynth @ SY3118 ) @ tc_Message_Omsg )
            | ( c_in @ SV1519 @ ( c_Message_Osynth @ SY3118 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ SY3118 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5618]) ).

thf(6866,plain,
    ! [SV1520: $i,SV1237: $i] :
      ( ( ! [SY3119: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ ( c_Message_Osynth @ SY3119 ) @ tc_Message_Omsg )
            | ( c_in @ SV1237 @ ( c_Message_Osynth @ SY3119 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ SY3119 @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5619]) ).

thf(6867,plain,
    ! [SV1521: $i,SV1238: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ ( c_Message_Osynth @ SV1521 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ SV1521 @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5620]) ).

thf(6868,plain,
    ! [SV1239: $i] :
      ( ( c_Message_Oagent_OServer
        = ( c_Message_Oagent_OFriend @ SV1239 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5621]) ).

thf(6869,plain,
    ! [SV1240: $i] :
      ( ( ( c_Message_Oagent_OFriend @ SV1240 )
        = c_Message_Oagent_OServer )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5622]) ).

thf(6870,plain,
    ! [SV1241: $i] :
      ( ( ( c_Message_Oagent_OFriend @ SV1241 )
        = c_Message_Oagent_OSpy )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5625]) ).

thf(6871,plain,
    ! [SV1242: $i] :
      ( ( c_Message_Oagent_OSpy
        = ( c_Message_Oagent_OFriend @ SV1242 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5626]) ).

thf(6872,plain,
    ! [SV1522: $i,SV1243: $i] :
      ( ( ( ( c_Message_Oagent_OFriend @ SV1243 )
         != ( c_Message_Oagent_OFriend @ SV1522 ) )
        | ( SV1243 = SV1522 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5627]) ).

thf(6873,plain,
    ! [SV1523: $i,SV1244: $i] :
      ( ( ! [SY3120: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1244 @ SV1523 ) @ ( c_Message_Oanalz @ SY3120 ) @ tc_Message_Omsg )
            | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1244 ) ) @ ( c_Message_Oanalz @ SY3120 ) @ tc_Message_Omsg )
            | ( c_in @ SV1523 @ ( c_Message_Oanalz @ SY3120 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5628]) ).

thf(6874,plain,
    ! [SV1524: $i,SV1245: $i] :
      ( ( ~ ( c_in @ SV1245 @ SV1524 @ tc_Message_Omsg )
        | ( c_in @ SV1245 @ ( c_Message_Oanalz @ SV1524 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5629]) ).

thf(6875,plain,
    ! [SV1525: $i,SV1246: $i] :
      ( ( ~ ( c_in @ SV1246 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SV1525 ) ) @ tc_Message_Omsg )
        | ( c_in @ SV1246 @ ( c_Message_Oanalz @ SV1525 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5630]) ).

thf(6876,plain,
    ! [SV1526: $i,SV1247: $i] :
      ( ( ! [SY3121: $i] :
            ( ~ ( c_in @ SV1247 @ ( c_Message_Oparts @ ( c_union @ SV1526 @ SY3121 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
            | ( c_in @ SV1247 @ ( c_Message_Oparts @ SY3121 ) @ tc_Message_Omsg )
            | ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1526 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5631]) ).

thf(6877,plain,
    ! [SV1527: $i,SV1248: $i] :
      ( ( ( ( c_Message_Omsg_OAgent @ SV1248 )
         != ( c_Message_Omsg_OAgent @ SV1527 ) )
        | ( SV1248 = SV1527 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5632]) ).

thf(6878,plain,
    ! [SV1528: $i,SV1249: $i] :
      ( ( ( ( c_Message_Omsg_ONumber @ SV1249 )
         != ( c_Message_Omsg_ONumber @ SV1528 ) )
        | ( SV1249 = SV1528 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5633]) ).

thf(6879,plain,
    ! [SV1529: $i,SV1250: $i] :
      ( ( ( ( c_Message_Omsg_ONonce @ SV1250 )
         != ( c_Message_Omsg_ONonce @ SV1529 ) )
        | ( SV1250 = SV1529 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5634]) ).

thf(6880,plain,
    ! [SV1530: $i,SV1251: $i] :
      ( ( ( ( c_Message_Omsg_OKey @ SV1251 )
         != ( c_Message_Omsg_OKey @ SV1530 ) )
        | ( SV1251 = SV1530 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5635]) ).

thf(6881,plain,
    ! [SV1531: $i,SV1252: $i] :
      ( ( ( ( c_Message_Omsg_OHash @ SV1252 )
         != ( c_Message_Omsg_OHash @ SV1531 ) )
        | ( SV1252 = SV1531 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5636]) ).

thf(6882,plain,
    ! [SV1532: $i,SV1253: $i] :
      ( ( ! [SY3122: $i] :
            ( ! [SY3123: $i] :
                ( ( c_Message_Omsg_OMPair @ SV1253 @ SV1532 )
               != ( c_Message_Omsg_OMPair @ SY3122 @ SY3123 ) )
            | ( SV1253 = SY3122 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5637]) ).

thf(6883,plain,
    ! [SV1533: $i,SV1254: $i] :
      ( ( ! [SY3124: $i,SY3125: $i] :
            ( ( ( c_Message_Omsg_OMPair @ SV1254 @ SV1533 )
             != ( c_Message_Omsg_OMPair @ SY3124 @ SY3125 ) )
            | ( SV1533 = SY3125 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5638]) ).

thf(6884,plain,
    ! [SV1534: $i,SV1255: $i] :
      ( ( ! [SY3126: $i] :
            ( ! [SY3127: $i] :
                ( ( c_Message_Omsg_OCrypt @ SV1255 @ SV1534 )
               != ( c_Message_Omsg_OCrypt @ SY3126 @ SY3127 ) )
            | ( SV1255 = SY3126 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5639]) ).

thf(6885,plain,
    ! [SV1535: $i,SV1256: $i] :
      ( ( ! [SY3128: $i,SY3129: $i] :
            ( ( ( c_Message_Omsg_OCrypt @ SV1256 @ SV1535 )
             != ( c_Message_Omsg_OCrypt @ SY3128 @ SY3129 ) )
            | ( SV1535 = SY3129 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5640]) ).

thf(6886,plain,
    ! [SV1536: $i,SV1257: $i] :
      ( ( ~ ( c_in @ SV1257 @ SV1536 @ tc_Message_Omsg )
        | ( c_in @ SV1257 @ ( c_Message_Oparts @ SV1536 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5641]) ).

thf(6887,plain,
    ! [SV1258: $i] :
      ( ( c_in @ SV1258 @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[5642]) ).

thf(6888,plain,
    ! [SV1537: $i,SV1259: $i] :
      ( ( ~ ( c_in @ SV1259 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SV1537 ) ) @ tc_Message_Omsg )
        | ( c_in @ SV1259 @ ( c_Message_Oparts @ SV1537 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5643]) ).

thf(6889,plain,
    ! [SV1538: $i,SV1260: $i] :
      ( ( c_in @ ( c_Message_Omsg_OAgent @ SV1260 ) @ ( c_Message_Osynth @ SV1538 ) @ tc_Message_Omsg )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5644]) ).

thf(6890,plain,
    ! [SV1539: $i,SV1261: $i] :
      ( ( ~ ( c_in @ SV1261 @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg )
        | ! [SY3130: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SY3130 ) @ SV1539 @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OCrypt @ SY3130 @ SV1261 ) @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5645]) ).

thf(6891,plain,
    ! [SV1540: $i,SV1262: $i] :
      ( ( ~ ( c_in @ SV1262 @ ( c_Message_Osynth @ SV1540 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OHash @ SV1262 ) @ ( c_Message_Osynth @ SV1540 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5646]) ).

thf(6892,plain,
    ! [SV1541: $i,SV1263: $i] :
      ( ( ~ ( c_in @ SV1263 @ SV1541 @ tc_Message_Omsg )
        | ( c_in @ SV1263 @ ( c_Message_Osynth @ SV1541 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5647]) ).

thf(6893,plain,
    ! [SV1542: $i,SV1264: $i] :
      ( ( ~ ( c_in @ SV1264 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        | ! [SY3131: $i] :
            ( ~ ( c_in @ SY3131 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_OMPair @ SY3131 @ SV1264 ) @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5648]) ).

thf(6894,plain,
    ! [SV1543: $i,SV1265: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONumber @ SV1265 ) @ ( c_Message_Osynth @ SV1543 ) @ tc_Message_Omsg )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5649]) ).

thf(6895,plain,
    ! [SV1544: $i,SV1266: $i] :
      ( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SV1544 ) @ ( tc_set @ tc_Message_Omsg ) )
        | ! [SY3132: $i,SY3133: $i] :
            ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SY3132 ) @ ( c_Message_Oanalz @ SY3133 ) @ ( tc_set @ tc_Message_Omsg ) )
            | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SY3132 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SY3133 @ SV1544 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5650]) ).

thf(6896,plain,
    ! [SV1545: $i,SV1267: $i] :
      ( ( ~ ( c_in @ SV1267 @ ( c_Message_Osynth @ ( c_Message_Osynth @ SV1545 ) ) @ tc_Message_Omsg )
        | ( c_in @ SV1267 @ ( c_Message_Osynth @ SV1545 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5651]) ).

thf(6897,plain,
    ! [SV1546: $i,SV1268: $i,SV1: $i] :
      ( ( ! [SY3134: $i] :
            ( ( ( c_Datatype__Universe_OLeaf @ SV1 @ SV1268 @ SV1546 )
             != ( c_Datatype__Universe_OLeaf @ SY3134 @ SV1268 @ SV1546 ) )
            | ( SV1 = SY3134 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5653]) ).

thf(6898,plain,
    ! [SV1547: $i,SV1269: $i,SV2: $i] :
      ( ( ! [SY3135: $i] :
            ( ( ( c_Datatype__Universe_ONumb @ SV2 @ SV1269 @ SV1547 )
             != ( c_Datatype__Universe_ONumb @ SY3135 @ SV1269 @ SV1547 ) )
            | ( SV2 = SY3135 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5654]) ).

thf(6899,plain,
    ! [SV1548: $i,SV1270: $i,SV3: $i] :
      ( ( ! [SY3136: $i,SY3137: $i] :
            ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1270 @ SV1548 @ SY3136 @ SY3137 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) ) )
            | ( SV3
              = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV3 @ SV1270 @ SV1548 @ SY3136 @ SY3137 ) @ ( c_Main_OdprodE__2 @ SV3 @ SV1270 @ SV1548 @ SY3136 @ SY3137 ) @ SY3136 @ SY3137 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV3 @ SV1270 @ SV1548 @ SY3136 @ SY3137 ) @ ( c_Main_OdprodE__4 @ SV3 @ SV1270 @ SV1548 @ SY3136 @ SY3137 ) @ SY3136 @ SY3137 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5655]) ).

thf(6900,plain,
    ! [SV1549: $i,SV1271: $i,SV4: $i] :
      ( ( ! [SY3138: $i,SY3139: $i] :
            ( ~ ( c_in @ SV4 @ ( c_Datatype__Universe_Odprod @ SV1271 @ SV1549 @ SY3138 @ SY3139 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV4 @ SV1271 @ SV1549 @ SY3138 @ SY3139 ) @ ( c_Main_OdprodE__4 @ SV4 @ SV1271 @ SV1549 @ SY3138 @ SY3139 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) ) @ SV1549 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5656]) ).

thf(6901,plain,
    ! [SV1550: $i,SV1272: $i,SV5: $i] :
      ( ( ! [SY3140: $i,SY3141: $i] :
            ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odprod @ SV1272 @ SV1550 @ SY3140 @ SY3141 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV5 @ SV1272 @ SV1550 @ SY3140 @ SY3141 ) @ ( c_Main_OdprodE__3 @ SV5 @ SV1272 @ SV1550 @ SY3140 @ SY3141 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) ) @ SV1272 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5657]) ).

thf(6902,plain,
    ! [SV1551: $i,SV1273: $i,SV6: $i] :
      ( ( ! [SY3142: $i,SY3143: $i,SY3144: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) ) @ SY3143 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) ) )
            | ! [SY3145: $i,SY3146: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY3144 @ SY3145 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) ) @ SY3146 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) ) )
                | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY3144 @ SV6 @ SV1551 @ SY3142 ) @ ( c_Datatype__Universe_OScons @ SY3145 @ SV1273 @ SV1551 @ SY3142 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3146 @ SY3143 @ SV1551 @ SY3142 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SY3142 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5658]) ).

thf(6903,plain,
    ! [SV1552: $i,SV1274: $i,SV7: $i] :
      ( ( ! [SY3147: $i,SY3148: $i] :
            ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1274 @ SV1552 @ SY3147 @ SY3148 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3147 @ SY3148 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3147 @ SY3148 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1274 @ SV7 @ SY3147 @ SY3148 ) @ SY3147 @ SY3148 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1274 @ SV7 @ SY3147 @ SY3148 ) @ SY3147 @ SY3148 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3147 @ SY3148 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3147 @ SY3148 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1552 @ SV7 @ SY3147 @ SY3148 ) @ SY3147 @ SY3148 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1552 @ SV7 @ SY3147 @ SY3148 ) @ SY3147 @ SY3148 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3147 @ SY3148 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3147 @ SY3148 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5659]) ).

thf(6904,plain,
    ! [SV1553: $i,SV1275: $i,SV8: $i] :
      ( ( ! [SY3149: $i,SY3150: $i] :
            ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1275 @ SV1553 @ SY3149 @ SY3150 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) ) )
            | ( SV8
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1275 @ SV8 @ SY3149 @ SY3150 ) @ SY3149 @ SY3150 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1275 @ SV8 @ SY3149 @ SY3150 ) @ SY3149 @ SY3150 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1553 @ SV8 @ SY3149 @ SY3150 ) @ ( c_Main_OdsumE__4 @ SV1553 @ SV8 @ SY3149 @ SY3150 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) ) @ SV1553 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3149 @ SY3150 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5660]) ).

thf(6905,plain,
    ! [SV1554: $i,SV1276: $i,SV9: $i] :
      ( ( ! [SY3151: $i,SY3152: $i] :
            ( ~ ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SV1276 @ SV1554 @ SY3151 @ SY3152 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) ) )
            | ( SV9
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1554 @ SV9 @ SY3151 @ SY3152 ) @ SY3151 @ SY3152 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1554 @ SV9 @ SY3151 @ SY3152 ) @ SY3151 @ SY3152 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1276 @ SV9 @ SY3151 @ SY3152 ) @ ( c_Main_OdsumE__2 @ SV1276 @ SV9 @ SY3151 @ SY3152 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) ) @ SV1276 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3151 @ SY3152 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5661]) ).

thf(6906,plain,
    ! [SV1555: $i,SV1277: $i,SV10: $i] :
      ( ( ! [SY3153: $i,SY3154: $i] :
            ( ~ ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SV1277 @ SV1555 @ SY3153 @ SY3154 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1277 @ SV10 @ SY3153 @ SY3154 ) @ ( c_Main_OdsumE__2 @ SV1277 @ SV10 @ SY3153 @ SY3154 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) ) @ SV1277 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1555 @ SV10 @ SY3153 @ SY3154 ) @ ( c_Main_OdsumE__4 @ SV1555 @ SV10 @ SY3153 @ SY3154 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) ) @ SV1555 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3153 @ SY3154 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5662]) ).

thf(6907,plain,
    ! [SV1556: $i,SV1278: $i,SV11: $i] :
      ( ( ! [SY3155: $i,SY3156: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV11 @ SV1278 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) ) @ SY3156 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) ) )
            | ! [SY3157: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SV1556 @ SY3155 ) @ ( c_Datatype__Universe_OIn0 @ SV1278 @ SV1556 @ SY3155 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3156 @ SY3157 @ SV1556 @ SY3155 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SY3155 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5663]) ).

thf(6908,plain,
    ! [SV1557: $i,SV1279: $i,SV12: $i] :
      ( ( ! [SY3158: $i,SY3159: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV12 @ SV1279 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) ) @ SY3159 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) ) )
            | ! [SY3160: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SV1557 @ SY3158 ) @ ( c_Datatype__Universe_OIn1 @ SV1279 @ SV1557 @ SY3158 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3160 @ SY3159 @ SV1557 @ SY3158 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SY3158 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5664]) ).

thf(6909,plain,
    ! [SV1558: $i,SV1280: $i,SV13: $i] :
      ( ( ! [SY3161: $i,SY3162: $i] :
            ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1280 @ SV1558 @ SY3161 @ SY3162 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3161 @ SY3162 ) ) )
            | ( SV13
              = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1280 @ SV1558 @ SV13 @ SY3161 @ SY3162 ) @ ( c_Main_OuprodE__2 @ SV1280 @ SV1558 @ SV13 @ SY3161 @ SY3162 ) @ SY3161 @ SY3162 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5665]) ).

thf(6910,plain,
    ! [SV1559: $i,SV1281: $i,SV14: $i] :
      ( ( ! [SY3163: $i,SY3164: $i] :
            ( ~ ( c_in @ SV14 @ ( c_Datatype__Universe_Ouprod @ SV1281 @ SV1559 @ SY3163 @ SY3164 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3163 @ SY3164 ) ) )
            | ( c_in @ ( c_Main_OuprodE__2 @ SV1281 @ SV1559 @ SV14 @ SY3163 @ SY3164 ) @ SV1559 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3163 @ SY3164 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5666]) ).

thf(6911,plain,
    ! [SV1560: $i,SV1282: $i,SV15: $i] :
      ( ( ! [SY3165: $i,SY3166: $i] :
            ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ouprod @ SV1282 @ SV1560 @ SY3165 @ SY3166 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3165 @ SY3166 ) ) )
            | ( c_in @ ( c_Main_OuprodE__1 @ SV1282 @ SV1560 @ SV15 @ SY3165 @ SY3166 ) @ SV1282 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3165 @ SY3166 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5667]) ).

thf(6912,plain,
    ! [SV1561: $i,SV1283: $i,SV16: $i] :
      ( ( ! [SY3167: $i] :
            ( ~ ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SY3167 ) ) )
            | ! [SY3168: $i,SY3169: $i] :
                ( ~ ( c_in @ SY3168 @ SY3169 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SY3167 ) ) )
                | ( c_in @ ( c_Datatype__Universe_OScons @ SY3168 @ SV16 @ SV1561 @ SY3167 ) @ ( c_Datatype__Universe_Ouprod @ SY3169 @ SV1283 @ SV1561 @ SY3167 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SY3167 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5668]) ).

thf(6913,plain,
    ! [SV1562: $i,SV1284: $i,SV17: $i] :
      ( ( ! [SY3170: $i,SY3171: $i] :
            ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1284 @ SV1562 @ SY3170 @ SY3171 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3170 @ SY3171 ) ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1284 @ SV17 @ SY3170 @ SY3171 ) @ SY3170 @ SY3171 ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1562 @ SV17 @ SY3170 @ SY3171 ) @ SY3170 @ SY3171 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5669]) ).

thf(6914,plain,
    ! [SV1563: $i,SV1285: $i,SV18: $i] :
      ( ( ! [SY3172: $i,SY3173: $i] :
            ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1285 @ SV1563 @ SY3172 @ SY3173 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3172 @ SY3173 ) ) )
            | ( SV18
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1285 @ SV18 @ SY3172 @ SY3173 ) @ SY3172 @ SY3173 ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SV1563 @ SV18 @ SY3172 @ SY3173 ) @ SV1563 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3172 @ SY3173 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5670]) ).

thf(6915,plain,
    ! [SV1564: $i,SV1286: $i,SV19: $i] :
      ( ( ! [SY3174: $i,SY3175: $i] :
            ( ~ ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SV1286 @ SV1564 @ SY3174 @ SY3175 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3174 @ SY3175 ) ) )
            | ( SV19
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1564 @ SV19 @ SY3174 @ SY3175 ) @ SY3174 @ SY3175 ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SV1286 @ SV19 @ SY3174 @ SY3175 ) @ SV1286 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3174 @ SY3175 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5671]) ).

thf(6916,plain,
    ! [SV1565: $i,SV1287: $i,SV20: $i] :
      ( ( ! [SY3176: $i,SY3177: $i] :
            ( ~ ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SV1287 @ SV1565 @ SY3176 @ SY3177 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3176 @ SY3177 ) ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SV1287 @ SV20 @ SY3176 @ SY3177 ) @ SV1287 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3176 @ SY3177 ) ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SV1565 @ SV20 @ SY3176 @ SY3177 ) @ SV1565 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3176 @ SY3177 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5672]) ).

thf(6917,plain,
    ! [SV1566: $i,SV1288: $i,SV21: $i] :
      ( ( ! [SY3178: $i] :
            ( ~ ( c_in @ SV21 @ SV1288 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SY3178 ) ) )
            | ! [SY3179: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ SV21 @ SV1566 @ SY3178 ) @ ( c_Datatype__Universe_Ousum @ SV1288 @ SY3179 @ SV1566 @ SY3178 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SY3178 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5673]) ).

thf(6918,plain,
    ! [SV1567: $i,SV1289: $i,SV22: $i] :
      ( ( ! [SY3180: $i] :
            ( ~ ( c_in @ SV22 @ SV1289 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SY3180 ) ) )
            | ! [SY3181: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ SV22 @ SV1567 @ SY3180 ) @ ( c_Datatype__Universe_Ousum @ SY3181 @ SV1289 @ SV1567 @ SY3180 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SY3180 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5674]) ).

thf(6919,plain,
    ! [SV1292: $i,SV27: $i] :
      ( ( ( ( c_Divides_Oop_Amod @ SV27 @ SV1292 @ tc_nat )
         != c_0 )
        = $true )
      | ( ( SV27
          = ( c_times @ SV1292 @ ( c_Main_Omod__eq__0D__dest__1 @ SV1292 @ SV27 ) @ tc_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5677]) ).

thf(6920,plain,
    ! [SV1293: $i,SV29: $i] :
      ( ( ( ~ ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) ) )
        = $true )
      | ( ( ! [SY2813: $i] : ( c_in @ ( c_insert @ SY2813 @ SV29 @ SV1293 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5678]) ).

thf(6921,plain,
    ! [SV1294: $i,SV30: $i] :
      ( ( ( ~ ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) ) )
        = $true )
      | ( ( ! [SY2814: $i] : ( c_in @ ( c_inter @ SV30 @ SY2814 @ SV1294 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5679]) ).

thf(6922,plain,
    ! [SV1295: $i,SV31: $i] :
      ( ( ( ~ ( c_in @ SV31 @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) ) )
        = $true )
      | ( ( ! [SY2815: $i] : ( c_in @ ( c_inter @ SY2815 @ SV31 @ SV1295 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5680]) ).

thf(6923,plain,
    ! [SV1296: $i,SV32: $i] :
      ( ( ( ~ ( c_in @ SV32 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1296 ) ) ) )
        = $true )
      | ( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV32 @ SV1296 ) @ SV32 @ ( tc_set @ SV1296 ) )
          | ( c_in @ ( c_Union @ SV32 @ SV1296 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1296 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5681]) ).

thf(6924,plain,
    ! [SV1297: $i,SV33: $i] :
      ( ( ( ~ ( c_in @ SV33 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1297 ) ) ) )
        = $true )
      | ( ( ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) )
          | ( c_in @ ( c_Union @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5682]) ).

thf(6925,plain,
    ! [SV1300: $i,SV36: $i] :
      ( ( ( ~ ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 ) )
        = $true )
      | ( ( ! [SY2816: $i] :
              ( ~ ( c_in @ SY2816 @ SV36 @ SV1300 )
              | ! [SY2817: $i] :
                  ( ~ ( c_in @ SY2817 @ SV36 @ SV1300 )
                  | ( SY2816 = SY2817 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5685]) ).

thf(6926,plain,
    ! [SV1305: $i,SV43: $i] :
      ( ( ( ( c_Divides_Oop_Amod @ SV43 @ SV1305 @ tc_IntDef_Oint )
         != c_0 )
        = $true )
      | ( ( SV43
          = ( c_times @ SV1305 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SV1305 @ SV43 ) @ tc_IntDef_Oint ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5690]) ).

thf(6927,plain,
    ! [SV1568: $i,SV1308: $i,SV46: $i] :
      ( ( ~ ( c_in @ SV46 @ ( c_List_Olists @ SV1308 @ SV1568 ) @ ( tc_List_Olist @ SV1568 ) )
        | ! [SY3182: $i] :
            ( ~ ( c_in @ SY3182 @ ( c_List_Oset @ SV46 @ SV1568 ) @ SV1568 )
            | ( c_in @ SY3182 @ SV1308 @ SV1568 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5693]) ).

thf(6928,plain,
    ! [SV1569: $i,SV1309: $i,SV47: $i] :
      ( ( ( c_in @ SV47 @ ( c_List_Olists @ SV1309 @ SV1569 ) @ ( tc_List_Olist @ SV1569 ) )
        | ( c_in @ ( c_Main_Oin__listsI__1 @ SV1309 @ SV47 @ SV1569 ) @ ( c_List_Oset @ SV47 @ SV1569 ) @ SV1569 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5694]) ).

thf(6929,plain,
    ! [SV1570: $i,SV1310: $i,SV48: $i] :
      ( ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV48 @ SV1310 @ SV1570 ) @ SV48 @ SV1570 )
        | ( c_in @ SV1310 @ ( c_List_Olists @ SV48 @ SV1570 ) @ ( tc_List_Olist @ SV1570 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5695]) ).

thf(6930,plain,
    ! [SV1571: $i,SV1312: $i,SV50: $i] :
      ( ( ! [SY3183: $i,SY3184: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV50 @ SV1312 @ SV1571 ) @ SY3183 @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) @ ( c_List_Olistrel @ SY3184 @ SV1571 ) @ ( tc_prod @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) )
            | ( SY3183
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY3184 @ SY3183 @ SV50 @ SV1312 @ SV1571 ) @ ( c_Main_Olistrel__Cons1__2 @ SY3184 @ SY3183 @ SV50 @ SV1312 @ SV1571 ) @ SV1571 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5697]) ).

thf(6931,plain,
    ! [SV1572: $i,SV1313: $i,SV51: $i] :
      ( ( ! [SY3185: $i,SY3186: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV51 @ SV1313 @ SV1572 ) @ SY3185 @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SY3186 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) )
            | ( c_in @ ( c_Pair @ SV1313 @ ( c_Main_Olistrel__Cons1__2 @ SY3186 @ SY3185 @ SV51 @ SV1313 @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SY3186 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5698]) ).

thf(6932,plain,
    ! [SV1573: $i,SV1314: $i,SV52: $i] :
      ( ( ! [SY3187: $i,SY3188: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV52 @ SV1314 @ SV1573 ) @ SY3187 @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) @ ( c_List_Olistrel @ SY3188 @ SV1573 ) @ ( tc_prod @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) )
            | ( c_in @ ( c_Pair @ SV52 @ ( c_Main_Olistrel__Cons1__1 @ SY3188 @ SY3187 @ SV52 @ SV1314 @ SV1573 ) @ SV1573 @ SV1573 ) @ SY3188 @ ( tc_prod @ SV1573 @ SV1573 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5699]) ).

thf(6933,plain,
    ! [SV1574: $i,SV1315: $i,SV53: $i] :
      ( ( ! [SY3189: $i,SY3190: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV53 @ ( c_List_Olist_OCons @ SV1315 @ SV1574 @ SY3189 ) @ ( tc_List_Olist @ SY3189 ) @ ( tc_List_Olist @ SY3189 ) ) @ ( c_List_Olistrel @ SY3190 @ SY3189 ) @ ( tc_prod @ ( tc_List_Olist @ SY3189 ) @ ( tc_List_Olist @ SY3189 ) ) )
            | ( SV53
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY3190 @ SV53 @ SV1315 @ SV1574 @ SY3189 ) @ ( c_Main_Olistrel__Cons2__2 @ SY3190 @ SV53 @ SV1315 @ SV1574 @ SY3189 ) @ SY3189 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5700]) ).

thf(6934,plain,
    ! [SV1575: $i,SV1316: $i,SV54: $i] :
      ( ( ! [SY3191: $i,SY3192: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV54 @ ( c_List_Olist_OCons @ SV1316 @ SV1575 @ SY3191 ) @ ( tc_List_Olist @ SY3191 ) @ ( tc_List_Olist @ SY3191 ) ) @ ( c_List_Olistrel @ SY3192 @ SY3191 ) @ ( tc_prod @ ( tc_List_Olist @ SY3191 ) @ ( tc_List_Olist @ SY3191 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY3192 @ SV54 @ SV1316 @ SV1575 @ SY3191 ) @ SV1575 @ ( tc_List_Olist @ SY3191 ) @ ( tc_List_Olist @ SY3191 ) ) @ ( c_List_Olistrel @ SY3192 @ SY3191 ) @ ( tc_prod @ ( tc_List_Olist @ SY3191 ) @ ( tc_List_Olist @ SY3191 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5701]) ).

thf(6935,plain,
    ! [SV1576: $i,SV1317: $i,SV55: $i] :
      ( ( ! [SY3193: $i,SY3194: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV55 @ ( c_List_Olist_OCons @ SV1317 @ SV1576 @ SY3193 ) @ ( tc_List_Olist @ SY3193 ) @ ( tc_List_Olist @ SY3193 ) ) @ ( c_List_Olistrel @ SY3194 @ SY3193 ) @ ( tc_prod @ ( tc_List_Olist @ SY3193 ) @ ( tc_List_Olist @ SY3193 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY3194 @ SV55 @ SV1317 @ SV1576 @ SY3193 ) @ SV1317 @ SY3193 @ SY3193 ) @ SY3194 @ ( tc_prod @ SY3193 @ SY3193 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5702]) ).

thf(6936,plain,
    ! [SV1577: $i,SV56: $i] :
      ( ( ( ! [SY3195: $i] :
              ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV56 @ ( tc_List_Olist @ SV1577 ) @ ( tc_List_Olist @ SV1577 ) ) @ ( c_List_Olistrel @ SY3195 @ SV1577 ) @ ( tc_prod @ ( tc_List_Olist @ SV1577 ) @ ( tc_List_Olist @ SV1577 ) ) ) )
        = $true )
      | ( ( SV56 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[5703]) ).

thf(6937,plain,
    ! [SV1578: $i,SV57: $i] :
      ( ( ( ! [SY3196: $i] :
              ~ ( c_in @ ( c_Pair @ SV57 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1578 ) @ ( tc_List_Olist @ SV1578 ) ) @ ( c_List_Olistrel @ SY3196 @ SV1578 ) @ ( tc_prod @ ( tc_List_Olist @ SV1578 ) @ ( tc_List_Olist @ SV1578 ) ) ) )
        = $true )
      | ( ( SV57 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[5704]) ).

thf(6938,plain,
    ! [SV1579: $i,SV1318: $i,SV58: $i] :
      ( ( ! [SY3197: $i] :
            ( ~ ( c_in @ ( c_List_Olist_OCons @ SV58 @ SV1318 @ SV1579 ) @ ( c_List_Olists @ SY3197 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) )
            | ( c_in @ SV1318 @ ( c_List_Olists @ SY3197 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5705]) ).

thf(6939,plain,
    ! [SV1580: $i,SV1319: $i,SV59: $i] :
      ( ( ! [SY3198: $i] :
            ( ~ ( c_in @ ( c_List_Olist_OCons @ SV59 @ SV1319 @ SV1580 ) @ ( c_List_Olists @ SY3198 @ SV1580 ) @ ( tc_List_Olist @ SV1580 ) )
            | ( c_in @ SV59 @ SY3198 @ SV1580 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5706]) ).

thf(6940,plain,
    ! [SV1581: $i,SV1320: $i,SV60: $i] :
      ( ( ~ ( c_in @ SV60 @ SV1320 @ SV1581 )
        | ! [SY3199: $i] :
            ( ~ ( c_in @ SY3199 @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) )
            | ( c_in @ ( c_List_Olist_OCons @ SV60 @ SY3199 @ SV1581 ) @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5707]) ).

thf(6941,plain,
    ! [SV1322: $i,SV62: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV62 @ SV1322 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV62 @ SV1322 ) @ ( tc_List_Olist @ SV1322 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5709]) ).

thf(6942,plain,
    ! [SV1323: $i,SV63: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV63 @ SV1323 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV63 @ SV1323 ) @ ( tc_List_Olist @ SV1323 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5710]) ).

thf(6943,plain,
    ! [SV68: $i] :
      ( ( ( class_Orderings_Oorder @ SV68 )
        = $false )
      | ( ( ! [SY2168: $i] : ( c_lessequals @ SY2168 @ SY2168 @ SV68 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5712]) ).

thf(6944,plain,
    ! [SV1582: $i,SV1324: $i,SV69: $i] :
      ( ( ! [SY3200: $i] :
            ( ~ ( c_in @ SV69 @ ( c_Relation_ODomain @ SV1324 @ SV1582 @ SY3200 ) @ SV1582 )
            | ( c_in @ ( c_Pair @ SV69 @ ( c_Main_ODomainE__1 @ SV69 @ SV1324 @ SV1582 @ SY3200 ) @ SV1582 @ SY3200 ) @ SV1324 @ ( tc_prod @ SV1582 @ SY3200 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5713]) ).

thf(6945,plain,
    ! [SV1583: $i,SV1325: $i,SV70: $i] :
      ( ( ! [SY3201: $i,SY3202: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1325 @ SV1583 @ SY3201 ) @ SY3202 @ ( tc_prod @ SV1583 @ SY3201 ) )
            | ( c_in @ SV70 @ ( c_Relation_ODomain @ SY3202 @ SV1583 @ SY3201 ) @ SV1583 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5714]) ).

thf(6946,plain,
    ! [SV1326: $i,SV71: $i] :
      ( ( ( ~ ( c_in @ SV71 @ c_Relation_OId @ ( tc_prod @ SV1326 @ SV1326 ) ) )
        = $true )
      | ( ( SV71
          = ( c_Pair @ ( c_Main_OIdE__1 @ SV71 @ SV1326 ) @ ( c_Main_OIdE__1 @ SV71 @ SV1326 ) @ SV1326 @ SV1326 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5715]) ).

thf(6947,plain,
    ! [SV1584: $i,SV1327: $i,SV72: $i] :
      ( ( ! [SY3203: $i,SY3204: $i] :
            ( ~ ( c_in @ SV72 @ ( c_Relation_OImage @ SV1327 @ SV1584 @ SY3203 @ SY3204 ) @ SY3204 )
            | ( c_in @ ( c_Main_OImageE__1 @ SV1584 @ SV72 @ SV1327 @ SY3203 @ SY3204 ) @ SV1584 @ SY3203 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5716]) ).

thf(6948,plain,
    ! [SV1585: $i,SV1328: $i,SV73: $i] :
      ( ( ! [SY3205: $i,SY3206: $i] :
            ( ~ ( c_in @ SV73 @ ( c_Relation_OImage @ SV1328 @ SV1585 @ SY3205 @ SY3206 ) @ SY3206 )
            | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1585 @ SV73 @ SV1328 @ SY3205 @ SY3206 ) @ SV73 @ SY3205 @ SY3206 ) @ SV1328 @ ( tc_prod @ SY3205 @ SY3206 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5717]) ).

thf(6949,plain,
    ! [SV1586: $i,SV1329: $i,SV74: $i] :
      ( ( ! [SY3207: $i] :
            ( ~ ( c_in @ SV74 @ SV1329 @ SV1586 )
            | ! [SY3208: $i,SY3209: $i] :
                ( ~ ( c_in @ ( c_Pair @ SV74 @ SY3207 @ SV1586 @ SY3208 ) @ SY3209 @ ( tc_prod @ SV1586 @ SY3208 ) )
                | ( c_in @ SY3207 @ ( c_Relation_OImage @ SY3209 @ SV1329 @ SV1586 @ SY3208 ) @ SY3208 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5718]) ).

thf(6950,plain,
    ! [SV1587: $i,SV1330: $i,SV75: $i] :
      ( ( ! [SY3210: $i] :
            ( ~ ( c_in @ SV75 @ ( c_Relation_ORange @ SV1330 @ SV1587 @ SY3210 ) @ SY3210 )
            | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV75 @ SV1330 @ SY3210 @ SV1587 ) @ SV75 @ SV1587 @ SY3210 ) @ SV1330 @ ( tc_prod @ SV1587 @ SY3210 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5719]) ).

thf(6951,plain,
    ! [SV1588: $i,SV1331: $i,SV76: $i] :
      ( ( ! [SY3211: $i,SY3212: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV76 @ SV1331 @ SV1588 @ SY3211 ) @ SY3212 @ ( tc_prod @ SV1588 @ SY3211 ) )
            | ( c_in @ SV1331 @ ( c_Relation_ORange @ SY3212 @ SV1588 @ SY3211 ) @ SY3211 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5720]) ).

thf(6952,plain,
    ! [SV1589: $i,SV1332: $i,SV77: $i] :
      ( ( ! [SY3213: $i] :
            ( ~ ( c_in @ SV77 @ ( c_Relation_Oconverse @ SV1332 @ SV1589 @ SY3213 ) @ ( tc_prod @ SY3213 @ SV1589 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1332 @ SV77 @ SV1589 @ SY3213 ) @ ( c_Main_OconverseE__2 @ SV1332 @ SV77 @ SV1589 @ SY3213 ) @ SV1589 @ SY3213 ) @ SV1332 @ ( tc_prod @ SV1589 @ SY3213 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5721]) ).

thf(6953,plain,
    ! [SV1590: $i,SV1333: $i,SV78: $i] :
      ( ( ! [SY3214: $i] :
            ( ~ ( c_in @ SV78 @ ( c_Relation_Oconverse @ SV1333 @ SV1590 @ SY3214 ) @ ( tc_prod @ SY3214 @ SV1590 ) )
            | ( SV78
              = ( c_Pair @ ( c_Main_OconverseE__2 @ SV1333 @ SV78 @ SV1590 @ SY3214 ) @ ( c_Main_OconverseE__1 @ SV1333 @ SV78 @ SV1590 @ SY3214 ) @ SY3214 @ SV1590 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5722]) ).

thf(6954,plain,
    ! [SV1591: $i,SV1334: $i,SV79: $i] :
      ( ( ~ ( c_in @ SV79 @ ( c_Relation_Odiag @ SV1334 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) )
        | ( SV79
          = ( c_Pair @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SV1591 ) @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SV1591 ) @ SV1591 @ SV1591 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5723]) ).

thf(6955,plain,
    ! [SV1592: $i,SV1335: $i,SV80: $i] :
      ( ( ~ ( c_in @ SV80 @ ( c_Relation_Odiag @ SV1335 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) )
        | ( c_in @ ( c_Main_OdiagE__1 @ SV1335 @ SV80 @ SV1592 ) @ SV1335 @ SV1592 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5724]) ).

thf(6956,plain,
    ! [SV1593: $i,SV1336: $i,SV81: $i] :
      ( ( ~ ( c_in @ SV81 @ SV1336 @ SV1593 )
        | ( c_in @ ( c_Pair @ SV81 @ SV81 @ SV1593 @ SV1593 ) @ ( c_Relation_Odiag @ SV1336 @ SV1593 ) @ ( tc_prod @ SV1593 @ SV1593 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5725]) ).

thf(6957,plain,
    ! [SV1594: $i,SV1337: $i,SV82: $i] :
      ( ( ! [SY3215: $i,SY3216: $i,SY3217: $i] :
            ( ~ ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SV1337 @ SV1594 @ SY3215 @ SY3216 @ SY3217 ) @ ( tc_prod @ SY3217 @ SY3216 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1337 @ SV1594 @ SV82 @ SY3215 @ SY3216 @ SY3217 ) @ ( c_Main_Orel__compE__3 @ SV1337 @ SV1594 @ SV82 @ SY3215 @ SY3216 @ SY3217 ) @ SY3215 @ SY3216 ) @ SV1337 @ ( tc_prod @ SY3215 @ SY3216 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5726]) ).

thf(6958,plain,
    ! [SV1595: $i,SV1338: $i,SV83: $i] :
      ( ( ! [SY3218: $i,SY3219: $i,SY3220: $i] :
            ( ~ ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SV1338 @ SV1595 @ SY3218 @ SY3219 @ SY3220 ) @ ( tc_prod @ SY3220 @ SY3219 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1338 @ SV1595 @ SV83 @ SY3218 @ SY3219 @ SY3220 ) @ ( c_Main_Orel__compE__2 @ SV1338 @ SV1595 @ SV83 @ SY3218 @ SY3219 @ SY3220 ) @ SY3220 @ SY3218 ) @ SV1595 @ ( tc_prod @ SY3220 @ SY3218 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5727]) ).

thf(6959,plain,
    ! [SV1596: $i,SV1339: $i,SV84: $i] :
      ( ( ! [SY3221: $i,SY3222: $i,SY3223: $i] :
            ( ~ ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SV1339 @ SV1596 @ SY3221 @ SY3222 @ SY3223 ) @ ( tc_prod @ SY3223 @ SY3222 ) )
            | ( SV84
              = ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1339 @ SV1596 @ SV84 @ SY3221 @ SY3222 @ SY3223 ) @ ( c_Main_Orel__compE__3 @ SV1339 @ SV1596 @ SV84 @ SY3221 @ SY3222 @ SY3223 ) @ SY3223 @ SY3222 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5728]) ).

thf(6960,plain,
    ! [SV1597: $i,SV1340: $i,SV85: $i] :
      ( ( ! [SY3224: $i,SY3225: $i,SY3226: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SY3224 ) @ SY3225 @ ( tc_prod @ SV1597 @ SY3224 ) )
            | ! [SY3227: $i,SY3228: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY3226 @ SV85 @ SY3227 @ SV1597 ) @ SY3228 @ ( tc_prod @ SY3227 @ SV1597 ) )
                | ( c_in @ ( c_Pair @ SY3226 @ SV1340 @ SY3227 @ SY3224 ) @ ( c_Relation_Orel__comp @ SY3225 @ SY3228 @ SV1597 @ SY3224 @ SY3227 ) @ ( tc_prod @ SY3227 @ SY3224 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5729]) ).

thf(6961,plain,
    ! [SV1598: $i,SV1349: $i,SV96: $i] :
      ( ( ( c_in @ SV96 @ ( c_Inter @ SV1349 @ SV1598 ) @ SV1598 )
        | ( c_in @ ( c_Main_OInterI__1 @ SV96 @ SV1349 @ SV1598 ) @ SV1349 @ ( tc_set @ SV1598 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5738]) ).

thf(6962,plain,
    ! [SV1599: $i,SV1350: $i,SV97: $i] :
      ( ( ~ ( c_in @ SV97 @ ( c_Main_OInterI__1 @ SV97 @ SV1350 @ SV1599 ) @ SV1599 )
        | ( c_in @ SV97 @ ( c_Inter @ SV1350 @ SV1599 ) @ SV1599 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5739]) ).

thf(6963,plain,
    ! [SV1600: $i,SV1352: $i,SV99: $i] :
      ( ( ~ ( c_in @ SV99 @ ( c_Union @ SV1352 @ SV1600 ) @ SV1600 )
        | ( c_in @ ( c_Main_OUnionE__1 @ SV99 @ SV1352 @ SV1600 ) @ SV1352 @ ( tc_set @ SV1600 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5741]) ).

thf(6964,plain,
    ! [SV1601: $i,SV1353: $i,SV100: $i] :
      ( ( ~ ( c_in @ SV100 @ ( c_Union @ SV1353 @ SV1601 ) @ SV1601 )
        | ( c_in @ SV100 @ ( c_Main_OUnionE__1 @ SV100 @ SV1353 @ SV1601 ) @ SV1601 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5742]) ).

thf(6965,plain,
    ! [SV1602: $i,SV1355: $i,SV102: $i] :
      ( ( ~ ( c_less @ SV102 @ SV1355 @ ( tc_set @ SV1602 ) )
        | ~ ( c_lessequals @ SV1355 @ SV102 @ ( tc_set @ SV1602 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5744]) ).

thf(6966,plain,
    ! [SV1603: $i,SV1356: $i,SV103: $i] :
      ( ( ~ ( c_less @ SV103 @ SV1356 @ ( tc_set @ SV1603 ) )
        | ( c_lessequals @ SV103 @ SV1356 @ ( tc_set @ SV1603 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5745]) ).

thf(6967,plain,
    ! [SV1604: $i,SV1357: $i,SV104: $i] :
      ( ( ~ ( c_lessequals @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) )
        | ( SV104 = SV1357 )
        | ( c_less @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5746]) ).

thf(6968,plain,
    ! [SV1358: $i,SV105: $i] :
      ( ( ( ! [SY2898: $i] :
              ~ ( c_in @ SV105 @ ( c_insert @ SV1358 @ c_emptyset @ SY2898 ) @ SY2898 ) )
        = $true )
      | ( ( SV105 = SV1358 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5747]) ).

thf(6969,plain,
    ! [SV1605: $i,SV1360: $i,SV107: $i] :
      ( ( ( ( c_insert @ SV107 @ c_emptyset @ SV1360 )
         != ( c_insert @ SV1605 @ c_emptyset @ SV1360 ) )
        | ( SV107 = SV1605 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5749]) ).

thf(6970,plain,
    ! [SV1606: $i,SV1361: $i,SV108: $i] :
      ( ( ~ ( c_in @ SV108 @ SV1361 @ SV1606 )
        | ! [SY3229: $i] :
            ( ~ ( c_lessequals @ SV1361 @ SY3229 @ ( tc_set @ SV1606 ) )
            | ( c_in @ SV108 @ SY3229 @ SV1606 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5750]) ).

thf(6971,plain,
    ! [SV1607: $i,SV1362: $i,SV109: $i] :
      ( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV109 @ SV1362 @ SV1607 ) @ SV109 @ SV1607 )
        | ( c_lessequals @ SV109 @ SV1362 @ ( tc_set @ SV1607 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5751]) ).

thf(6972,plain,
    ! [SV1608: $i,SV1363: $i,SV110: $i] :
      ( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV110 @ SV1363 @ SV1608 ) @ SV1363 @ SV1608 )
        | ( c_lessequals @ SV110 @ SV1363 @ ( tc_set @ SV1608 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5752]) ).

thf(6973,plain,
    ! [SV1609: $i,SV1364: $i,SV111: $i] :
      ( ( ~ ( c_lessequals @ SV111 @ SV1364 @ ( tc_set @ SV1609 ) )
        | ~ ( c_lessequals @ SV1364 @ SV111 @ ( tc_set @ SV1609 ) )
        | ( SV1364 = SV111 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5753]) ).

thf(6974,plain,
    ! [SV1610: $i,SV1366: $i,SV113: $i] :
      ( ( ~ ( c_in @ SV113 @ SV1366 @ SV1610 )
        | ! [SY3230: $i,SY3231: $i] : ( c_in @ ( c_Sum__Type_OInl @ SV113 @ SV1610 @ SY3230 ) @ ( c_Sum__Type_OPlus @ SV1366 @ SY3231 @ SV1610 @ SY3230 ) @ ( tc_sum @ SV1610 @ SY3230 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5755]) ).

thf(6975,plain,
    ! [SV1611: $i,SV1367: $i,SV114: $i] :
      ( ( ~ ( c_in @ SV114 @ SV1367 @ SV1611 )
        | ! [SY3232: $i,SY3233: $i] : ( c_in @ ( c_Sum__Type_OInr @ SV114 @ SV1611 @ SY3232 ) @ ( c_Sum__Type_OPlus @ SY3233 @ SV1367 @ SY3232 @ SV1611 ) @ ( tc_sum @ SY3232 @ SV1611 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5756]) ).

thf(6976,plain,
    ! [SV1612: $i,SV1368: $i,SV115: $i] :
      ( ( ! [SY3234: $i,SY3235: $i] :
            ( ~ ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SV1368 @ SV1612 @ SY3234 @ SY3235 ) @ ( tc_sum @ SY3234 @ SY3235 ) )
            | ( SV115
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1368 @ SV115 @ SY3234 @ SY3235 ) @ SY3234 @ SY3235 ) )
            | ( SV115
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1612 @ SV115 @ SY3235 @ SY3234 ) @ SY3235 @ SY3234 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5757]) ).

thf(6977,plain,
    ! [SV1613: $i,SV1369: $i,SV116: $i] :
      ( ( ! [SY3236: $i,SY3237: $i] :
            ( ~ ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SV1369 @ SV1613 @ SY3236 @ SY3237 ) @ ( tc_sum @ SY3236 @ SY3237 ) )
            | ( SV116
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1369 @ SV116 @ SY3236 @ SY3237 ) @ SY3236 @ SY3237 ) )
            | ( c_in @ ( c_Main_OPlusE__2 @ SV1613 @ SV116 @ SY3237 @ SY3236 ) @ SV1613 @ SY3237 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5758]) ).

thf(6978,plain,
    ! [SV1614: $i,SV1370: $i,SV117: $i] :
      ( ( ! [SY3238: $i,SY3239: $i] :
            ( ~ ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SV1370 @ SV1614 @ SY3238 @ SY3239 ) @ ( tc_sum @ SY3238 @ SY3239 ) )
            | ( SV117
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1614 @ SV117 @ SY3239 @ SY3238 ) @ SY3239 @ SY3238 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SV1370 @ SV117 @ SY3238 @ SY3239 ) @ SV1370 @ SY3238 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5759]) ).

thf(6979,plain,
    ! [SV1615: $i,SV1371: $i,SV118: $i] :
      ( ( ! [SY3240: $i,SY3241: $i] :
            ( ~ ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SV1371 @ SV1615 @ SY3240 @ SY3241 ) @ ( tc_sum @ SY3240 @ SY3241 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SV1371 @ SV118 @ SY3240 @ SY3241 ) @ SV1371 @ SY3240 )
            | ( c_in @ ( c_Main_OPlusE__2 @ SV1615 @ SV118 @ SY3241 @ SY3240 ) @ SV1615 @ SY3241 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5760]) ).

thf(6980,plain,
    ! [SV1616: $i,SV1372: $i,SV119: $i] :
      ( ( ~ ( c_in @ SV119 @ SV1372 @ ( tc_prod @ SV1616 @ SV1616 ) )
        | ( c_in @ SV119 @ ( c_Transitive__Closure_Ortrancl @ SV1372 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5761]) ).

thf(6981,plain,
    ! [SV1617: $i,SV1373: $i,SV120: $i] :
      ( ( c_in @ ( c_Pair @ SV120 @ SV120 @ SV1373 @ SV1373 ) @ ( c_Transitive__Closure_Ortrancl @ SV1617 @ SV1373 ) @ ( tc_prod @ SV1373 @ SV1373 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5762]) ).

thf(6982,plain,
    ! [SV1618: $i,SV1374: $i,SV121: $i] :
      ( ( ! [SY3242: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ SY3242 @ ( tc_prod @ SV1618 @ SV1618 ) )
            | ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SY3242 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5763]) ).

thf(6983,plain,
    ! [SV1619: $i,SV1375: $i,SV122: $i] :
      ( ( ! [SY3243: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Otrancl @ SY3243 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
            | ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SY3243 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5764]) ).

thf(6984,plain,
    ! [SV1376: $i,SV124: $i] :
      ( ( ( ~ ( c_Relation_Otrans @ SV124 @ SV1376 ) )
        = $true )
      | ( ( ! [SY2929: $i,SY2930: $i] :
              ( ~ ( c_Relation_Otrans @ SY2929 @ SY2930 )
              | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SY2929 @ SV124 @ SY2930 @ SV1376 ) @ ( tc_prod @ SY2930 @ SV1376 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5765]) ).

thf(6985,plain,
    ! [SV1377: $i,SV125: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV125 @ SV1377 ) )
        = $true )
      | ( ( ! [SY2931: $i,SY2932: $i] :
              ( ~ ( c_Wellfounded__Recursion_Owf @ SY2931 @ SY2932 )
              | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SY2931 @ SV125 @ SY2932 @ SV1377 ) @ ( tc_prod @ SY2932 @ SV1377 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5766]) ).

thf(6986,plain,
    ! [SV126: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV126 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ SV126 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5767]) ).

thf(6987,plain,
    ! [SV1378: $i,SV127: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV127 @ SV1378 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV1378 )
          | ~ ( class_Finite__Set_Ofinite @ SV127 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5768]) ).

thf(6988,plain,
    ! [SV1380: $i,SV129: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV129 @ SV1380 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV1380 )
          | ~ ( class_Finite__Set_Ofinite @ SV129 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5770]) ).

thf(6989,plain,
    ! [SV133: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV133 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ ( tc_set @ SV133 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5771]) ).

thf(6990,plain,
    ! [SV1381: $i,SV135: $i] :
      ( ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV135 @ SV1381 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV1381 )
          | ~ ( class_Finite__Set_Ofinite @ SV135 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5772]) ).

thf(6991,plain,
    ! [SV136: $i] :
      ( ( ( class_LOrder_Ojoin__semilorder @ SV136 )
        = $false )
      | ( ( class_Orderings_Oord @ SV136 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5773]) ).

thf(6992,plain,
    ! [SV137: $i] :
      ( ( ( class_LOrder_Ojoin__semilorder @ SV137 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV137 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5774]) ).

thf(6993,plain,
    ! [SV138: $i] :
      ( ( ( class_LOrder_Olorder @ SV138 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV138 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5775]) ).

thf(6994,plain,
    ! [SV139: $i] :
      ( ( ( class_LOrder_Olorder @ SV139 )
        = $false )
      | ( ( class_Orderings_Oord @ SV139 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5776]) ).

thf(6995,plain,
    ! [SV140: $i] :
      ( ( ( class_LOrder_Olorder @ SV140 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV140 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5777]) ).

thf(6996,plain,
    ! [SV141: $i] :
      ( ( ( class_LOrder_Olorder @ SV141 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV141 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5778]) ).

thf(6997,plain,
    ! [SV142: $i] :
      ( ( ( class_LOrder_Omeet__semilorder @ SV142 )
        = $false )
      | ( ( class_Orderings_Oord @ SV142 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5779]) ).

thf(6998,plain,
    ! [SV143: $i] :
      ( ( ( class_LOrder_Omeet__semilorder @ SV143 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV143 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5780]) ).

thf(6999,plain,
    ! [SV144: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV144 )
        = $false )
      | ( ( class_HOL_Oplus @ SV144 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5781]) ).

thf(7000,plain,
    ! [SV145: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV145 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV145 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5782]) ).

thf(7001,plain,
    ! [SV146: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV146 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV146 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5783]) ).

thf(7002,plain,
    ! [SV147: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV147 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV147 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5784]) ).

thf(7003,plain,
    ! [SV148: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV148 )
        = $false )
      | ( ( class_HOL_Ominus @ SV148 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5785]) ).

thf(7004,plain,
    ! [SV149: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV149 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV149 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5786]) ).

thf(7005,plain,
    ! [SV150: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV150 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV150 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5787]) ).

thf(7006,plain,
    ! [SV151: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV151 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV151 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5788]) ).

thf(7007,plain,
    ! [SV152: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV152 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV152 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5789]) ).

thf(7008,plain,
    ! [SV153: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV153 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV153 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5790]) ).

thf(7009,plain,
    ! [SV154: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV154 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV154 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5791]) ).

thf(7010,plain,
    ! [SV155: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV155 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV155 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5792]) ).

thf(7011,plain,
    ! [SV156: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV156 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV156 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5793]) ).

thf(7012,plain,
    ! [SV157: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV157 )
        = $false )
      | ( ( class_HOL_Oone @ SV157 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5794]) ).

thf(7013,plain,
    ! [SV158: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV158 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV158 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5795]) ).

thf(7014,plain,
    ! [SV159: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV159 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV159 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5796]) ).

thf(7015,plain,
    ! [SV160: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV160 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV160 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5797]) ).

thf(7016,plain,
    ! [SV161: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV161 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV161 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5798]) ).

thf(7017,plain,
    ! [SV162: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV162 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5799]) ).

thf(7018,plain,
    ! [SV163: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV163 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV163 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5800]) ).

thf(7019,plain,
    ! [SV164: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV164 )
        = $false )
      | ( ( class_Ring__and__Field_Oring__1 @ SV164 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5801]) ).

thf(7020,plain,
    ! [SV165: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV165 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV165 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5802]) ).

thf(7021,plain,
    ! [SV166: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV166 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV166 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5803]) ).

thf(7022,plain,
    ! [SV167: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV167 )
        = $false )
      | ( ( class_HOL_Otimes @ SV167 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5804]) ).

thf(7023,plain,
    ! [SV168: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV168 )
        = $false )
      | ( ( class_Numeral_Onumber @ SV168 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5805]) ).

thf(7024,plain,
    ! [SV169: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV169 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV169 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5806]) ).

thf(7025,plain,
    ! [SV170: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV170 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV170 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5807]) ).

thf(7026,plain,
    ! [SV171: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV171 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV171 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5808]) ).

thf(7027,plain,
    ! [SV172: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV172 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV172 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5809]) ).

thf(7028,plain,
    ! [SV173: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV173 )
        = $false )
      | ( ( class_HOL_Ozero @ SV173 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5810]) ).

thf(7029,plain,
    ! [SV174: $i] :
      ( ( ( class_Numeral_Onumber__ring @ SV174 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV174 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5811]) ).

thf(7030,plain,
    ! [SV175: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV175 )
        = $false )
      | ( ( class_HOL_Ominus @ SV175 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5812]) ).

thf(7031,plain,
    ! [SV176: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV176 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV176 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5813]) ).

thf(7032,plain,
    ! [SV177: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV177 )
        = $false )
      | ( ( class_HOL_Ozero @ SV177 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5814]) ).

thf(7033,plain,
    ! [SV178: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV178 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV178 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5815]) ).

thf(7034,plain,
    ! [SV179: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV179 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV179 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5816]) ).

thf(7035,plain,
    ! [SV180: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV180 )
        = $false )
      | ( ( class_HOL_Oplus @ SV180 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5817]) ).

thf(7036,plain,
    ! [SV181: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV181 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV181 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5818]) ).

thf(7037,plain,
    ! [SV182: $i] :
      ( ( ( class_OrderedGroup_Oab__group__add @ SV182 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV182 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5819]) ).

thf(7038,plain,
    ! [SV183: $i] :
      ( ( ( class_OrderedGroup_Oab__semigroup__add @ SV183 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV183 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5820]) ).

thf(7039,plain,
    ! [SV184: $i] :
      ( ( ( class_OrderedGroup_Oab__semigroup__add @ SV184 )
        = $false )
      | ( ( class_HOL_Oplus @ SV184 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5821]) ).

thf(7040,plain,
    ! [SV185: $i] :
      ( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV185 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV185 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5822]) ).

thf(7041,plain,
    ! [SV186: $i] :
      ( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV186 )
        = $false )
      | ( ( class_HOL_Otimes @ SV186 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5823]) ).

thf(7042,plain,
    ! [SV187: $i] :
      ( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV187 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV187 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5824]) ).

thf(7043,plain,
    ! [SV188: $i] :
      ( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV188 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV188 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5825]) ).

thf(7044,plain,
    ! [SV189: $i] :
      ( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV189 )
        = $false )
      | ( ( class_HOL_Oplus @ SV189 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5826]) ).

thf(7045,plain,
    ! [SV190: $i] :
      ( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV190 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV190 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5827]) ).

thf(7046,plain,
    ! [SV191: $i] :
      ( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV191 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV191 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5828]) ).

thf(7047,plain,
    ! [SV192: $i] :
      ( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV192 )
        = $false )
      | ( ( class_HOL_Oplus @ SV192 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5829]) ).

thf(7048,plain,
    ! [SV193: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV193 )
        = $false )
      | ( ( class_HOL_Ozero @ SV193 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5830]) ).

thf(7049,plain,
    ! [SV194: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV194 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV194 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5831]) ).

thf(7050,plain,
    ! [SV195: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV195 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV195 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5832]) ).

thf(7051,plain,
    ! [SV196: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV196 )
        = $false )
      | ( ( class_HOL_Oplus @ SV196 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5833]) ).

thf(7052,plain,
    ! [SV197: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV197 )
        = $false )
      | ( ( class_HOL_Oone @ SV197 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5834]) ).

thf(7053,plain,
    ! [SV198: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV198 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV198 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5835]) ).

thf(7054,plain,
    ! [SV199: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV199 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV199 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5836]) ).

thf(7055,plain,
    ! [SV200: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV200 )
        = $false )
      | ( ( class_HOL_Otimes @ SV200 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5837]) ).

thf(7056,plain,
    ! [SV201: $i] :
      ( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV201 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV201 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5838]) ).

thf(7057,plain,
    ! [SV202: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV202 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV202 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5839]) ).

thf(7058,plain,
    ! [SV203: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV203 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV203 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5840]) ).

thf(7059,plain,
    ! [SV204: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV204 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV204 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5841]) ).

thf(7060,plain,
    ! [SV205: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV205 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV205 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5842]) ).

thf(7061,plain,
    ! [SV206: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV206 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV206 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5843]) ).

thf(7062,plain,
    ! [SV207: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV207 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV207 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5844]) ).

thf(7063,plain,
    ! [SV208: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV208 )
        = $false )
      | ( ( class_HOL_Oplus @ SV208 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5845]) ).

thf(7064,plain,
    ! [SV209: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV209 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV209 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5846]) ).

thf(7065,plain,
    ! [SV210: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV210 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV210 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5847]) ).

thf(7066,plain,
    ! [SV211: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV211 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV211 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5848]) ).

thf(7067,plain,
    ! [SV212: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV212 )
        = $false )
      | ( ( class_HOL_Ominus @ SV212 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5849]) ).

thf(7068,plain,
    ! [SV213: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV213 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV213 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5850]) ).

thf(7069,plain,
    ! [SV214: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV214 )
        = $false )
      | ( ( class_HOL_Ozero @ SV214 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5851]) ).

thf(7070,plain,
    ! [SV215: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV215 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV215 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5852]) ).

thf(7071,plain,
    ! [SV216: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV216 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV216 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5853]) ).

thf(7072,plain,
    ! [SV217: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV217 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV217 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5854]) ).

thf(7073,plain,
    ! [SV218: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV218 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV218 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5855]) ).

thf(7074,plain,
    ! [SV219: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group @ SV219 )
        = $false )
      | ( ( class_Orderings_Oord @ SV219 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5856]) ).

thf(7075,plain,
    ! [SV220: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV220 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV220 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5857]) ).

thf(7076,plain,
    ! [SV221: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV221 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV221 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5858]) ).

thf(7077,plain,
    ! [SV222: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV222 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV222 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5859]) ).

thf(7078,plain,
    ! [SV223: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV223 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV223 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5860]) ).

thf(7079,plain,
    ! [SV224: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV224 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV224 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5861]) ).

thf(7080,plain,
    ! [SV225: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV225 )
        = $false )
      | ( ( class_HOL_Oplus @ SV225 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5862]) ).

thf(7081,plain,
    ! [SV226: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV226 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV226 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5863]) ).

thf(7082,plain,
    ! [SV227: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV227 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV227 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5864]) ).

thf(7083,plain,
    ! [SV228: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV228 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV228 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5865]) ).

thf(7084,plain,
    ! [SV229: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV229 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV229 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5866]) ).

thf(7085,plain,
    ! [SV230: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV230 )
        = $false )
      | ( ( class_Orderings_Oord @ SV230 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5867]) ).

thf(7086,plain,
    ! [SV231: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV231 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV231 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5868]) ).

thf(7087,plain,
    ! [SV232: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV232 )
        = $false )
      | ( ( class_HOL_Ominus @ SV232 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5869]) ).

thf(7088,plain,
    ! [SV233: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV233 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV233 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5870]) ).

thf(7089,plain,
    ! [SV234: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV234 )
        = $false )
      | ( ( class_HOL_Ozero @ SV234 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5871]) ).

thf(7090,plain,
    ! [SV235: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV235 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV235 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5872]) ).

thf(7091,plain,
    ! [SV236: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV236 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV236 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5873]) ).

thf(7092,plain,
    ! [SV237: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV237 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV237 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5874]) ).

thf(7093,plain,
    ! [SV238: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV238 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV238 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5875]) ).

thf(7094,plain,
    ! [SV239: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV239 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV239 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5876]) ).

thf(7095,plain,
    ! [SV240: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV240 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV240 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5877]) ).

thf(7096,plain,
    ! [SV241: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV241 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV241 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5878]) ).

thf(7097,plain,
    ! [SV242: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV242 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV242 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5879]) ).

thf(7098,plain,
    ! [SV243: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV243 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV243 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5880]) ).

thf(7099,plain,
    ! [SV244: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV244 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV244 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5881]) ).

thf(7100,plain,
    ! [SV245: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV245 )
        = $false )
      | ( ( class_HOL_Oplus @ SV245 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5882]) ).

thf(7101,plain,
    ! [SV246: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV246 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV246 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5883]) ).

thf(7102,plain,
    ! [SV247: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV247 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV247 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5884]) ).

thf(7103,plain,
    ! [SV248: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV248 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV248 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5885]) ).

thf(7104,plain,
    ! [SV249: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV249 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV249 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5886]) ).

thf(7105,plain,
    ! [SV250: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV250 )
        = $false )
      | ( ( class_HOL_Ominus @ SV250 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5887]) ).

thf(7106,plain,
    ! [SV251: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV251 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV251 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5888]) ).

thf(7107,plain,
    ! [SV252: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV252 )
        = $false )
      | ( ( class_HOL_Ozero @ SV252 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5889]) ).

thf(7108,plain,
    ! [SV253: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV253 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV253 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5890]) ).

thf(7109,plain,
    ! [SV254: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV254 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV254 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5891]) ).

thf(7110,plain,
    ! [SV255: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV255 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV255 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5892]) ).

thf(7111,plain,
    ! [SV256: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV256 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV256 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5893]) ).

thf(7112,plain,
    ! [SV257: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV257 )
        = $false )
      | ( ( class_Orderings_Oord @ SV257 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5894]) ).

thf(7113,plain,
    ! [SV258: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV258 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV258 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5895]) ).

thf(7114,plain,
    ! [SV259: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV259 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV259 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5896]) ).

thf(7115,plain,
    ! [SV260: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV260 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV260 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5897]) ).

thf(7116,plain,
    ! [SV261: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV261 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV261 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5898]) ).

thf(7117,plain,
    ! [SV262: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV262 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV262 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5899]) ).

thf(7118,plain,
    ! [SV263: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV263 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV263 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5900]) ).

thf(7119,plain,
    ! [SV264: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV264 )
        = $false )
      | ( ( class_HOL_Oplus @ SV264 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5901]) ).

thf(7120,plain,
    ! [SV265: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV265 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV265 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5902]) ).

thf(7121,plain,
    ! [SV266: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV266 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV266 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5903]) ).

thf(7122,plain,
    ! [SV267: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV267 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV267 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5904]) ).

thf(7123,plain,
    ! [SV268: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV268 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV268 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5905]) ).

thf(7124,plain,
    ! [SV269: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV269 )
        = $false )
      | ( ( class_HOL_Ominus @ SV269 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5906]) ).

thf(7125,plain,
    ! [SV270: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV270 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV270 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5907]) ).

thf(7126,plain,
    ! [SV271: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV271 )
        = $false )
      | ( ( class_HOL_Ozero @ SV271 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5908]) ).

thf(7127,plain,
    ! [SV272: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV272 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV272 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5909]) ).

thf(7128,plain,
    ! [SV273: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV273 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV273 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5910]) ).

thf(7129,plain,
    ! [SV274: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV274 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV274 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5911]) ).

thf(7130,plain,
    ! [SV275: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV275 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV275 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5912]) ).

thf(7131,plain,
    ! [SV276: $i] :
      ( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV276 )
        = $false )
      | ( ( class_Orderings_Oord @ SV276 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5913]) ).

thf(7132,plain,
    ! [SV277: $i] :
      ( ( ( class_OrderedGroup_Omonoid__mult @ SV277 )
        = $false )
      | ( ( class_HOL_Oone @ SV277 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5914]) ).

thf(7133,plain,
    ! [SV278: $i] :
      ( ( ( class_OrderedGroup_Omonoid__mult @ SV278 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV278 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5915]) ).

thf(7134,plain,
    ! [SV279: $i] :
      ( ( ( class_OrderedGroup_Omonoid__mult @ SV279 )
        = $false )
      | ( ( class_HOL_Otimes @ SV279 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5916]) ).

thf(7135,plain,
    ! [SV280: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV280 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV280 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5917]) ).

thf(7136,plain,
    ! [SV281: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV281 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV281 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5918]) ).

thf(7137,plain,
    ! [SV282: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV282 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV282 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5919]) ).

thf(7138,plain,
    ! [SV283: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV283 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV283 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5920]) ).

thf(7139,plain,
    ! [SV284: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV284 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV284 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5921]) ).

thf(7140,plain,
    ! [SV285: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV285 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV285 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5922]) ).

thf(7141,plain,
    ! [SV286: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV286 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV286 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5923]) ).

thf(7142,plain,
    ! [SV287: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV287 )
        = $false )
      | ( ( class_Orderings_Oord @ SV287 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5924]) ).

thf(7143,plain,
    ! [SV288: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV288 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV288 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5925]) ).

thf(7144,plain,
    ! [SV289: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV289 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV289 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5926]) ).

thf(7145,plain,
    ! [SV290: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV290 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV290 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5927]) ).

thf(7146,plain,
    ! [SV291: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV291 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV291 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5928]) ).

thf(7147,plain,
    ! [SV292: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV292 )
        = $false )
      | ( ( class_HOL_Oplus @ SV292 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5929]) ).

thf(7148,plain,
    ! [SV293: $i] :
      ( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV293 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV293 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5930]) ).

thf(7149,plain,
    ! [SV294: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV294 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV294 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5931]) ).

thf(7150,plain,
    ! [SV295: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV295 )
        = $false )
      | ( ( class_HOL_Ominus @ SV295 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5932]) ).

thf(7151,plain,
    ! [SV296: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV296 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV296 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5933]) ).

thf(7152,plain,
    ! [SV297: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV297 )
        = $false )
      | ( ( class_Orderings_Oord @ SV297 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5934]) ).

thf(7153,plain,
    ! [SV298: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV298 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV298 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5935]) ).

thf(7154,plain,
    ! [SV299: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV299 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV299 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5936]) ).

thf(7155,plain,
    ! [SV300: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV300 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV300 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5937]) ).

thf(7156,plain,
    ! [SV301: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV301 )
        = $false )
      | ( ( class_HOL_Ozero @ SV301 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5938]) ).

thf(7157,plain,
    ! [SV302: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV302 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV302 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5939]) ).

thf(7158,plain,
    ! [SV303: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV303 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV303 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5940]) ).

thf(7159,plain,
    ! [SV304: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV304 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV304 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5941]) ).

thf(7160,plain,
    ! [SV305: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV305 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV305 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5942]) ).

thf(7161,plain,
    ! [SV306: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV306 )
        = $false )
      | ( ( class_HOL_Oplus @ SV306 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5943]) ).

thf(7162,plain,
    ! [SV307: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV307 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5944]) ).

thf(7163,plain,
    ! [SV308: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV308 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV308 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5945]) ).

thf(7164,plain,
    ! [SV309: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV309 )
        = $false )
      | ( ( class_Orderings_Oord @ SV309 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5946]) ).

thf(7165,plain,
    ! [SV310: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV310 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV310 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5947]) ).

thf(7166,plain,
    ! [SV311: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV311 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV311 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5948]) ).

thf(7167,plain,
    ! [SV312: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV312 )
        = $false )
      | ( ( class_HOL_Oplus @ SV312 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5949]) ).

thf(7168,plain,
    ! [SV313: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV313 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV313 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5950]) ).

thf(7169,plain,
    ! [SV314: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV314 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV314 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5951]) ).

thf(7170,plain,
    ! [SV315: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV315 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV315 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5952]) ).

thf(7171,plain,
    ! [SV316: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV316 )
        = $false )
      | ( ( class_Orderings_Oord @ SV316 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5953]) ).

thf(7172,plain,
    ! [SV317: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV317 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV317 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5954]) ).

thf(7173,plain,
    ! [SV318: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV318 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV318 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5955]) ).

thf(7174,plain,
    ! [SV319: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV319 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV319 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5956]) ).

thf(7175,plain,
    ! [SV320: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV320 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV320 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5957]) ).

thf(7176,plain,
    ! [SV321: $i] :
      ( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV321 )
        = $false )
      | ( ( class_HOL_Oplus @ SV321 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5958]) ).

thf(7177,plain,
    ! [SV322: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV322 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV322 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5959]) ).

thf(7178,plain,
    ! [SV323: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV323 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV323 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5960]) ).

thf(7179,plain,
    ! [SV324: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV324 )
        = $false )
      | ( ( class_Orderings_Oord @ SV324 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5961]) ).

thf(7180,plain,
    ! [SV325: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV325 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV325 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5962]) ).

thf(7181,plain,
    ! [SV326: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV326 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV326 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5963]) ).

thf(7182,plain,
    ! [SV327: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV327 )
        = $false )
      | ( ( class_HOL_Oplus @ SV327 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5964]) ).

thf(7183,plain,
    ! [SV328: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV328 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV328 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5965]) ).

thf(7184,plain,
    ! [SV329: $i] :
      ( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV329 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV329 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5966]) ).

thf(7185,plain,
    ! [SV330: $i] :
      ( ( ( class_OrderedGroup_Osemigroup__add @ SV330 )
        = $false )
      | ( ( class_HOL_Oplus @ SV330 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5967]) ).

thf(7186,plain,
    ! [SV331: $i] :
      ( ( ( class_OrderedGroup_Osemigroup__mult @ SV331 )
        = $false )
      | ( ( class_HOL_Otimes @ SV331 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5968]) ).

thf(7187,plain,
    ! [SV332: $i] :
      ( ( ( class_Orderings_Olinorder @ SV332 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV332 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5969]) ).

thf(7188,plain,
    ! [SV333: $i] :
      ( ( ( class_Orderings_Olinorder @ SV333 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV333 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5970]) ).

thf(7189,plain,
    ! [SV334: $i] :
      ( ( ( class_Orderings_Olinorder @ SV334 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV334 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5971]) ).

thf(7190,plain,
    ! [SV335: $i] :
      ( ( ( class_Orderings_Olinorder @ SV335 )
        = $false )
      | ( ( class_Orderings_Oord @ SV335 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5972]) ).

thf(7191,plain,
    ! [SV336: $i] :
      ( ( ( class_Orderings_Olinorder @ SV336 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV336 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5973]) ).

thf(7192,plain,
    ! [SV337: $i] :
      ( ( ( class_Orderings_Oorder @ SV337 )
        = $false )
      | ( ( class_Orderings_Oord @ SV337 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5974]) ).

thf(7193,plain,
    ! [SV338: $i] :
      ( ( ( class_Power_Orecpower @ SV338 )
        = $false )
      | ( ( class_Nat_Opower @ SV338 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5975]) ).

thf(7194,plain,
    ! [SV339: $i] :
      ( ( ( class_Power_Orecpower @ SV339 )
        = $false )
      | ( ( class_HOL_Ozero @ SV339 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5976]) ).

thf(7195,plain,
    ! [SV340: $i] :
      ( ( ( class_Power_Orecpower @ SV340 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV340 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5977]) ).

thf(7196,plain,
    ! [SV341: $i] :
      ( ( ( class_Power_Orecpower @ SV341 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV341 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5978]) ).

thf(7197,plain,
    ! [SV342: $i] :
      ( ( ( class_Power_Orecpower @ SV342 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV342 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5979]) ).

thf(7198,plain,
    ! [SV343: $i] :
      ( ( ( class_Power_Orecpower @ SV343 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV343 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5980]) ).

thf(7199,plain,
    ! [SV344: $i] :
      ( ( ( class_Power_Orecpower @ SV344 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV344 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5981]) ).

thf(7200,plain,
    ! [SV345: $i] :
      ( ( ( class_Power_Orecpower @ SV345 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV345 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5982]) ).

thf(7201,plain,
    ! [SV346: $i] :
      ( ( ( class_Power_Orecpower @ SV346 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV346 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5983]) ).

thf(7202,plain,
    ! [SV347: $i] :
      ( ( ( class_Power_Orecpower @ SV347 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV347 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5984]) ).

thf(7203,plain,
    ! [SV348: $i] :
      ( ( ( class_Power_Orecpower @ SV348 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV348 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5985]) ).

thf(7204,plain,
    ! [SV349: $i] :
      ( ( ( class_Power_Orecpower @ SV349 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV349 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5986]) ).

thf(7205,plain,
    ! [SV350: $i] :
      ( ( ( class_Power_Orecpower @ SV350 )
        = $false )
      | ( ( class_HOL_Oone @ SV350 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5987]) ).

thf(7206,plain,
    ! [SV351: $i] :
      ( ( ( class_Power_Orecpower @ SV351 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV351 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5988]) ).

thf(7207,plain,
    ! [SV352: $i] :
      ( ( ( class_Power_Orecpower @ SV352 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV352 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5989]) ).

thf(7208,plain,
    ! [SV353: $i] :
      ( ( ( class_Power_Orecpower @ SV353 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV353 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5990]) ).

thf(7209,plain,
    ! [SV354: $i] :
      ( ( ( class_Power_Orecpower @ SV354 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV354 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5991]) ).

thf(7210,plain,
    ! [SV355: $i] :
      ( ( ( class_Power_Orecpower @ SV355 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV355 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5992]) ).

thf(7211,plain,
    ! [SV356: $i] :
      ( ( ( class_Power_Orecpower @ SV356 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV356 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5993]) ).

thf(7212,plain,
    ! [SV357: $i] :
      ( ( ( class_Power_Orecpower @ SV357 )
        = $false )
      | ( ( class_HOL_Oplus @ SV357 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5994]) ).

thf(7213,plain,
    ! [SV358: $i] :
      ( ( ( class_Power_Orecpower @ SV358 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV358 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5995]) ).

thf(7214,plain,
    ! [SV359: $i] :
      ( ( ( class_Power_Orecpower @ SV359 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV359 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5996]) ).

thf(7215,plain,
    ! [SV360: $i] :
      ( ( ( class_Power_Orecpower @ SV360 )
        = $false )
      | ( ( class_HOL_Otimes @ SV360 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5997]) ).

thf(7216,plain,
    ! [SV361: $i] :
      ( ( ( class_Power_Orecpower @ SV361 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV361 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5998]) ).

thf(7217,plain,
    ! [SV362: $i] :
      ( ( ( class_Power_Orecpower @ SV362 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV362 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5999]) ).

thf(7218,plain,
    ! [SV363: $i] :
      ( ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV363 )
        = $false )
      | ( ( class_HOL_Ozero @ SV363 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6000]) ).

thf(7219,plain,
    ! [SV364: $i] :
      ( ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV364 )
        = $false )
      | ( ( class_HOL_Oone @ SV364 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6001]) ).

thf(7220,plain,
    ! [SV365: $i] :
      ( ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV365 )
        = $false )
      | ( ( class_HOL_Ominus @ SV365 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6002]) ).

thf(7221,plain,
    ! [SV366: $i] :
      ( ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV366 )
        = $false )
      | ( ( class_Orderings_Oord @ SV366 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6003]) ).

thf(7222,plain,
    ! [SV367: $i] :
      ( ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV367 )
        = $false )
      | ( ( class_HOL_Ozero @ SV367 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6004]) ).

thf(7223,plain,
    ! [SV368: $i] :
      ( ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV368 )
        = $false )
      | ( ( class_HOL_Ozero @ SV368 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6005]) ).

thf(7224,plain,
    ! [SV369: $i] :
      ( ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV369 )
        = $false )
      | ( ( class_HOL_Otimes @ SV369 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6006]) ).

thf(7225,plain,
    ! [SV370: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV370 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV370 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6007]) ).

thf(7226,plain,
    ! [SV371: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV371 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV371 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6008]) ).

thf(7227,plain,
    ! [SV372: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV372 )
        = $false )
      | ( ( class_HOL_Oplus @ SV372 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6009]) ).

thf(7228,plain,
    ! [SV373: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV373 )
        = $false )
      | ( ( class_HOL_Ozero @ SV373 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6010]) ).

thf(7229,plain,
    ! [SV374: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV374 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV374 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6011]) ).

thf(7230,plain,
    ! [SV375: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV375 )
        = $false )
      | ( ( class_HOL_Ominus @ SV375 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6012]) ).

thf(7231,plain,
    ! [SV376: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV376 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV376 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6013]) ).

thf(7232,plain,
    ! [SV377: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV377 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6014]) ).

thf(7233,plain,
    ! [SV378: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV378 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV378 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6015]) ).

thf(7234,plain,
    ! [SV379: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV379 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV379 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6016]) ).

thf(7235,plain,
    ! [SV380: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV380 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV380 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6017]) ).

thf(7236,plain,
    ! [SV381: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV381 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV381 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6018]) ).

thf(7237,plain,
    ! [SV382: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV382 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV382 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6019]) ).

thf(7238,plain,
    ! [SV383: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV383 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV383 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6020]) ).

thf(7239,plain,
    ! [SV384: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV384 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV384 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6021]) ).

thf(7240,plain,
    ! [SV385: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV385 )
        = $false )
      | ( ( class_HOL_Otimes @ SV385 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6022]) ).

thf(7241,plain,
    ! [SV386: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV386 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV386 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6023]) ).

thf(7242,plain,
    ! [SV387: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV387 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV387 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6024]) ).

thf(7243,plain,
    ! [SV388: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring @ SV388 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV388 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6025]) ).

thf(7244,plain,
    ! [SV389: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV389 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV389 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6026]) ).

thf(7245,plain,
    ! [SV390: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV390 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV390 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6027]) ).

thf(7246,plain,
    ! [SV391: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV391 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV391 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6028]) ).

thf(7247,plain,
    ! [SV392: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV392 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV392 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6029]) ).

thf(7248,plain,
    ! [SV393: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV393 )
        = $false )
      | ( ( class_HOL_Otimes @ SV393 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6030]) ).

thf(7249,plain,
    ! [SV394: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV394 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV394 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6031]) ).

thf(7250,plain,
    ! [SV395: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV395 )
        = $false )
      | ( ( class_HOL_Ozero @ SV395 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6032]) ).

thf(7251,plain,
    ! [SV396: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV396 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV396 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6033]) ).

thf(7252,plain,
    ! [SV397: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV397 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV397 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6034]) ).

thf(7253,plain,
    ! [SV398: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV398 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV398 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6035]) ).

thf(7254,plain,
    ! [SV399: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV399 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV399 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6036]) ).

thf(7255,plain,
    ! [SV400: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV400 )
        = $false )
      | ( ( class_HOL_Oplus @ SV400 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6037]) ).

thf(7256,plain,
    ! [SV401: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV401 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV401 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6038]) ).

thf(7257,plain,
    ! [SV402: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV402 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6039]) ).

thf(7258,plain,
    ! [SV403: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV403 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV403 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6040]) ).

thf(7259,plain,
    ! [SV404: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV404 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV404 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6041]) ).

thf(7260,plain,
    ! [SV405: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV405 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV405 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6042]) ).

thf(7261,plain,
    ! [SV406: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV406 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV406 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6043]) ).

thf(7262,plain,
    ! [SV407: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV407 )
        = $false )
      | ( ( class_HOL_Oone @ SV407 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6044]) ).

thf(7263,plain,
    ! [SV408: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV408 )
        = $false )
      | ( ( class_Ring__and__Field_Oring__1 @ SV408 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6045]) ).

thf(7264,plain,
    ! [SV409: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV409 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV409 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6046]) ).

thf(7265,plain,
    ! [SV410: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV410 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV410 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6047]) ).

thf(7266,plain,
    ! [SV411: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV411 )
        = $false )
      | ( ( class_HOL_Ominus @ SV411 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6048]) ).

thf(7267,plain,
    ! [SV412: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV412 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV412 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6049]) ).

thf(7268,plain,
    ! [SV413: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV413 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV413 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6050]) ).

thf(7269,plain,
    ! [SV414: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV414 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV414 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6051]) ).

thf(7270,plain,
    ! [SV415: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV415 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV415 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6052]) ).

thf(7271,plain,
    ! [SV416: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV416 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV416 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6053]) ).

thf(7272,plain,
    ! [SV417: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV417 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV417 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6054]) ).

thf(7273,plain,
    ! [SV418: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring @ SV418 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV418 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6055]) ).

thf(7274,plain,
    ! [SV419: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring @ SV419 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV419 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6056]) ).

thf(7275,plain,
    ! [SV420: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring @ SV420 )
        = $false )
      | ( ( class_HOL_Oplus @ SV420 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6057]) ).

thf(7276,plain,
    ! [SV421: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring @ SV421 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV421 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6058]) ).

thf(7277,plain,
    ! [SV422: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring @ SV422 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV422 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6059]) ).

thf(7278,plain,
    ! [SV423: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring @ SV423 )
        = $false )
      | ( ( class_HOL_Otimes @ SV423 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6060]) ).

thf(7279,plain,
    ! [SV424: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring @ SV424 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV424 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6061]) ).

thf(7280,plain,
    ! [SV425: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV425 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV425 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6062]) ).

thf(7281,plain,
    ! [SV426: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV426 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV426 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6063]) ).

thf(7282,plain,
    ! [SV427: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV427 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV427 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6064]) ).

thf(7283,plain,
    ! [SV428: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV428 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV428 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6065]) ).

thf(7284,plain,
    ! [SV429: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV429 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV429 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6066]) ).

thf(7285,plain,
    ! [SV430: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV430 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV430 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6067]) ).

thf(7286,plain,
    ! [SV431: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV431 )
        = $false )
      | ( ( class_HOL_Oplus @ SV431 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6068]) ).

thf(7287,plain,
    ! [SV432: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV432 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV432 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6069]) ).

thf(7288,plain,
    ! [SV433: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV433 )
        = $false )
      | ( ( class_HOL_Otimes @ SV433 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6070]) ).

thf(7289,plain,
    ! [SV434: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV434 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV434 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6071]) ).

thf(7290,plain,
    ! [SV435: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV435 )
        = $false )
      | ( ( class_HOL_Ozero @ SV435 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6072]) ).

thf(7291,plain,
    ! [SV436: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV436 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV436 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6073]) ).

thf(7292,plain,
    ! [SV437: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV437 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV437 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6074]) ).

thf(7293,plain,
    ! [SV438: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV438 )
        = $false )
      | ( ( class_HOL_Oplus @ SV438 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6075]) ).

thf(7294,plain,
    ! [SV439: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV439 )
        = $false )
      | ( ( class_HOL_Ozero @ SV439 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6076]) ).

thf(7295,plain,
    ! [SV440: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV440 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV440 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6077]) ).

thf(7296,plain,
    ! [SV441: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV441 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV441 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6078]) ).

thf(7297,plain,
    ! [SV442: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV442 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV442 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6079]) ).

thf(7298,plain,
    ! [SV443: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV443 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV443 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6080]) ).

thf(7299,plain,
    ! [SV444: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV444 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV444 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6081]) ).

thf(7300,plain,
    ! [SV445: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV445 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV445 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6082]) ).

thf(7301,plain,
    ! [SV446: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV446 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV446 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6083]) ).

thf(7302,plain,
    ! [SV447: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV447 )
        = $false )
      | ( ( class_HOL_Otimes @ SV447 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6084]) ).

thf(7303,plain,
    ! [SV448: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV448 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV448 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6085]) ).

thf(7304,plain,
    ! [SV449: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV449 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV449 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6086]) ).

thf(7305,plain,
    ! [SV450: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV450 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV450 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6087]) ).

thf(7306,plain,
    ! [SV451: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV451 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV451 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6088]) ).

thf(7307,plain,
    ! [SV452: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV452 )
        = $false )
      | ( ( class_HOL_Ozero @ SV452 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6089]) ).

thf(7308,plain,
    ! [SV453: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV453 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV453 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6090]) ).

thf(7309,plain,
    ! [SV454: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV454 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV454 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6091]) ).

thf(7310,plain,
    ! [SV455: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV455 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV455 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6092]) ).

thf(7311,plain,
    ! [SV456: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV456 )
        = $false )
      | ( ( class_HOL_Oplus @ SV456 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6093]) ).

thf(7312,plain,
    ! [SV457: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV457 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV457 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6094]) ).

thf(7313,plain,
    ! [SV458: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV458 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV458 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6095]) ).

thf(7314,plain,
    ! [SV459: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV459 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV459 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6096]) ).

thf(7315,plain,
    ! [SV460: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV460 )
        = $false )
      | ( ( class_HOL_Oone @ SV460 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6097]) ).

thf(7316,plain,
    ! [SV461: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV461 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV461 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6098]) ).

thf(7317,plain,
    ! [SV462: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV462 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV462 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6099]) ).

thf(7318,plain,
    ! [SV463: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV463 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV463 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6100]) ).

thf(7319,plain,
    ! [SV464: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV464 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV464 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6101]) ).

thf(7320,plain,
    ! [SV465: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV465 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV465 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6102]) ).

thf(7321,plain,
    ! [SV466: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV466 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV466 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6103]) ).

thf(7322,plain,
    ! [SV467: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV467 )
        = $false )
      | ( ( class_HOL_Otimes @ SV467 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6104]) ).

thf(7323,plain,
    ! [SV468: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV468 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV468 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6105]) ).

thf(7324,plain,
    ! [SV469: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV469 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV469 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6106]) ).

thf(7325,plain,
    ! [SV470: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV470 )
        = $false )
      | ( ( class_HOL_Ozero @ SV470 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6107]) ).

thf(7326,plain,
    ! [SV471: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV471 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV471 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6108]) ).

thf(7327,plain,
    ! [SV472: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV472 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV472 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6109]) ).

thf(7328,plain,
    ! [SV473: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV473 )
        = $false )
      | ( ( class_HOL_Oplus @ SV473 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6110]) ).

thf(7329,plain,
    ! [SV474: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV474 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV474 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6111]) ).

thf(7330,plain,
    ! [SV475: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV475 )
        = $false )
      | ( ( class_HOL_Oone @ SV475 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6112]) ).

thf(7331,plain,
    ! [SV476: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV476 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV476 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6113]) ).

thf(7332,plain,
    ! [SV477: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV477 )
        = $false )
      | ( ( class_HOL_Otimes @ SV477 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6114]) ).

thf(7333,plain,
    ! [SV478: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV478 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV478 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6115]) ).

thf(7334,plain,
    ! [SV479: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV479 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV479 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6116]) ).

thf(7335,plain,
    ! [SV480: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV480 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV480 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6117]) ).

thf(7336,plain,
    ! [SV481: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV481 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV481 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6118]) ).

thf(7337,plain,
    ! [SV482: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV482 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV482 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6119]) ).

thf(7338,plain,
    ! [SV483: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV483 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV483 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6120]) ).

thf(7339,plain,
    ! [SV484: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV484 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV484 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6121]) ).

thf(7340,plain,
    ! [SV485: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV485 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV485 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6122]) ).

thf(7341,plain,
    ! [SV486: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV486 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV486 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6123]) ).

thf(7342,plain,
    ! [SV487: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV487 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV487 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6124]) ).

thf(7343,plain,
    ! [SV488: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV488 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV488 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6125]) ).

thf(7344,plain,
    ! [SV489: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV489 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV489 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6126]) ).

thf(7345,plain,
    ! [SV490: $i] :
      ( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV490 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV490 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6127]) ).

thf(7346,plain,
    ! [SV491: $i] :
      ( ( ( class_Ring__and__Field_Odivision__by__zero @ SV491 )
        = $false )
      | ( ( class_HOL_Ozero @ SV491 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6128]) ).

thf(7347,plain,
    ! [SV492: $i] :
      ( ( ( class_Ring__and__Field_Odivision__by__zero @ SV492 )
        = $false )
      | ( ( class_HOL_Oinverse @ SV492 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6129]) ).

thf(7348,plain,
    ! [SV493: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV493 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV493 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6130]) ).

thf(7349,plain,
    ! [SV494: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV494 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV494 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6131]) ).

thf(7350,plain,
    ! [SV495: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV495 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV495 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6132]) ).

thf(7351,plain,
    ! [SV496: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV496 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV496 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6133]) ).

thf(7352,plain,
    ! [SV497: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV497 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV497 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6134]) ).

thf(7353,plain,
    ! [SV498: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV498 )
        = $false )
      | ( ( class_HOL_Oone @ SV498 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6135]) ).

thf(7354,plain,
    ! [SV499: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV499 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV499 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6136]) ).

thf(7355,plain,
    ! [SV500: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV500 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV500 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6137]) ).

thf(7356,plain,
    ! [SV501: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV501 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV501 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6138]) ).

thf(7357,plain,
    ! [SV502: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV502 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV502 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6139]) ).

thf(7358,plain,
    ! [SV503: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV503 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV503 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6140]) ).

thf(7359,plain,
    ! [SV504: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV504 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV504 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6141]) ).

thf(7360,plain,
    ! [SV505: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV505 )
        = $false )
      | ( ( class_Ring__and__Field_Oring__1 @ SV505 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6142]) ).

thf(7361,plain,
    ! [SV506: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV506 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV506 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6143]) ).

thf(7362,plain,
    ! [SV507: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV507 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV507 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6144]) ).

thf(7363,plain,
    ! [SV508: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV508 )
        = $false )
      | ( ( class_HOL_Otimes @ SV508 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6145]) ).

thf(7364,plain,
    ! [SV509: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV509 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV509 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6146]) ).

thf(7365,plain,
    ! [SV510: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV510 )
        = $false )
      | ( ( class_HOL_Ozero @ SV510 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6147]) ).

thf(7366,plain,
    ! [SV511: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV511 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV511 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6148]) ).

thf(7367,plain,
    ! [SV512: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV512 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV512 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6149]) ).

thf(7368,plain,
    ! [SV513: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV513 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV513 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6150]) ).

thf(7369,plain,
    ! [SV514: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV514 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV514 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6151]) ).

thf(7370,plain,
    ! [SV515: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV515 )
        = $false )
      | ( ( class_HOL_Oplus @ SV515 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6152]) ).

thf(7371,plain,
    ! [SV516: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV516 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV516 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6153]) ).

thf(7372,plain,
    ! [SV517: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV517 )
        = $false )
      | ( ( class_HOL_Oinverse @ SV517 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6154]) ).

thf(7373,plain,
    ! [SV518: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV518 )
        = $false )
      | ( ( class_Ring__and__Field_Oidom @ SV518 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6155]) ).

thf(7374,plain,
    ! [SV519: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV519 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV519 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6156]) ).

thf(7375,plain,
    ! [SV520: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV520 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV520 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6157]) ).

thf(7376,plain,
    ! [SV521: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV521 )
        = $false )
      | ( ( class_HOL_Ominus @ SV521 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6158]) ).

thf(7377,plain,
    ! [SV522: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV522 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV522 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6159]) ).

thf(7378,plain,
    ! [SV523: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV523 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV523 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6160]) ).

thf(7379,plain,
    ! [SV524: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV524 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV524 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6161]) ).

thf(7380,plain,
    ! [SV525: $i] :
      ( ( ( class_Ring__and__Field_Ofield @ SV525 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV525 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6162]) ).

thf(7381,plain,
    ! [SV526: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV526 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV526 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6163]) ).

thf(7382,plain,
    ! [SV527: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV527 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV527 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6164]) ).

thf(7383,plain,
    ! [SV528: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV528 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV528 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6165]) ).

thf(7384,plain,
    ! [SV529: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV529 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV529 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6166]) ).

thf(7385,plain,
    ! [SV530: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV530 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV530 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6167]) ).

thf(7386,plain,
    ! [SV531: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV531 )
        = $false )
      | ( ( class_HOL_Oone @ SV531 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6168]) ).

thf(7387,plain,
    ! [SV532: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV532 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV532 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6169]) ).

thf(7388,plain,
    ! [SV533: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV533 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV533 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6170]) ).

thf(7389,plain,
    ! [SV534: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV534 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV534 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6171]) ).

thf(7390,plain,
    ! [SV535: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV535 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV535 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6172]) ).

thf(7391,plain,
    ! [SV536: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV536 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV536 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6173]) ).

thf(7392,plain,
    ! [SV537: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV537 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV537 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6174]) ).

thf(7393,plain,
    ! [SV538: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV538 )
        = $false )
      | ( ( class_Ring__and__Field_Oring__1 @ SV538 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6175]) ).

thf(7394,plain,
    ! [SV539: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV539 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV539 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6176]) ).

thf(7395,plain,
    ! [SV540: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV540 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV540 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6177]) ).

thf(7396,plain,
    ! [SV541: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV541 )
        = $false )
      | ( ( class_HOL_Otimes @ SV541 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6178]) ).

thf(7397,plain,
    ! [SV542: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV542 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV542 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6179]) ).

thf(7398,plain,
    ! [SV543: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV543 )
        = $false )
      | ( ( class_HOL_Ozero @ SV543 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6180]) ).

thf(7399,plain,
    ! [SV544: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV544 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV544 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6181]) ).

thf(7400,plain,
    ! [SV545: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV545 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV545 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6182]) ).

thf(7401,plain,
    ! [SV546: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV546 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV546 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6183]) ).

thf(7402,plain,
    ! [SV547: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV547 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV547 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6184]) ).

thf(7403,plain,
    ! [SV548: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV548 )
        = $false )
      | ( ( class_HOL_Oplus @ SV548 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6185]) ).

thf(7404,plain,
    ! [SV549: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV549 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV549 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6186]) ).

thf(7405,plain,
    ! [SV550: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV550 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV550 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6187]) ).

thf(7406,plain,
    ! [SV551: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV551 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV551 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6188]) ).

thf(7407,plain,
    ! [SV552: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV552 )
        = $false )
      | ( ( class_HOL_Ominus @ SV552 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6189]) ).

thf(7408,plain,
    ! [SV553: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV553 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV553 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6190]) ).

thf(7409,plain,
    ! [SV554: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV554 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV554 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6191]) ).

thf(7410,plain,
    ! [SV555: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV555 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV555 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6192]) ).

thf(7411,plain,
    ! [SV556: $i] :
      ( ( ( class_Ring__and__Field_Oidom @ SV556 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV556 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6193]) ).

thf(7412,plain,
    ! [SV557: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV557 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV557 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6194]) ).

thf(7413,plain,
    ! [SV558: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV558 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV558 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6195]) ).

thf(7414,plain,
    ! [SV559: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV559 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV559 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6196]) ).

thf(7415,plain,
    ! [SV560: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV560 )
        = $false )
      | ( ( class_Orderings_Oord @ SV560 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6197]) ).

thf(7416,plain,
    ! [SV561: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV561 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV561 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6198]) ).

thf(7417,plain,
    ! [SV562: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV562 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV562 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6199]) ).

thf(7418,plain,
    ! [SV563: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV563 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV563 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6200]) ).

thf(7419,plain,
    ! [SV564: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV564 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV564 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6201]) ).

thf(7420,plain,
    ! [SV565: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV565 )
        = $false )
      | ( ( class_HOL_Otimes @ SV565 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6202]) ).

thf(7421,plain,
    ! [SV566: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV566 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV566 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6203]) ).

thf(7422,plain,
    ! [SV567: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV567 )
        = $false )
      | ( ( class_HOL_Ozero @ SV567 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6204]) ).

thf(7423,plain,
    ! [SV568: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV568 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV568 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6205]) ).

thf(7424,plain,
    ! [SV569: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV569 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV569 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6206]) ).

thf(7425,plain,
    ! [SV570: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV570 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV570 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6207]) ).

thf(7426,plain,
    ! [SV571: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV571 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV571 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6208]) ).

thf(7427,plain,
    ! [SV572: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV572 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV572 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6209]) ).

thf(7428,plain,
    ! [SV573: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV573 )
        = $false )
      | ( ( class_HOL_Oplus @ SV573 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6210]) ).

thf(7429,plain,
    ! [SV574: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV574 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV574 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6211]) ).

thf(7430,plain,
    ! [SV575: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV575 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV575 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6212]) ).

thf(7431,plain,
    ! [SV576: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV576 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV576 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6213]) ).

thf(7432,plain,
    ! [SV577: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV577 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV577 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6214]) ).

thf(7433,plain,
    ! [SV578: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV578 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV578 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6215]) ).

thf(7434,plain,
    ! [SV579: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV579 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV579 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6216]) ).

thf(7435,plain,
    ! [SV580: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV580 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV580 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6217]) ).

thf(7436,plain,
    ! [SV581: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV581 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV581 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6218]) ).

thf(7437,plain,
    ! [SV582: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV582 )
        = $false )
      | ( ( class_HOL_Ominus @ SV582 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6219]) ).

thf(7438,plain,
    ! [SV583: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV583 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV583 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6220]) ).

thf(7439,plain,
    ! [SV584: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV584 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV584 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6221]) ).

thf(7440,plain,
    ! [SV585: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV585 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV585 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6222]) ).

thf(7441,plain,
    ! [SV586: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV586 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV586 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6223]) ).

thf(7442,plain,
    ! [SV587: $i] :
      ( ( ( class_Ring__and__Field_Olordered__ring @ SV587 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV587 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6224]) ).

thf(7443,plain,
    ! [SV588: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV588 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV588 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6225]) ).

thf(7444,plain,
    ! [SV589: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV589 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV589 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6226]) ).

thf(7445,plain,
    ! [SV590: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV590 )
        = $false )
      | ( ( class_HOL_Oplus @ SV590 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6227]) ).

thf(7446,plain,
    ! [SV591: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV591 )
        = $false )
      | ( ( class_HOL_Ozero @ SV591 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6228]) ).

thf(7447,plain,
    ! [SV592: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV592 )
        = $false )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV592 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6229]) ).

thf(7448,plain,
    ! [SV593: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV593 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV593 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6230]) ).

thf(7449,plain,
    ! [SV594: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV594 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV594 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6231]) ).

thf(7450,plain,
    ! [SV595: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV595 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV595 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6232]) ).

thf(7451,plain,
    ! [SV596: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV596 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV596 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6233]) ).

thf(7452,plain,
    ! [SV597: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV597 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV597 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6234]) ).

thf(7453,plain,
    ! [SV598: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV598 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV598 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6235]) ).

thf(7454,plain,
    ! [SV599: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV599 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV599 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6236]) ).

thf(7455,plain,
    ! [SV600: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV600 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV600 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6237]) ).

thf(7456,plain,
    ! [SV601: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV601 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV601 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6238]) ).

thf(7457,plain,
    ! [SV602: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV602 )
        = $false )
      | ( ( class_Orderings_Oord @ SV602 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6239]) ).

thf(7458,plain,
    ! [SV603: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV603 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV603 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6240]) ).

thf(7459,plain,
    ! [SV604: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV604 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV604 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6241]) ).

thf(7460,plain,
    ! [SV605: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV605 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV605 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6242]) ).

thf(7461,plain,
    ! [SV606: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV606 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV606 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6243]) ).

thf(7462,plain,
    ! [SV607: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV607 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV607 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6244]) ).

thf(7463,plain,
    ! [SV608: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV608 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV608 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6245]) ).

thf(7464,plain,
    ! [SV609: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV609 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV609 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6246]) ).

thf(7465,plain,
    ! [SV610: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV610 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV610 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6247]) ).

thf(7466,plain,
    ! [SV611: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV611 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV611 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6248]) ).

thf(7467,plain,
    ! [SV612: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV612 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV612 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6249]) ).

thf(7468,plain,
    ! [SV613: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV613 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV613 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6250]) ).

thf(7469,plain,
    ! [SV614: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV614 )
        = $false )
      | ( ( class_HOL_Otimes @ SV614 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6251]) ).

thf(7470,plain,
    ! [SV615: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV615 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV615 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6252]) ).

thf(7471,plain,
    ! [SV616: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV616 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV616 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6253]) ).

thf(7472,plain,
    ! [SV617: $i] :
      ( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV617 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV617 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6254]) ).

thf(7473,plain,
    ! [SV618: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV618 )
        = $false )
      | ( ( class_Ring__and__Field_Ofield @ SV618 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6255]) ).

thf(7474,plain,
    ! [SV619: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV619 )
        = $false )
      | ( ( class_HOL_Oinverse @ SV619 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6256]) ).

thf(7475,plain,
    ! [SV620: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV620 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV620 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6257]) ).

thf(7476,plain,
    ! [SV621: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV621 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV621 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6258]) ).

thf(7477,plain,
    ! [SV622: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV622 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV622 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6259]) ).

thf(7478,plain,
    ! [SV623: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV623 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV623 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6260]) ).

thf(7479,plain,
    ! [SV624: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV624 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV624 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6261]) ).

thf(7480,plain,
    ! [SV625: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV625 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV625 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6262]) ).

thf(7481,plain,
    ! [SV626: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV626 )
        = $false )
      | ( ( class_HOL_Oone @ SV626 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6263]) ).

thf(7482,plain,
    ! [SV627: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV627 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV627 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6264]) ).

thf(7483,plain,
    ! [SV628: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV628 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV628 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6265]) ).

thf(7484,plain,
    ! [SV629: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV629 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV629 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6266]) ).

thf(7485,plain,
    ! [SV630: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV630 )
        = $false )
      | ( ( class_Ring__and__Field_Oidom @ SV630 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6267]) ).

thf(7486,plain,
    ! [SV631: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV631 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV631 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6268]) ).

thf(7487,plain,
    ! [SV632: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV632 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV632 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6269]) ).

thf(7488,plain,
    ! [SV633: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV633 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV633 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6270]) ).

thf(7489,plain,
    ! [SV634: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV634 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV634 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6271]) ).

thf(7490,plain,
    ! [SV635: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV635 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV635 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6272]) ).

thf(7491,plain,
    ! [SV636: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV636 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV636 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6273]) ).

thf(7492,plain,
    ! [SV637: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV637 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV637 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6274]) ).

thf(7493,plain,
    ! [SV638: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV638 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV638 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6275]) ).

thf(7494,plain,
    ! [SV639: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV639 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV639 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6276]) ).

thf(7495,plain,
    ! [SV640: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV640 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV640 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6277]) ).

thf(7496,plain,
    ! [SV641: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV641 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV641 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6278]) ).

thf(7497,plain,
    ! [SV642: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV642 )
        = $false )
      | ( ( class_HOL_Oplus @ SV642 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6279]) ).

thf(7498,plain,
    ! [SV643: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV643 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV643 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6280]) ).

thf(7499,plain,
    ! [SV644: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV644 )
        = $false )
      | ( ( class_HOL_Ozero @ SV644 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6281]) ).

thf(7500,plain,
    ! [SV645: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV645 )
        = $false )
      | ( ( class_HOL_Otimes @ SV645 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6282]) ).

thf(7501,plain,
    ! [SV646: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV646 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__idom @ SV646 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6283]) ).

thf(7502,plain,
    ! [SV647: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV647 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV647 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6284]) ).

thf(7503,plain,
    ! [SV648: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV648 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV648 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6285]) ).

thf(7504,plain,
    ! [SV649: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV649 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV649 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6286]) ).

thf(7505,plain,
    ! [SV650: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV650 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__ring__strict @ SV650 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6287]) ).

thf(7506,plain,
    ! [SV651: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV651 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV651 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6288]) ).

thf(7507,plain,
    ! [SV652: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV652 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV652 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6289]) ).

thf(7508,plain,
    ! [SV653: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV653 )
        = $false )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV653 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6290]) ).

thf(7509,plain,
    ! [SV654: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV654 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV654 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6291]) ).

thf(7510,plain,
    ! [SV655: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV655 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV655 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6292]) ).

thf(7511,plain,
    ! [SV656: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV656 )
        = $false )
      | ( ( class_Ring__and__Field_Olordered__ring @ SV656 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6293]) ).

thf(7512,plain,
    ! [SV657: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV657 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV657 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6294]) ).

thf(7513,plain,
    ! [SV658: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV658 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV658 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6295]) ).

thf(7514,plain,
    ! [SV659: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV659 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV659 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6296]) ).

thf(7515,plain,
    ! [SV660: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV660 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV660 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6297]) ).

thf(7516,plain,
    ! [SV661: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV661 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV661 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6298]) ).

thf(7517,plain,
    ! [SV662: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV662 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV662 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6299]) ).

thf(7518,plain,
    ! [SV663: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV663 )
        = $false )
      | ( ( class_Ring__and__Field_Oring__1 @ SV663 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6300]) ).

thf(7519,plain,
    ! [SV664: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV664 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV664 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6301]) ).

thf(7520,plain,
    ! [SV665: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV665 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV665 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6302]) ).

thf(7521,plain,
    ! [SV666: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV666 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV666 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6303]) ).

thf(7522,plain,
    ! [SV667: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV667 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV667 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6304]) ).

thf(7523,plain,
    ! [SV668: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV668 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV668 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6305]) ).

thf(7524,plain,
    ! [SV669: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV669 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV669 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6306]) ).

thf(7525,plain,
    ! [SV670: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV670 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV670 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6307]) ).

thf(7526,plain,
    ! [SV671: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV671 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV671 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6308]) ).

thf(7527,plain,
    ! [SV672: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV672 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV672 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6309]) ).

thf(7528,plain,
    ! [SV673: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV673 )
        = $false )
      | ( ( class_Orderings_Oord @ SV673 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6310]) ).

thf(7529,plain,
    ! [SV674: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV674 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV674 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6311]) ).

thf(7530,plain,
    ! [SV675: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV675 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__semidom @ SV675 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6312]) ).

thf(7531,plain,
    ! [SV676: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV676 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV676 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6313]) ).

thf(7532,plain,
    ! [SV677: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV677 )
        = $false )
      | ( ( class_HOL_Ominus @ SV677 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6314]) ).

thf(7533,plain,
    ! [SV678: $i] :
      ( ( ( class_Ring__and__Field_Oordered__field @ SV678 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV678 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6315]) ).

thf(7534,plain,
    ! [SV679: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV679 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV679 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6316]) ).

thf(7535,plain,
    ! [SV680: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV680 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV680 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6317]) ).

thf(7536,plain,
    ! [SV681: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV681 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV681 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6318]) ).

thf(7537,plain,
    ! [SV682: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV682 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV682 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6319]) ).

thf(7538,plain,
    ! [SV683: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV683 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV683 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6320]) ).

thf(7539,plain,
    ! [SV684: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV684 )
        = $false )
      | ( ( class_HOL_Oone @ SV684 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6321]) ).

thf(7540,plain,
    ! [SV685: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV685 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV685 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6322]) ).

thf(7541,plain,
    ! [SV686: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV686 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV686 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6323]) ).

thf(7542,plain,
    ! [SV687: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV687 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV687 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6324]) ).

thf(7543,plain,
    ! [SV688: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV688 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV688 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6325]) ).

thf(7544,plain,
    ! [SV689: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV689 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV689 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6326]) ).

thf(7545,plain,
    ! [SV690: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV690 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV690 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6327]) ).

thf(7546,plain,
    ! [SV691: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV691 )
        = $false )
      | ( ( class_Ring__and__Field_Oring__1 @ SV691 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6328]) ).

thf(7547,plain,
    ! [SV692: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV692 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV692 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6329]) ).

thf(7548,plain,
    ! [SV693: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV693 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV693 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6330]) ).

thf(7549,plain,
    ! [SV694: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV694 )
        = $false )
      | ( ( class_HOL_Otimes @ SV694 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6331]) ).

thf(7550,plain,
    ! [SV695: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV695 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV695 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6332]) ).

thf(7551,plain,
    ! [SV696: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV696 )
        = $false )
      | ( ( class_HOL_Ozero @ SV696 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6333]) ).

thf(7552,plain,
    ! [SV697: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV697 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV697 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6334]) ).

thf(7553,plain,
    ! [SV698: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV698 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV698 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6335]) ).

thf(7554,plain,
    ! [SV699: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV699 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV699 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6336]) ).

thf(7555,plain,
    ! [SV700: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV700 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV700 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6337]) ).

thf(7556,plain,
    ! [SV701: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV701 )
        = $false )
      | ( ( class_HOL_Oplus @ SV701 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6338]) ).

thf(7557,plain,
    ! [SV702: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV702 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV702 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6339]) ).

thf(7558,plain,
    ! [SV703: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV703 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV703 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6340]) ).

thf(7559,plain,
    ! [SV704: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV704 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV704 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6341]) ).

thf(7560,plain,
    ! [SV705: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV705 )
        = $false )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV705 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6342]) ).

thf(7561,plain,
    ! [SV706: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV706 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV706 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6343]) ).

thf(7562,plain,
    ! [SV707: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV707 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV707 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6344]) ).

thf(7563,plain,
    ! [SV708: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV708 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV708 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6345]) ).

thf(7564,plain,
    ! [SV709: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV709 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV709 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6346]) ).

thf(7565,plain,
    ! [SV710: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV710 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV710 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6347]) ).

thf(7566,plain,
    ! [SV711: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV711 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV711 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6348]) ).

thf(7567,plain,
    ! [SV712: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV712 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV712 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6349]) ).

thf(7568,plain,
    ! [SV713: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV713 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV713 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6350]) ).

thf(7569,plain,
    ! [SV714: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV714 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV714 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6351]) ).

thf(7570,plain,
    ! [SV715: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV715 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV715 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6352]) ).

thf(7571,plain,
    ! [SV716: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV716 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV716 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6353]) ).

thf(7572,plain,
    ! [SV717: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV717 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV717 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6354]) ).

thf(7573,plain,
    ! [SV718: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV718 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV718 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6355]) ).

thf(7574,plain,
    ! [SV719: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV719 )
        = $false )
      | ( ( class_Orderings_Oord @ SV719 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6356]) ).

thf(7575,plain,
    ! [SV720: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV720 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV720 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6357]) ).

thf(7576,plain,
    ! [SV721: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV721 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__ring__strict @ SV721 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6358]) ).

thf(7577,plain,
    ! [SV722: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV722 )
        = $false )
      | ( ( class_Ring__and__Field_Olordered__ring @ SV722 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6359]) ).

thf(7578,plain,
    ! [SV723: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV723 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV723 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6360]) ).

thf(7579,plain,
    ! [SV724: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV724 )
        = $false )
      | ( ( class_HOL_Ominus @ SV724 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6361]) ).

thf(7580,plain,
    ! [SV725: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV725 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV725 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6362]) ).

thf(7581,plain,
    ! [SV726: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV726 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV726 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6363]) ).

thf(7582,plain,
    ! [SV727: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV727 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV727 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6364]) ).

thf(7583,plain,
    ! [SV728: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV728 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV728 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6365]) ).

thf(7584,plain,
    ! [SV729: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV729 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV729 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6366]) ).

thf(7585,plain,
    ! [SV730: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV730 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__semidom @ SV730 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6367]) ).

thf(7586,plain,
    ! [SV731: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV731 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV731 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6368]) ).

thf(7587,plain,
    ! [SV732: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV732 )
        = $false )
      | ( ( class_Ring__and__Field_Oidom @ SV732 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6369]) ).

thf(7588,plain,
    ! [SV733: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV733 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV733 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6370]) ).

thf(7589,plain,
    ! [SV734: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV734 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV734 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6371]) ).

thf(7590,plain,
    ! [SV735: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV735 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV735 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6372]) ).

thf(7591,plain,
    ! [SV736: $i] :
      ( ( ( class_Ring__and__Field_Oordered__idom @ SV736 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV736 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6373]) ).

thf(7592,plain,
    ! [SV737: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV737 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV737 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6374]) ).

thf(7593,plain,
    ! [SV738: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV738 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV738 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6375]) ).

thf(7594,plain,
    ! [SV739: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV739 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV739 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6376]) ).

thf(7595,plain,
    ! [SV740: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV740 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV740 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6377]) ).

thf(7596,plain,
    ! [SV741: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV741 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV741 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6378]) ).

thf(7597,plain,
    ! [SV742: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV742 )
        = $false )
      | ( ( class_HOL_Oplus @ SV742 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6379]) ).

thf(7598,plain,
    ! [SV743: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV743 )
        = $false )
      | ( ( class_HOL_Ozero @ SV743 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6380]) ).

thf(7599,plain,
    ! [SV744: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV744 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV744 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6381]) ).

thf(7600,plain,
    ! [SV745: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV745 )
        = $false )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV745 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6382]) ).

thf(7601,plain,
    ! [SV746: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV746 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV746 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6383]) ).

thf(7602,plain,
    ! [SV747: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV747 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6384]) ).

thf(7603,plain,
    ! [SV748: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV748 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV748 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6385]) ).

thf(7604,plain,
    ! [SV749: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV749 )
        = $false )
      | ( ( class_HOL_Ominus @ SV749 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6386]) ).

thf(7605,plain,
    ! [SV750: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV750 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV750 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6387]) ).

thf(7606,plain,
    ! [SV751: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV751 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV751 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6388]) ).

thf(7607,plain,
    ! [SV752: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV752 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV752 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6389]) ).

thf(7608,plain,
    ! [SV753: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV753 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV753 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6390]) ).

thf(7609,plain,
    ! [SV754: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV754 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV754 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6391]) ).

thf(7610,plain,
    ! [SV755: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV755 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV755 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6392]) ).

thf(7611,plain,
    ! [SV756: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV756 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV756 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6393]) ).

thf(7612,plain,
    ! [SV757: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV757 )
        = $false )
      | ( ( class_Orderings_Oord @ SV757 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6394]) ).

thf(7613,plain,
    ! [SV758: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV758 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV758 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6395]) ).

thf(7614,plain,
    ! [SV759: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV759 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group @ SV759 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6396]) ).

thf(7615,plain,
    ! [SV760: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV760 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV760 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6397]) ).

thf(7616,plain,
    ! [SV761: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV761 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV761 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6398]) ).

thf(7617,plain,
    ! [SV762: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV762 )
        = $false )
      | ( ( class_Ring__and__Field_Olordered__ring @ SV762 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6399]) ).

thf(7618,plain,
    ! [SV763: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV763 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__ring @ SV763 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6400]) ).

thf(7619,plain,
    ! [SV764: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV764 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV764 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6401]) ).

thf(7620,plain,
    ! [SV765: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV765 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV765 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6402]) ).

thf(7621,plain,
    ! [SV766: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV766 )
        = $false )
      | ( ( class_OrderedGroup_Olordered__ab__group__join @ SV766 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6403]) ).

thf(7622,plain,
    ! [SV767: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV767 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV767 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6404]) ).

thf(7623,plain,
    ! [SV768: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV768 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV768 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6405]) ).

thf(7624,plain,
    ! [SV769: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV769 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV769 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6406]) ).

thf(7625,plain,
    ! [SV770: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV770 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV770 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6407]) ).

thf(7626,plain,
    ! [SV771: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV771 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV771 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6408]) ).

thf(7627,plain,
    ! [SV772: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV772 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV772 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6409]) ).

thf(7628,plain,
    ! [SV773: $i] :
      ( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV773 )
        = $false )
      | ( ( class_HOL_Otimes @ SV773 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6410]) ).

thf(7629,plain,
    ! [SV774: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV774 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV774 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6411]) ).

thf(7630,plain,
    ! [SV775: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV775 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV775 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6412]) ).

thf(7631,plain,
    ! [SV776: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV776 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV776 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6413]) ).

thf(7632,plain,
    ! [SV777: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV777 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV777 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6414]) ).

thf(7633,plain,
    ! [SV778: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV778 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV778 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6415]) ).

thf(7634,plain,
    ! [SV779: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV779 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV779 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6416]) ).

thf(7635,plain,
    ! [SV780: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV780 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV780 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6417]) ).

thf(7636,plain,
    ! [SV781: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV781 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV781 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6418]) ).

thf(7637,plain,
    ! [SV782: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV782 )
        = $false )
      | ( ( class_HOL_Otimes @ SV782 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6419]) ).

thf(7638,plain,
    ! [SV783: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV783 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV783 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6420]) ).

thf(7639,plain,
    ! [SV784: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV784 )
        = $false )
      | ( ( class_HOL_Ozero @ SV784 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6421]) ).

thf(7640,plain,
    ! [SV785: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV785 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV785 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6422]) ).

thf(7641,plain,
    ! [SV786: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV786 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV786 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6423]) ).

thf(7642,plain,
    ! [SV787: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV787 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV787 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6424]) ).

thf(7643,plain,
    ! [SV788: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV788 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV788 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6425]) ).

thf(7644,plain,
    ! [SV789: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV789 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV789 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6426]) ).

thf(7645,plain,
    ! [SV790: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV790 )
        = $false )
      | ( ( class_HOL_Oplus @ SV790 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6427]) ).

thf(7646,plain,
    ! [SV791: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV791 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV791 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6428]) ).

thf(7647,plain,
    ! [SV792: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV792 )
        = $false )
      | ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV792 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6429]) ).

thf(7648,plain,
    ! [SV793: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV793 )
        = $false )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV793 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6430]) ).

thf(7649,plain,
    ! [SV794: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV794 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV794 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6431]) ).

thf(7650,plain,
    ! [SV795: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV795 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV795 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6432]) ).

thf(7651,plain,
    ! [SV796: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV796 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV796 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6433]) ).

thf(7652,plain,
    ! [SV797: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV797 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV797 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6434]) ).

thf(7653,plain,
    ! [SV798: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV798 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV798 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6435]) ).

thf(7654,plain,
    ! [SV799: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV799 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV799 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6436]) ).

thf(7655,plain,
    ! [SV800: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV800 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV800 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6437]) ).

thf(7656,plain,
    ! [SV801: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV801 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV801 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6438]) ).

thf(7657,plain,
    ! [SV802: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV802 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV802 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6439]) ).

thf(7658,plain,
    ! [SV803: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV803 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV803 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6440]) ).

thf(7659,plain,
    ! [SV804: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV804 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV804 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6441]) ).

thf(7660,plain,
    ! [SV805: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV805 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV805 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6442]) ).

thf(7661,plain,
    ! [SV806: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV806 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV806 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6443]) ).

thf(7662,plain,
    ! [SV807: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV807 )
        = $false )
      | ( ( class_Orderings_Oord @ SV807 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6444]) ).

thf(7663,plain,
    ! [SV808: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV808 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV808 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6445]) ).

thf(7664,plain,
    ! [SV809: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV809 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV809 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6446]) ).

thf(7665,plain,
    ! [SV810: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV810 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV810 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6447]) ).

thf(7666,plain,
    ! [SV811: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV811 )
        = $false )
      | ( ( class_HOL_Oone @ SV811 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6448]) ).

thf(7667,plain,
    ! [SV812: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV812 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV812 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6449]) ).

thf(7668,plain,
    ! [SV813: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semidom @ SV813 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV813 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6450]) ).

thf(7669,plain,
    ! [SV814: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV814 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV814 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6451]) ).

thf(7670,plain,
    ! [SV815: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV815 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV815 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6452]) ).

thf(7671,plain,
    ! [SV816: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV816 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV816 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6453]) ).

thf(7672,plain,
    ! [SV817: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV817 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV817 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6454]) ).

thf(7673,plain,
    ! [SV818: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV818 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV818 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6455]) ).

thf(7674,plain,
    ! [SV819: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV819 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV819 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6456]) ).

thf(7675,plain,
    ! [SV820: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV820 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV820 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6457]) ).

thf(7676,plain,
    ! [SV821: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV821 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV821 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6458]) ).

thf(7677,plain,
    ! [SV822: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV822 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV822 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6459]) ).

thf(7678,plain,
    ! [SV823: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV823 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV823 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6460]) ).

thf(7679,plain,
    ! [SV824: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV824 )
        = $false )
      | ( ( class_Orderings_Oord @ SV824 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6461]) ).

thf(7680,plain,
    ! [SV825: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV825 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV825 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6462]) ).

thf(7681,plain,
    ! [SV826: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV826 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV826 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6463]) ).

thf(7682,plain,
    ! [SV827: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV827 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV827 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6464]) ).

thf(7683,plain,
    ! [SV828: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV828 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV828 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6465]) ).

thf(7684,plain,
    ! [SV829: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV829 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV829 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6466]) ).

thf(7685,plain,
    ! [SV830: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV830 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV830 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6467]) ).

thf(7686,plain,
    ! [SV831: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV831 )
        = $false )
      | ( ( class_HOL_Otimes @ SV831 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6468]) ).

thf(7687,plain,
    ! [SV832: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV832 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV832 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6469]) ).

thf(7688,plain,
    ! [SV833: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV833 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV833 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6470]) ).

thf(7689,plain,
    ! [SV834: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV834 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV834 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6471]) ).

thf(7690,plain,
    ! [SV835: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV835 )
        = $false )
      | ( ( class_HOL_Oplus @ SV835 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6472]) ).

thf(7691,plain,
    ! [SV836: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV836 )
        = $false )
      | ( ( class_HOL_Ozero @ SV836 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6473]) ).

thf(7692,plain,
    ! [SV837: $i] :
      ( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV837 )
        = $false )
      | ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV837 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6474]) ).

thf(7693,plain,
    ! [SV838: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV838 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV838 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6475]) ).

thf(7694,plain,
    ! [SV839: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV839 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV839 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6476]) ).

thf(7695,plain,
    ! [SV840: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV840 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV840 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6477]) ).

thf(7696,plain,
    ! [SV841: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV841 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV841 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6478]) ).

thf(7697,plain,
    ! [SV842: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV842 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV842 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6479]) ).

thf(7698,plain,
    ! [SV843: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV843 )
        = $false )
      | ( ( class_HOL_Oplus @ SV843 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6480]) ).

thf(7699,plain,
    ! [SV844: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV844 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV844 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6481]) ).

thf(7700,plain,
    ! [SV845: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV845 )
        = $false )
      | ( ( class_Orderings_Oord @ SV845 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6482]) ).

thf(7701,plain,
    ! [SV846: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV846 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV846 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6483]) ).

thf(7702,plain,
    ! [SV847: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV847 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV847 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6484]) ).

thf(7703,plain,
    ! [SV848: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV848 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV848 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6485]) ).

thf(7704,plain,
    ! [SV849: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV849 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV849 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6486]) ).

thf(7705,plain,
    ! [SV850: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV850 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV850 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6487]) ).

thf(7706,plain,
    ! [SV851: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV851 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV851 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6488]) ).

thf(7707,plain,
    ! [SV852: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV852 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV852 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6489]) ).

thf(7708,plain,
    ! [SV853: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV853 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV853 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6490]) ).

thf(7709,plain,
    ! [SV854: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV854 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV854 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6491]) ).

thf(7710,plain,
    ! [SV855: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV855 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV855 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6492]) ).

thf(7711,plain,
    ! [SV856: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV856 )
        = $false )
      | ( ( class_HOL_Otimes @ SV856 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6493]) ).

thf(7712,plain,
    ! [SV857: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV857 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV857 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6494]) ).

thf(7713,plain,
    ! [SV858: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV858 )
        = $false )
      | ( ( class_HOL_Ozero @ SV858 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6495]) ).

thf(7714,plain,
    ! [SV859: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV859 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV859 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6496]) ).

thf(7715,plain,
    ! [SV860: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV860 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV860 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6497]) ).

thf(7716,plain,
    ! [SV861: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV861 )
        = $false )
      | ( ( class_HOL_Oplus @ SV861 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6498]) ).

thf(7717,plain,
    ! [SV862: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV862 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV862 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6499]) ).

thf(7718,plain,
    ! [SV863: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV863 )
        = $false )
      | ( ( class_Orderings_Oord @ SV863 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6500]) ).

thf(7719,plain,
    ! [SV864: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV864 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV864 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6501]) ).

thf(7720,plain,
    ! [SV865: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV865 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV865 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6502]) ).

thf(7721,plain,
    ! [SV866: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV866 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV866 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6503]) ).

thf(7722,plain,
    ! [SV867: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV867 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV867 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6504]) ).

thf(7723,plain,
    ! [SV868: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV868 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV868 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6505]) ).

thf(7724,plain,
    ! [SV869: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV869 )
        = $false )
      | ( ( class_HOL_Otimes @ SV869 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6506]) ).

thf(7725,plain,
    ! [SV870: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV870 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV870 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6507]) ).

thf(7726,plain,
    ! [SV871: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV871 )
        = $false )
      | ( ( class_HOL_Ozero @ SV871 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6508]) ).

thf(7727,plain,
    ! [SV872: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV872 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV872 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6509]) ).

thf(7728,plain,
    ! [SV873: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV873 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV873 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6510]) ).

thf(7729,plain,
    ! [SV874: $i] :
      ( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV874 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV874 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6511]) ).

thf(7730,plain,
    ! [SV875: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV875 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__ring @ SV875 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6512]) ).

thf(7731,plain,
    ! [SV876: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV876 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV876 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6513]) ).

thf(7732,plain,
    ! [SV877: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV877 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV877 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6514]) ).

thf(7733,plain,
    ! [SV878: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV878 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV878 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6515]) ).

thf(7734,plain,
    ! [SV879: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV879 )
        = $false )
      | ( ( class_HOL_Otimes @ SV879 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6516]) ).

thf(7735,plain,
    ! [SV880: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV880 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV880 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6517]) ).

thf(7736,plain,
    ! [SV881: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV881 )
        = $false )
      | ( ( class_HOL_Ozero @ SV881 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6518]) ).

thf(7737,plain,
    ! [SV882: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV882 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV882 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6519]) ).

thf(7738,plain,
    ! [SV883: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV883 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV883 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6520]) ).

thf(7739,plain,
    ! [SV884: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV884 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV884 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6521]) ).

thf(7740,plain,
    ! [SV885: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV885 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV885 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6522]) ).

thf(7741,plain,
    ! [SV886: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV886 )
        = $false )
      | ( ( class_HOL_Oplus @ SV886 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6523]) ).

thf(7742,plain,
    ! [SV887: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV887 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV887 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6524]) ).

thf(7743,plain,
    ! [SV888: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV888 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV888 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6525]) ).

thf(7744,plain,
    ! [SV889: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV889 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV889 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6526]) ).

thf(7745,plain,
    ! [SV890: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV890 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV890 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6527]) ).

thf(7746,plain,
    ! [SV891: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV891 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV891 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6528]) ).

thf(7747,plain,
    ! [SV892: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV892 )
        = $false )
      | ( ( class_Orderings_Oord @ SV892 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6529]) ).

thf(7748,plain,
    ! [SV893: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV893 )
        = $false )
      | ( ( class_HOL_Ominus @ SV893 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6530]) ).

thf(7749,plain,
    ! [SV894: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV894 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV894 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6531]) ).

thf(7750,plain,
    ! [SV895: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV895 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV895 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6532]) ).

thf(7751,plain,
    ! [SV896: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV896 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV896 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6533]) ).

thf(7752,plain,
    ! [SV897: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV897 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV897 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6534]) ).

thf(7753,plain,
    ! [SV898: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV898 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV898 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6535]) ).

thf(7754,plain,
    ! [SV899: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV899 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV899 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6536]) ).

thf(7755,plain,
    ! [SV900: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV900 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV900 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6537]) ).

thf(7756,plain,
    ! [SV901: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV901 )
        = $false )
      | ( ( class_Ring__and__Field_Ocomm__semiring @ SV901 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6538]) ).

thf(7757,plain,
    ! [SV902: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV902 )
        = $false )
      | ( ( class_HOL_Oplus @ SV902 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6539]) ).

thf(7758,plain,
    ! [SV903: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV903 )
        = $false )
      | ( ( class_HOL_Ozero @ SV903 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6540]) ).

thf(7759,plain,
    ! [SV904: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV904 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV904 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6541]) ).

thf(7760,plain,
    ! [SV905: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV905 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV905 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6542]) ).

thf(7761,plain,
    ! [SV906: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV906 )
        = $false )
      | ( ( class_Orderings_Oord @ SV906 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6543]) ).

thf(7762,plain,
    ! [SV907: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV907 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV907 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6544]) ).

thf(7763,plain,
    ! [SV908: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV908 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__mult @ SV908 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6545]) ).

thf(7764,plain,
    ! [SV909: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV909 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV909 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6546]) ).

thf(7765,plain,
    ! [SV910: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV910 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV910 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6547]) ).

thf(7766,plain,
    ! [SV911: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV911 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV911 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6548]) ).

thf(7767,plain,
    ! [SV912: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV912 )
        = $false )
      | ( ( class_HOL_Otimes @ SV912 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6549]) ).

thf(7768,plain,
    ! [SV913: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV913 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV913 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6550]) ).

thf(7769,plain,
    ! [SV914: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV914 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV914 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6551]) ).

thf(7770,plain,
    ! [SV915: $i] :
      ( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV915 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV915 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6552]) ).

thf(7771,plain,
    ! [SV916: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV916 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV916 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6553]) ).

thf(7772,plain,
    ! [SV917: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV917 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV917 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6554]) ).

thf(7773,plain,
    ! [SV918: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV918 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV918 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6555]) ).

thf(7774,plain,
    ! [SV919: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV919 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV919 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6556]) ).

thf(7775,plain,
    ! [SV920: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV920 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV920 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6557]) ).

thf(7776,plain,
    ! [SV921: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV921 )
        = $false )
      | ( ( class_HOL_Oplus @ SV921 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6558]) ).

thf(7777,plain,
    ! [SV922: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV922 )
        = $false )
      | ( ( class_HOL_Ozero @ SV922 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6559]) ).

thf(7778,plain,
    ! [SV923: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV923 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__semiring @ SV923 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6560]) ).

thf(7779,plain,
    ! [SV924: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV924 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV924 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6561]) ).

thf(7780,plain,
    ! [SV925: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV925 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV925 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6562]) ).

thf(7781,plain,
    ! [SV926: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV926 )
        = $false )
      | ( ( class_Orderings_Oord @ SV926 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6563]) ).

thf(7782,plain,
    ! [SV927: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV927 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__group__add @ SV927 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6564]) ).

thf(7783,plain,
    ! [SV928: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV928 )
        = $false )
      | ( ( class_HOL_Ominus @ SV928 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6565]) ).

thf(7784,plain,
    ! [SV929: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV929 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV929 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6566]) ).

thf(7785,plain,
    ! [SV930: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV930 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV930 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6567]) ).

thf(7786,plain,
    ! [SV931: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV931 )
        = $false )
      | ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV931 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6568]) ).

thf(7787,plain,
    ! [SV932: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV932 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV932 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6569]) ).

thf(7788,plain,
    ! [SV933: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV933 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV933 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6570]) ).

thf(7789,plain,
    ! [SV934: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV934 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV934 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6571]) ).

thf(7790,plain,
    ! [SV935: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV935 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV935 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6572]) ).

thf(7791,plain,
    ! [SV936: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV936 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV936 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6573]) ).

thf(7792,plain,
    ! [SV937: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV937 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV937 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6574]) ).

thf(7793,plain,
    ! [SV938: $i] :
      ( ( ( class_Ring__and__Field_Opordered__ring @ SV938 )
        = $false )
      | ( ( class_HOL_Otimes @ SV938 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6575]) ).

thf(7794,plain,
    ! [SV939: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV939 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV939 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6576]) ).

thf(7795,plain,
    ! [SV940: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV940 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV940 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6577]) ).

thf(7796,plain,
    ! [SV941: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV941 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV941 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6578]) ).

thf(7797,plain,
    ! [SV942: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV942 )
        = $false )
      | ( ( class_Orderings_Oord @ SV942 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6579]) ).

thf(7798,plain,
    ! [SV943: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV943 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV943 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6580]) ).

thf(7799,plain,
    ! [SV944: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV944 )
        = $false )
      | ( ( class_HOL_Otimes @ SV944 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6581]) ).

thf(7800,plain,
    ! [SV945: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV945 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV945 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6582]) ).

thf(7801,plain,
    ! [SV946: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV946 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV946 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6583]) ).

thf(7802,plain,
    ! [SV947: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV947 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV947 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6584]) ).

thf(7803,plain,
    ! [SV948: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV948 )
        = $false )
      | ( ( class_HOL_Oplus @ SV948 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6585]) ).

thf(7804,plain,
    ! [SV949: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV949 )
        = $false )
      | ( ( class_HOL_Ozero @ SV949 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6586]) ).

thf(7805,plain,
    ! [SV950: $i] :
      ( ( ( class_Ring__and__Field_Opordered__semiring @ SV950 )
        = $false )
      | ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV950 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6587]) ).

thf(7806,plain,
    ! [SV951: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV951 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV951 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6588]) ).

thf(7807,plain,
    ! [SV952: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV952 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV952 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6589]) ).

thf(7808,plain,
    ! [SV953: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV953 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV953 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6590]) ).

thf(7809,plain,
    ! [SV954: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV954 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV954 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6591]) ).

thf(7810,plain,
    ! [SV955: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV955 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV955 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6592]) ).

thf(7811,plain,
    ! [SV956: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV956 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV956 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6593]) ).

thf(7812,plain,
    ! [SV957: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV957 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV957 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6594]) ).

thf(7813,plain,
    ! [SV958: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV958 )
        = $false )
      | ( ( class_HOL_Oplus @ SV958 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6595]) ).

thf(7814,plain,
    ! [SV959: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV959 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV959 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6596]) ).

thf(7815,plain,
    ! [SV960: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV960 )
        = $false )
      | ( ( class_HOL_Otimes @ SV960 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6597]) ).

thf(7816,plain,
    ! [SV961: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV961 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV961 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6598]) ).

thf(7817,plain,
    ! [SV962: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV962 )
        = $false )
      | ( ( class_HOL_Ominus @ SV962 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6599]) ).

thf(7818,plain,
    ! [SV963: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV963 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV963 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6600]) ).

thf(7819,plain,
    ! [SV964: $i] :
      ( ( ( class_Ring__and__Field_Oring @ SV964 )
        = $false )
      | ( ( class_HOL_Ozero @ SV964 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6601]) ).

thf(7820,plain,
    ! [SV965: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV965 )
        = $false )
      | ( ( class_Ring__and__Field_Oring @ SV965 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6602]) ).

thf(7821,plain,
    ! [SV966: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV966 )
        = $false )
      | ( ( class_OrderedGroup_Oab__group__add @ SV966 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6603]) ).

thf(7822,plain,
    ! [SV967: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV967 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV967 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6604]) ).

thf(7823,plain,
    ! [SV968: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV968 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV968 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6605]) ).

thf(7824,plain,
    ! [SV969: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV969 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV969 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6606]) ).

thf(7825,plain,
    ! [SV970: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV970 )
        = $false )
      | ( ( class_HOL_Oplus @ SV970 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6607]) ).

thf(7826,plain,
    ! [SV971: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV971 )
        = $false )
      | ( ( class_HOL_Ozero @ SV971 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6608]) ).

thf(7827,plain,
    ! [SV972: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV972 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV972 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6609]) ).

thf(7828,plain,
    ! [SV973: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV973 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV973 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6610]) ).

thf(7829,plain,
    ! [SV974: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV974 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV974 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6611]) ).

thf(7830,plain,
    ! [SV975: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV975 )
        = $false )
      | ( ( class_HOL_Oone @ SV975 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6612]) ).

thf(7831,plain,
    ! [SV976: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV976 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV976 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6613]) ).

thf(7832,plain,
    ! [SV977: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV977 )
        = $false )
      | ( ( class_HOL_Ominus @ SV977 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6614]) ).

thf(7833,plain,
    ! [SV978: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV978 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV978 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6615]) ).

thf(7834,plain,
    ! [SV979: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV979 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV979 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6616]) ).

thf(7835,plain,
    ! [SV980: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV980 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV980 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6617]) ).

thf(7836,plain,
    ! [SV981: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV981 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV981 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6618]) ).

thf(7837,plain,
    ! [SV982: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV982 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV982 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6619]) ).

thf(7838,plain,
    ! [SV983: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV983 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV983 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6620]) ).

thf(7839,plain,
    ! [SV984: $i] :
      ( ( ( class_Ring__and__Field_Oring__1 @ SV984 )
        = $false )
      | ( ( class_HOL_Otimes @ SV984 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6621]) ).

thf(7840,plain,
    ! [SV985: $i] :
      ( ( ( class_Ring__and__Field_Osemiring @ SV985 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV985 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6622]) ).

thf(7841,plain,
    ! [SV986: $i] :
      ( ( ( class_Ring__and__Field_Osemiring @ SV986 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV986 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6623]) ).

thf(7842,plain,
    ! [SV987: $i] :
      ( ( ( class_Ring__and__Field_Osemiring @ SV987 )
        = $false )
      | ( ( class_HOL_Oplus @ SV987 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6624]) ).

thf(7843,plain,
    ! [SV988: $i] :
      ( ( ( class_Ring__and__Field_Osemiring @ SV988 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV988 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6625]) ).

thf(7844,plain,
    ! [SV989: $i] :
      ( ( ( class_Ring__and__Field_Osemiring @ SV989 )
        = $false )
      | ( ( class_HOL_Otimes @ SV989 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6626]) ).

thf(7845,plain,
    ! [SV990: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV990 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV990 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6627]) ).

thf(7846,plain,
    ! [SV991: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV991 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV991 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6628]) ).

thf(7847,plain,
    ! [SV992: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV992 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV992 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6629]) ).

thf(7848,plain,
    ! [SV993: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV993 )
        = $false )
      | ( ( class_HOL_Oplus @ SV993 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6630]) ).

thf(7849,plain,
    ! [SV994: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV994 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV994 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6631]) ).

thf(7850,plain,
    ! [SV995: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV995 )
        = $false )
      | ( ( class_HOL_Otimes @ SV995 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6632]) ).

thf(7851,plain,
    ! [SV996: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV996 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV996 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6633]) ).

thf(7852,plain,
    ! [SV997: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0 @ SV997 )
        = $false )
      | ( ( class_HOL_Ozero @ SV997 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6634]) ).

thf(7853,plain,
    ! [SV998: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV998 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV998 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6635]) ).

thf(7854,plain,
    ! [SV999: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV999 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV999 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6636]) ).

thf(7855,plain,
    ! [SV1000: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1000 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV1000 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6637]) ).

thf(7856,plain,
    ! [SV1001: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1001 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV1001 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6638]) ).

thf(7857,plain,
    ! [SV1002: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1002 )
        = $false )
      | ( ( class_HOL_Otimes @ SV1002 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6639]) ).

thf(7858,plain,
    ! [SV1003: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1003 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1003 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6640]) ).

thf(7859,plain,
    ! [SV1004: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1004 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV1004 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6641]) ).

thf(7860,plain,
    ! [SV1005: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1005 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV1005 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6642]) ).

thf(7861,plain,
    ! [SV1006: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1006 )
        = $false )
      | ( ( class_HOL_Oplus @ SV1006 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6643]) ).

thf(7862,plain,
    ! [SV1007: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1007 )
        = $false )
      | ( ( class_HOL_Ozero @ SV1007 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6644]) ).

thf(7863,plain,
    ! [SV1008: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1008 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1008 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6645]) ).

thf(7864,plain,
    ! [SV1009: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1009 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1009 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6646]) ).

thf(7865,plain,
    ! [SV1010: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1010 )
        = $false )
      | ( ( class_HOL_Ozero @ SV1010 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6647]) ).

thf(7866,plain,
    ! [SV1011: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1011 )
        = $false )
      | ( ( class_HOL_Oplus @ SV1011 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6648]) ).

thf(7867,plain,
    ! [SV1012: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1012 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV1012 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6649]) ).

thf(7868,plain,
    ! [SV1013: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1013 )
        = $false )
      | ( ( class_HOL_Oone @ SV1013 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6650]) ).

thf(7869,plain,
    ! [SV1014: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1014 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV1014 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6651]) ).

thf(7870,plain,
    ! [SV1015: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1015 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV1015 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6652]) ).

thf(7871,plain,
    ! [SV1016: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1016 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV1016 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6653]) ).

thf(7872,plain,
    ! [SV1017: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1017 )
        = $false )
      | ( ( class_HOL_Otimes @ SV1017 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6654]) ).

thf(7873,plain,
    ! [SV1018: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1018 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1018 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6655]) ).

thf(7874,plain,
    ! [SV1019: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1019 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV1019 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6656]) ).

thf(7875,plain,
    ! [SV1020: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1 @ SV1020 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV1020 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6657]) ).

thf(7876,plain,
    ! [SV1021: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1021 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__1 @ SV1021 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6658]) ).

thf(7877,plain,
    ! [SV1022: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1022 )
        = $false )
      | ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1022 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6659]) ).

thf(7878,plain,
    ! [SV1023: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1023 )
        = $false )
      | ( ( class_HOL_Oone @ SV1023 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6660]) ).

thf(7879,plain,
    ! [SV1024: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1024 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__mult @ SV1024 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6661]) ).

thf(7880,plain,
    ! [SV1025: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1025 )
        = $false )
      | ( ( class_HOL_Otimes @ SV1025 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6662]) ).

thf(7881,plain,
    ! [SV1026: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1026 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1026 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6663]) ).

thf(7882,plain,
    ! [SV1027: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1027 )
        = $false )
      | ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV1027 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6664]) ).

thf(7883,plain,
    ! [SV1028: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1028 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1028 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6665]) ).

thf(7884,plain,
    ! [SV1029: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1029 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring__0 @ SV1029 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6666]) ).

thf(7885,plain,
    ! [SV1030: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1030 )
        = $false )
      | ( ( class_Ring__and__Field_Osemiring @ SV1030 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6667]) ).

thf(7886,plain,
    ! [SV1031: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1031 )
        = $false )
      | ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1031 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6668]) ).

thf(7887,plain,
    ! [SV1032: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1032 )
        = $false )
      | ( ( class_HOL_Ozero @ SV1032 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6669]) ).

thf(7888,plain,
    ! [SV1033: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1033 )
        = $false )
      | ( ( class_OrderedGroup_Oab__semigroup__add @ SV1033 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6670]) ).

thf(7889,plain,
    ! [SV1034: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1034 )
        = $false )
      | ( ( class_OrderedGroup_Osemigroup__add @ SV1034 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6671]) ).

thf(7890,plain,
    ! [SV1035: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1035 )
        = $false )
      | ( ( class_HOL_Oplus @ SV1035 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6672]) ).

thf(7891,plain,
    ! [SV1036: $i] :
      ( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1036 )
        = $false )
      | ( ( class_OrderedGroup_Omonoid__mult @ SV1036 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6673]) ).

thf(7892,plain,
    ! [SV1037: $i] :
      ( ( ( class_Wellfounded__Recursion_Owellorder @ SV1037 )
        = $false )
      | ( ( class_Orderings_Oord @ SV1037 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6674]) ).

thf(7893,plain,
    ! [SV1038: $i] :
      ( ( ( class_Wellfounded__Recursion_Owellorder @ SV1038 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV1038 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6675]) ).

thf(7894,plain,
    ! [SV1039: $i] :
      ( ( ( class_Wellfounded__Recursion_Owellorder @ SV1039 )
        = $false )
      | ( ( class_LOrder_Omeet__semilorder @ SV1039 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6676]) ).

thf(7895,plain,
    ! [SV1040: $i] :
      ( ( ( class_Wellfounded__Recursion_Owellorder @ SV1040 )
        = $false )
      | ( ( class_LOrder_Ojoin__semilorder @ SV1040 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6677]) ).

thf(7896,plain,
    ! [SV1041: $i] :
      ( ( ( class_Wellfounded__Recursion_Owellorder @ SV1041 )
        = $false )
      | ( ( class_LOrder_Olorder @ SV1041 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6678]) ).

thf(7897,plain,
    ! [SV1042: $i] :
      ( ( ( class_Wellfounded__Recursion_Owellorder @ SV1042 )
        = $false )
      | ( ( class_Orderings_Olinorder @ SV1042 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6679]) ).

thf(7898,plain,
    ! [SV1620: $i,SV1382: $i,SV1043: $i] :
      ( ( ~ ( c_in @ SV1043 @ ( c_Datatype_Oo2s @ SV1382 @ SV1620 ) @ SV1620 )
        | ( SV1382
          = ( c_Datatype_Ooption_OSome @ SV1043 @ SV1620 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6680]) ).

thf(7899,plain,
    ! [SV1621: $i,SV1045: $i] :
      ( ( ( SV1045
          = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ SV1045 @ SV1621 ) @ SV1621 ) )
        = $true )
      | ( ( SV1045 = c_Datatype_Ooption_ONone )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6682]) ).

thf(7900,plain,
    ! [SV1622: $i,SV1046: $i] :
      ( ( ( SV1046
          = ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ SV1046 @ SV1622 ) @ SV1622 ) )
        = $true )
      | ( ( SV1046 = c_Datatype_Ooption_ONone )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6683]) ).

thf(7901,plain,
    ! [SV1384: $i,SV1047: $i] :
      ( ( c_Datatype_Ooption_ONone
        = ( c_Datatype_Ooption_OSome @ SV1047 @ SV1384 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6684]) ).

thf(7902,plain,
    ! [SV1385: $i,SV1048: $i] :
      ( ( ( c_Datatype_Ooption_OSome @ SV1048 @ SV1385 )
        = c_Datatype_Ooption_ONone )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6685]) ).

thf(7903,plain,
    ! [SV1623: $i,SV1386: $i,SV1049: $i] :
      ( ( ( ( c_Datatype_Ooption_OSome @ SV1049 @ SV1386 )
         != ( c_Datatype_Ooption_OSome @ SV1623 @ SV1386 ) )
        | ( SV1049 = SV1623 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6686]) ).

thf(7904,plain,
    ! [SV1624: $i,SV1387: $i,SV1050: $i] :
      ( ( ! [SY3244: $i] :
            ( ( ( c_Datatype__Universe_OAtom @ SV1050 @ SV1387 @ SV1624 )
             != ( c_Datatype__Universe_OAtom @ SY3244 @ SV1387 @ SV1624 ) )
            | ( SV1050 = SY3244 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6687]) ).

thf(7905,plain,
    ! [SV1625: $i,SV1388: $i,SV1051: $i] :
      ( ( ! [SY3245: $i,SY3246: $i] :
            ( ( c_Datatype__Universe_OAtom @ SV1051 @ SV1388 @ SV1625 )
           != ( c_Datatype__Universe_OScons @ SY3245 @ SY3246 @ SV1388 @ SV1625 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6688]) ).

thf(7906,plain,
    ! [SV1626: $i,SV1389: $i,SV1052: $i] :
      ( ( ! [SY3247: $i] :
            ( ( ( c_Datatype__Universe_OIn0 @ SV1052 @ SV1389 @ SV1626 )
             != ( c_Datatype__Universe_OIn0 @ SY3247 @ SV1389 @ SV1626 ) )
            | ( SV1052 = SY3247 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6689]) ).

thf(7907,plain,
    ! [SV1627: $i,SV1390: $i,SV1053: $i] :
      ( ( ! [SY3248: $i] :
            ( ( c_Datatype__Universe_OIn0 @ SV1053 @ SV1390 @ SV1627 )
           != ( c_Datatype__Universe_OIn1 @ SY3248 @ SV1390 @ SV1627 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6690]) ).

thf(7908,plain,
    ! [SV1628: $i,SV1391: $i,SV1054: $i] :
      ( ( ! [SY3249: $i] :
            ( ( ( c_Datatype__Universe_OIn1 @ SV1054 @ SV1391 @ SV1628 )
             != ( c_Datatype__Universe_OIn1 @ SY3249 @ SV1391 @ SV1628 ) )
            | ( SV1054 = SY3249 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6691]) ).

thf(7909,plain,
    ! [SV1629: $i,SV1392: $i,SV1055: $i] :
      ( ( ! [SY3250: $i] :
            ( ( c_Datatype__Universe_OIn1 @ SV1055 @ SV1392 @ SV1629 )
           != ( c_Datatype__Universe_OIn0 @ SY3250 @ SV1392 @ SV1629 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6692]) ).

thf(7910,plain,
    ! [SV1630: $i,SV1393: $i,SV1056: $i] :
      ( ( ! [SY3251: $i] :
            ( ( c_Datatype__Universe_OLeaf @ SV1056 @ SV1393 @ SV1630 )
           != ( c_Datatype__Universe_ONumb @ SY3251 @ SV1393 @ SV1630 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6693]) ).

thf(7911,plain,
    ! [SV1631: $i,SV1394: $i,SV1057: $i] :
      ( ( ! [SY3252: $i,SY3253: $i] :
            ( ( c_Datatype__Universe_OLeaf @ SV1057 @ SV1394 @ SV1631 )
           != ( c_Datatype__Universe_OScons @ SY3252 @ SY3253 @ SV1394 @ SV1631 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6694]) ).

thf(7912,plain,
    ! [SV1632: $i,SV1395: $i,SV1058: $i] :
      ( ( ! [SY3254: $i] :
            ( ( c_Datatype__Universe_ONumb @ SV1058 @ SV1395 @ SV1632 )
           != ( c_Datatype__Universe_OLeaf @ SY3254 @ SV1395 @ SV1632 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6695]) ).

thf(7913,plain,
    ! [SV1633: $i,SV1396: $i,SV1059: $i] :
      ( ( ! [SY3255: $i,SY3256: $i] :
            ( ( c_Datatype__Universe_ONumb @ SV1059 @ SV1396 @ SV1633 )
           != ( c_Datatype__Universe_OScons @ SY3255 @ SY3256 @ SV1396 @ SV1633 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6696]) ).

thf(7914,plain,
    ! [SV1634: $i,SV1397: $i,SV1060: $i] :
      ( ( ! [SY3257: $i,SY3258: $i] :
            ( ! [SY3259: $i] :
                ( ( c_Datatype__Universe_OScons @ SV1060 @ SV1397 @ SV1634 @ SY3257 )
               != ( c_Datatype__Universe_OScons @ SY3258 @ SY3259 @ SV1634 @ SY3257 ) )
            | ( SV1060 = SY3258 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6697]) ).

thf(7915,plain,
    ! [SV1635: $i,SV1398: $i,SV1061: $i] :
      ( ( ! [SY3260: $i,SY3261: $i,SY3262: $i] :
            ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SV1398 @ SV1635 @ SY3260 )
             != ( c_Datatype__Universe_OScons @ SY3261 @ SY3262 @ SV1635 @ SY3260 ) )
            | ( SV1398 = SY3262 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6698]) ).

thf(7916,plain,
    ! [SV1636: $i,SV1399: $i,SV1062: $i] :
      ( ( ! [SY3263: $i,SY3264: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1062 @ SV1399 @ SV1636 @ SY3263 )
           != ( c_Datatype__Universe_OAtom @ SY3264 @ SV1636 @ SY3263 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6699]) ).

thf(7917,plain,
    ! [SV1637: $i,SV1400: $i,SV1063: $i] :
      ( ( ! [SY3265: $i,SY3266: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1063 @ SV1400 @ SV1637 @ SY3265 )
           != ( c_Datatype__Universe_OLeaf @ SY3266 @ SV1637 @ SY3265 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6700]) ).

thf(7918,plain,
    ! [SV1638: $i,SV1401: $i,SV1064: $i] :
      ( ( ! [SY3267: $i,SY3268: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1064 @ SV1401 @ SV1638 @ SY3267 )
           != ( c_Datatype__Universe_ONumb @ SY3268 @ SV1638 @ SY3267 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6701]) ).

thf(7919,plain,
    ! [SV1065: $i] :
      ( ( ( c_Divides_Oop_Advd @ c_0 @ SV1065 @ tc_nat )
        = $false )
      | ( ( SV1065 = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6702]) ).

thf(7920,plain,
    ! [SV1639: $i,SV1066: $i] :
      ( ( ( ! [SY3269: $i] :
              ( c_emptyset
             != ( c_Equiv__Relations_Oquotient @ SV1066 @ SV1639 @ SY3269 ) ) )
        = $true )
      | ( ( SV1066 = c_emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6703]) ).

thf(7921,plain,
    ! [SV1640: $i,SV1068: $i] :
      ( ( ( ! [SY3270: $i] :
              ( ( c_Equiv__Relations_Oquotient @ SV1068 @ SV1640 @ SY3270 )
             != c_emptyset ) )
        = $true )
      | ( ( SV1068 = c_emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6705]) ).

thf(7922,plain,
    ! [SV1641: $i,SV1404: $i,SV1070: $i] :
      ( ( ! [SY3271: $i] :
            ( ~ ( c_in @ ( c_minus @ SV1070 @ ( c_insert @ SV1404 @ SV1641 @ SY3271 ) @ ( tc_set @ SY3271 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY3271 ) )
            | ( c_in @ ( c_minus @ SV1070 @ SV1641 @ ( tc_set @ SY3271 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY3271 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6707]) ).

thf(7923,plain,
    ! [SV1642: $i,SV1405: $i,SV1071: $i] :
      ( ( ~ ( c_in @ ( c_minus @ SV1071 @ SV1405 @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) )
        | ! [SY3272: $i] : ( c_in @ ( c_minus @ SV1071 @ ( c_insert @ SY3272 @ SV1405 @ SV1642 ) @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6708]) ).

thf(7924,plain,
    ! [SV1406: $i,SV1072: $i] :
      ( ( ( ~ ( c_in @ ( c_Pow @ SV1072 @ SV1406 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1406 ) ) ) )
        = $true )
      | ( ( c_in @ SV1072 @ c_Finite__Set_OFinites @ ( tc_set @ SV1406 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6709]) ).

thf(7925,plain,
    ! [SV1407: $i,SV1073: $i] :
      ( ( ( ~ ( c_in @ SV1073 @ c_Finite__Set_OFinites @ ( tc_set @ SV1407 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pow @ SV1073 @ SV1407 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1407 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6710]) ).

thf(7926,plain,
    ! [SV1643: $i,SV1408: $i,SV1074: $i] :
      ( ( ~ ( c_in @ ( c_union @ SV1074 @ SV1408 @ SV1643 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1643 ) )
        | ( c_in @ SV1074 @ c_Finite__Set_OFinites @ ( tc_set @ SV1643 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6711]) ).

thf(7927,plain,
    ! [SV1644: $i,SV1409: $i,SV1075: $i] :
      ( ( ~ ( c_in @ ( c_union @ SV1075 @ SV1409 @ SV1644 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1644 ) )
        | ( c_in @ SV1409 @ c_Finite__Set_OFinites @ ( tc_set @ SV1644 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6712]) ).

thf(7928,plain,
    ! [SV1410: $i,SV1076: $i] :
      ( ( ( ~ ( c_in @ SV1076 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) ) )
        = $true )
      | ( ( ! [SY2981: $i] :
              ( ~ ( c_in @ SY2981 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
              | ( c_in @ ( c_union @ SY2981 @ SV1076 @ SV1410 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6713]) ).

thf(7929,plain,
    ! [SV1645: $i,SV1411: $i,SV1077: $i] :
      ( ( ~ ( c_in @ ( c_Relation_Oconverse @ SV1077 @ SV1411 @ SV1645 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1645 @ SV1411 ) ) )
        | ( c_in @ SV1077 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1411 @ SV1645 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6714]) ).

thf(7930,plain,
    ! [SV1646: $i,SV1412: $i,SV1078: $i] :
      ( ( ~ ( c_in @ SV1078 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1412 @ SV1646 ) ) )
        | ( c_in @ ( c_Relation_Oconverse @ SV1078 @ SV1412 @ SV1646 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1646 @ SV1412 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6715]) ).

thf(7931,plain,
    ! [SV1413: $i,SV1079: $i] :
      ( ( ( ! [SY2984: $i] :
              ~ ( c_Divides_Oop_Advd @ SV1079 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1413 @ SY2984 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1079 @ SV1413 @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6716]) ).

thf(7932,plain,
    ! [SV1647: $i,SV1414: $i,SV1080: $i] :
      ( ( ~ ( c_Divides_Oop_Advd @ SV1080 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1414 @ SV1647 @ tc_nat @ tc_nat ) ) @ tc_nat )
        | ( c_Divides_Oop_Advd @ SV1080 @ SV1647 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6717]) ).

thf(7933,plain,
    ! [SV1415: $i,SV1081: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SV1415 @ tc_nat ) )
        = $true )
      | ( ( ! [SY2986: $i] :
              ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SY2986 @ tc_nat )
              | ( c_Divides_Oop_Advd @ SV1081 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2986 @ SV1415 @ tc_nat @ tc_nat ) ) @ tc_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6718]) ).

thf(7934,plain,
    ! [SV1416: $i,SV1082: $i] :
      ( ( ( ( c_IntDef_Oint @ SV1082 )
         != ( c_IntDef_Oint @ SV1416 ) )
        = $true )
      | ( ( SV1082 = SV1416 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6719]) ).

thf(7935,plain,
    ! [SV1417: $i,SV1083: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1083 @ ( c_uminus @ SV1417 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1083 @ SV1417 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6720]) ).

thf(7936,plain,
    ! [SV1418: $i,SV1084: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1084 @ SV1418 @ tc_IntDef_Oint ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1084 @ ( c_uminus @ SV1418 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6721]) ).

thf(7937,plain,
    ! [SV1085: $i] :
      ( ( ( c_Divides_Oop_Advd @ c_0 @ SV1085 @ tc_IntDef_Oint )
        = $false )
      | ( ( SV1085 = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6722]) ).

thf(7938,plain,
    ! [SV1419: $i,SV1086: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ SV1086 @ tc_IntDef_Oint ) @ SV1419 @ tc_IntDef_Oint ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1086 @ SV1419 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6723]) ).

thf(7939,plain,
    ! [SV1420: $i,SV1087: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1087 @ SV1420 @ tc_IntDef_Oint ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ ( c_uminus @ SV1087 @ tc_IntDef_Oint ) @ SV1420 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6724]) ).

thf(7940,plain,
    ! [SV1648: $i,SV1421: $i,SV1088: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV1088 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1421 ) @ ( tc_List_Olist @ SV1421 ) ) @ ( c_List_Olex @ SV1648 @ SV1421 ) @ ( tc_prod @ ( tc_List_Olist @ SV1421 ) @ ( tc_List_Olist @ SV1421 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6725]) ).

thf(7941,plain,
    ! [SV1649: $i,SV1089: $i] :
      ( ( ( ! [SY3273: $i] :
              ( c_List_Olist_ONil
             != ( c_append @ SV1089 @ SV1649 @ SY3273 ) ) )
        = $true )
      | ( ( SV1089 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6726]) ).

thf(7942,plain,
    ! [SV1422: $i,SV1090: $i] :
      ( ( ( ! [SY2988: $i] :
              ( c_List_Olist_ONil
             != ( c_append @ SV1090 @ SV1422 @ SY2988 ) ) )
        = $true )
      | ( ( SV1422 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6727]) ).

thf(7943,plain,
    ! [SV1650: $i,SV1092: $i] :
      ( ( ( c_List_Olist_ONil
         != ( c_List_Orev @ SV1092 @ SV1650 ) )
        = $true )
      | ( ( SV1092 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6728]) ).

thf(7944,plain,
    ! [SV1651: $i,SV1423: $i,SV1094: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1094 @ ( tc_List_Olist @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) @ ( c_List_Olex @ SV1651 @ SV1423 ) @ ( tc_prod @ ( tc_List_Olist @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6729]) ).

thf(7945,plain,
    ! [SV1652: $i,SV1424: $i,SV1095: $i] :
      ( ( ! [SY3274: $i] :
            ( ! [SY3275: $i] :
                ( ( c_append @ SV1095 @ ( c_List_Olist_OCons @ SV1424 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 )
               != ( c_append @ SY3274 @ ( c_List_Olist_OCons @ SY3275 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 ) )
            | ( SV1095 = SY3274 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6730]) ).

thf(7946,plain,
    ! [SV1653: $i,SV1425: $i,SV1096: $i] :
      ( ( ! [SY3276: $i,SY3277: $i] :
            ( ( ( c_append @ SV1096 @ ( c_List_Olist_OCons @ SV1425 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 )
             != ( c_append @ SY3276 @ ( c_List_Olist_OCons @ SY3277 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 ) )
            | ( SV1425 = SY3277 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6731]) ).

thf(7947,plain,
    ! [SV1654: $i,SV1426: $i,SV1097: $i] :
      ( ( ! [SY3278: $i] :
            ( ~ ( c_in @ ( c_append @ SV1097 @ SV1426 @ SV1654 ) @ ( c_List_Olists @ SY3278 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) )
            | ( c_in @ SV1097 @ ( c_List_Olists @ SY3278 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6732]) ).

thf(7948,plain,
    ! [SV1655: $i,SV1427: $i,SV1098: $i] :
      ( ( ! [SY3279: $i] :
            ( ~ ( c_in @ ( c_append @ SV1098 @ SV1427 @ SV1655 ) @ ( c_List_Olists @ SY3279 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) )
            | ( c_in @ SV1427 @ ( c_List_Olists @ SY3279 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6733]) ).

thf(7949,plain,
    ! [SV1656: $i,SV1428: $i,SV1099: $i] :
      ( ( ~ ( c_in @ SV1099 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        | ! [SY3280: $i] :
            ( ~ ( c_in @ SY3280 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
            | ( c_in @ ( c_append @ SY3280 @ SV1099 @ SV1656 ) @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6734]) ).

thf(7950,plain,
    ! [SV1657: $i,SV1100: $i] :
      ( ( ( ! [SY3281: $i] :
              ( ( c_append @ SV1100 @ SV1657 @ SY3281 )
             != c_List_Olist_ONil ) )
        = $true )
      | ( ( SV1100 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6735]) ).

thf(7951,plain,
    ! [SV1429: $i,SV1101: $i] :
      ( ( ( ! [SY3002: $i] :
              ( ( c_append @ SV1101 @ SV1429 @ SY3002 )
             != c_List_Olist_ONil ) )
        = $true )
      | ( ( SV1429 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6736]) ).

thf(7952,plain,
    ! [SV1658: $i,SV1430: $i,SV1103: $i] :
      ( ( ! [SY3282: $i] :
            ( ( ( c_append @ SV1103 @ SV1430 @ SV1658 )
             != ( c_append @ SY3282 @ SV1430 @ SV1658 ) )
            | ( SV1103 = SY3282 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6737]) ).

thf(7953,plain,
    ! [SV1659: $i,SV1104: $i] :
      ( ( ( ! [SY3283: $i] :
              ( ( c_append @ SV1104 @ SV1659 @ SY3283 )
             != SV1659 ) )
        = $true )
      | ( ( SV1104 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6738]) ).

thf(7954,plain,
    ! [SV1432: $i,SV1106: $i] :
      ( ( ( ! [SY3005: $i] :
              ( ( c_append @ SV1106 @ SV1432 @ SY3005 )
             != SV1106 ) )
        = $true )
      | ( ( SV1432 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6740]) ).

thf(7955,plain,
    ! [SV1660: $i,SV1434: $i,SV1108: $i] :
      ( ( ! [SY3284: $i] :
            ( ( c_List_Ochar_OChar @ SV1108 @ SV1434 )
           != ( c_List_Ochar_OChar @ SV1660 @ SY3284 ) )
        | ( SV1108 = SV1660 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6742]) ).

thf(7956,plain,
    ! [SV1661: $i,SV1435: $i,SV1109: $i] :
      ( ( ! [SY3285: $i] :
            ( ( ( c_List_Ochar_OChar @ SV1109 @ SV1435 )
             != ( c_List_Ochar_OChar @ SV1661 @ SY3285 ) )
            | ( SV1435 = SY3285 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6743]) ).

thf(7957,plain,
    ! [SV1662: $i,SV1110: $i] :
      ( ( ( ( c_Nat_Osize @ SV1110 @ ( tc_List_Olist @ SV1662 ) )
         != c_0 )
        = $true )
      | ( ( SV1110 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6744]) ).

thf(7958,plain,
    ! [SV1663: $i,SV1113: $i] :
      ( ( ( c_less @ c_0 @ ( c_Nat_Osize @ SV1113 @ ( tc_List_Olist @ SV1663 ) ) @ tc_nat )
        = $true )
      | ( ( SV1113 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6746]) ).

thf(7959,plain,
    ! [SV1436: $i,SV1114: $i] :
      ( ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1114 @ SV1436 ) @ ( tc_List_Olist @ SV1436 ) )
         != ( c_Nat_Osize @ SV1114 @ ( tc_List_Olist @ SV1436 ) ) )
        = $true )
      | ( ( ( c_List_Oremdups @ SV1114 @ SV1436 )
          = SV1114 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6747]) ).

thf(7960,plain,
    ! [SV1437: $i,SV1115: $i] :
      ( ( ( ( c_List_Oremdups @ SV1115 @ SV1437 )
         != SV1115 )
        = $true )
      | ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1115 @ SV1437 ) @ ( tc_List_Olist @ SV1437 ) )
          = ( c_Nat_Osize @ SV1115 @ ( tc_List_Olist @ SV1437 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6748]) ).

thf(7961,plain,
    ! [SV1664: $i,SV1438: $i,SV1116: $i] :
      ( ( c_List_Olist_ONil
       != ( c_List_Olist_OCons @ SV1116 @ SV1438 @ SV1664 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6749]) ).

thf(7962,plain,
    ! [SV1665: $i,SV1439: $i,SV1117: $i] :
      ( ( ( c_List_Olist_OCons @ SV1117 @ SV1439 @ SV1665 )
       != c_List_Olist_ONil )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6750]) ).

thf(7963,plain,
    ! [SV1666: $i,SV1440: $i,SV1118: $i] :
      ( ( ! [SY3286: $i] :
            ( ! [SY3287: $i] :
                ( ( c_List_Olist_OCons @ SV1118 @ SV1440 @ SV1666 )
               != ( c_List_Olist_OCons @ SY3286 @ SY3287 @ SV1666 ) )
            | ( SV1118 = SY3286 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6751]) ).

thf(7964,plain,
    ! [SV1667: $i,SV1441: $i,SV1119: $i] :
      ( ( ! [SY3288: $i,SY3289: $i] :
            ( ( ( c_List_Olist_OCons @ SV1119 @ SV1441 @ SV1667 )
             != ( c_List_Olist_OCons @ SY3288 @ SY3289 @ SV1667 ) )
            | ( SV1441 = SY3289 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6752]) ).

thf(7965,plain,
    ! [SV1668: $i,SV1442: $i,SV1120: $i] :
      ( ( ! [SY3290: $i] :
            ( ( ( c_List_Orev @ SV1120 @ SV1442 )
             != ( c_List_Olist_OCons @ SV1668 @ SY3290 @ SV1442 ) )
            | ( SV1120
              = ( c_append @ ( c_List_Orev @ SY3290 @ SV1442 ) @ ( c_List_Olist_OCons @ SV1668 @ c_List_Olist_ONil @ SV1442 ) @ SV1442 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6753]) ).

thf(7966,plain,
    ! [SV1669: $i,SV1443: $i,SV1121: $i] :
      ( ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ SV1121 @ SV1443 ) @ ( c_List_Olist_OCons @ SV1669 @ c_List_Olist_ONil @ SV1443 ) @ SV1443 ) @ SV1443 )
        = ( c_List_Olist_OCons @ SV1669 @ SV1121 @ SV1443 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6754]) ).

thf(7967,plain,
    ! [SV1670: $i,SV1122: $i] :
      ( ( ( ( c_List_Orev @ SV1122 @ SV1670 )
         != c_List_Olist_ONil )
        = $true )
      | ( ( SV1122 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6755]) ).

thf(7968,plain,
    ! [SV1671: $i,SV1444: $i,SV1124: $i] :
      ( ( ( ( c_List_Orev @ SV1124 @ SV1444 )
         != ( c_List_Orev @ SV1671 @ SV1444 ) )
        | ( SV1124 = SV1671 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6756]) ).

thf(7969,plain,
    ! [SV1672: $i,SV1445: $i,SV1125: $i] :
      ( ( ! [SY3291: $i] :
            ( ( ( c_append @ SV1125 @ SV1445 @ SV1672 )
             != ( c_append @ SV1125 @ SY3291 @ SV1672 ) )
            | ( SV1445 = SY3291 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6757]) ).

thf(7970,plain,
    ! [SV1446: $i,SV1126: $i] :
      ( ( ( ! [SY3024: $i] :
              ( SV1126
             != ( c_append @ SV1446 @ SV1126 @ SY3024 ) ) )
        = $true )
      | ( ( SV1446 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6758]) ).

thf(7971,plain,
    ! [SV1448: $i,SV1128: $i] :
      ( ( ( ! [SY3025: $i] :
              ( SV1128
             != ( c_append @ SV1128 @ SV1448 @ SY3025 ) ) )
        = $true )
      | ( ( SV1448 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6760]) ).

thf(7972,plain,
    ! [SV1673: $i,SV1130: $i] :
      ( ( ( c_emptyset
         != ( c_List_Oset @ SV1130 @ SV1673 ) )
        = $true )
      | ( ( SV1130 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6762]) ).

thf(7973,plain,
    ! [SV1674: $i,SV1132: $i] :
      ( ( ( ( c_List_Oset @ SV1132 @ SV1674 )
         != c_emptyset )
        = $true )
      | ( ( SV1132 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6763]) ).

thf(7974,plain,
    ! [SV1450: $i,SV1134: $i] :
      ( ( ( ( c_Suc @ SV1134 )
         != ( c_Suc @ SV1450 ) )
        = $true )
      | ( ( SV1134 = SV1450 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6764]) ).

thf(7975,plain,
    ! [SV1451: $i,SV1135: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_Suc @ SV1135 ) @ ( c_Suc @ SV1451 ) @ tc_nat ) )
        = $true )
      | ( ( c_lessequals @ SV1135 @ SV1451 @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6765]) ).

thf(7976,plain,
    ! [SV1452: $i,SV1136: $i] :
      ( ( ( ~ ( c_lessequals @ SV1136 @ SV1452 @ tc_nat ) )
        = $true )
      | ( ( c_lessequals @ ( c_Suc @ SV1136 ) @ ( c_Suc @ SV1452 ) @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6766]) ).

thf(7977,plain,
    ! [SV1453: $i,SV1137: $i] :
      ( ( ( ~ ( c_less @ ( c_Suc @ SV1137 ) @ ( c_Suc @ SV1453 ) @ tc_nat ) )
        = $true )
      | ( ( c_less @ SV1137 @ SV1453 @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6767]) ).

thf(7978,plain,
    ! [SV1454: $i,SV1138: $i] :
      ( ( ( ~ ( c_less @ SV1138 @ SV1454 @ tc_nat ) )
        = $true )
      | ( ( c_less @ ( c_Suc @ SV1138 ) @ ( c_Suc @ SV1454 ) @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6768]) ).

thf(7979,plain,
    ! [SV1455: $i,SV1141: $i] :
      ( ( ( ~ ( c_less @ c_0 @ ( c_plus @ SV1141 @ SV1455 @ tc_nat ) @ tc_nat ) )
        = $true )
      | ( ( ( c_less @ c_0 @ SV1455 @ tc_nat )
          | ( c_less @ c_0 @ SV1141 @ tc_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6771]) ).

thf(7980,plain,
    ! [SV1142: $i] :
      ( ( ( c_less @ c_0 @ SV1142 @ tc_nat )
        = $false )
      | ( ( ! [SY2499: $i] : ( c_less @ c_0 @ ( c_plus @ SV1142 @ SY2499 @ tc_nat ) @ tc_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6772]) ).

thf(7981,plain,
    ! [SV1143: $i] :
      ( ( ( c_less @ c_0 @ SV1143 @ tc_nat )
        = $false )
      | ( ( ! [SY2500: $i] : ( c_less @ c_0 @ ( c_plus @ SY2500 @ SV1143 @ tc_nat ) @ tc_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6773]) ).

thf(7982,plain,
    ! [SV1675: $i,SV1144: $i] :
      ( ( ( ( c_plus @ SV1144 @ SV1675 @ tc_nat )
         != c_0 )
        = $true )
      | ( ( SV1144 = c_0 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6774]) ).

thf(7983,plain,
    ! [SV1456: $i,SV1145: $i] :
      ( ( ( ( c_plus @ SV1145 @ SV1456 @ tc_nat )
         != c_0 )
        = $true )
      | ( ( SV1456 = c_0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6775]) ).

thf(7984,plain,
    ! [SV1146: $i] :
      ( ( ( c_lessequals @ SV1146 @ c_0 @ tc_nat )
        = $false )
      | ( ( SV1146 = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6776]) ).

thf(7985,plain,
    ! [SV1147: $i] :
      ( ( ( c_less @ SV1147 @ ( c_Suc @ c_0 ) @ tc_nat )
        = $false )
      | ( ( SV1147 = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6777]) ).

thf(7986,plain,
    ! [SV1148: $i] :
      ( ( ( c_less @ SV1148 @ c_1 @ tc_nat )
        = $false )
      | ( ( SV1148 = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6778]) ).

thf(7987,plain,
    ! [SV1457: $i,SV1150: $i] :
      ( ( c_less @ ( c_plus @ SV1150 @ SV1457 @ tc_nat ) @ SV1150 @ tc_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6780]) ).

thf(7988,plain,
    ! [SV1458: $i,SV1151: $i] :
      ( ( c_less @ ( c_plus @ SV1151 @ SV1458 @ tc_nat ) @ SV1458 @ tc_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6781]) ).

thf(7989,plain,
    ! [SV1153: $i] :
      ( ( ( class_Orderings_Oorder @ SV1153 )
        = $false )
      | ( ( ! [SY2505: $i] :
              ~ ( c_less @ SY2505 @ SY2505 @ SV1153 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6783]) ).

thf(7990,plain,
    ! [SV1676: $i,SV1459: $i,SV1154: $i] :
      ( ( ! [SY3292: $i,SY3293: $i] :
            ( ! [SY3294: $i] :
                ( ( c_Pair @ SV1154 @ SV1459 @ SV1676 @ SY3292 )
               != ( c_Pair @ SY3293 @ SY3294 @ SV1676 @ SY3292 ) )
            | ( SV1154 = SY3293 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6784]) ).

thf(7991,plain,
    ! [SV1677: $i,SV1460: $i,SV1155: $i] :
      ( ( ! [SY3295: $i,SY3296: $i,SY3297: $i] :
            ( ( ( c_Pair @ SV1155 @ SV1460 @ SV1677 @ SY3295 )
             != ( c_Pair @ SY3296 @ SY3297 @ SV1677 @ SY3295 ) )
            | ( SV1460 = SY3297 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6785]) ).

thf(7992,plain,
    ! [SV1678: $i,SV1462: $i,SV1157: $i] :
      ( ( ! [SY3298: $i,SY3299: $i] :
            ( ~ ( c_in @ SV1157 @ ( c_Relation_OImage @ SV1462 @ ( c_insert @ SV1678 @ c_emptyset @ SY3298 ) @ SY3298 @ SY3299 ) @ SY3299 )
            | ( c_in @ ( c_Pair @ SV1678 @ SV1157 @ SY3298 @ SY3299 ) @ SV1462 @ ( tc_prod @ SY3298 @ SY3299 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6787]) ).

thf(7993,plain,
    ! [SV1679: $i,SV1463: $i,SV1158: $i] :
      ( ( ! [SY3300: $i,SY3301: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1158 @ SV1463 @ SV1679 @ SY3300 ) @ SY3301 @ ( tc_prod @ SV1679 @ SY3300 ) )
            | ( c_in @ SV1463 @ ( c_Relation_OImage @ SY3301 @ ( c_insert @ SV1158 @ c_emptyset @ SV1679 ) @ SV1679 @ SY3300 ) @ SY3300 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6788]) ).

thf(7994,plain,
    ! [SV1680: $i,SV1464: $i,SV1159: $i] :
      ( ( ! [SY3302: $i,SY3303: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1159 @ SV1464 @ SV1680 @ SY3302 ) @ ( c_Relation_Oconverse @ SY3303 @ SY3302 @ SV1680 ) @ ( tc_prod @ SV1680 @ SY3302 ) )
            | ( c_in @ ( c_Pair @ SV1464 @ SV1159 @ SY3302 @ SV1680 ) @ SY3303 @ ( tc_prod @ SY3302 @ SV1680 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6789]) ).

thf(7995,plain,
    ! [SV1681: $i,SV1465: $i,SV1160: $i] :
      ( ( ! [SY3304: $i,SY3305: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1160 @ SV1465 @ SV1681 @ SY3304 ) @ SY3305 @ ( tc_prod @ SV1681 @ SY3304 ) )
            | ( c_in @ ( c_Pair @ SV1465 @ SV1160 @ SY3304 @ SV1681 ) @ ( c_Relation_Oconverse @ SY3305 @ SV1681 @ SY3304 ) @ ( tc_prod @ SY3304 @ SV1681 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6790]) ).

thf(7996,plain,
    ! [SV1466: $i,SV1161: $i] :
      ( ( ( ! [SY3046: $i] :
              ~ ( c_in @ ( c_Pair @ SV1161 @ SV1466 @ SY3046 @ SY3046 ) @ c_Relation_OId @ ( tc_prod @ SY3046 @ SY3046 ) ) )
        = $true )
      | ( ( SV1161 = SV1466 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6791]) ).

thf(7997,plain,
    ! [SV1162: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1162 )
        = $false )
      | ( ( ! [SY2535: $i,SY2536: $i] :
              ( ( ( c_SetInterval_OatLeast @ SY2535 @ SV1162 )
               != ( c_SetInterval_OatLeast @ SY2536 @ SV1162 ) )
              | ( SY2535 = SY2536 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6792]) ).

thf(7998,plain,
    ! [SV1163: $i] :
      ( ( ( class_Orderings_Oord @ SV1163 )
        = $false )
      | ( ( ! [SY2537: $i,SY2538: $i] :
              ( ~ ( c_in @ SY2537 @ ( c_SetInterval_OatLeast @ SY2538 @ SV1163 ) @ SV1163 )
              | ( c_lessequals @ SY2538 @ SY2537 @ SV1163 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6793]) ).

thf(7999,plain,
    ! [SV1164: $i] :
      ( ( ( class_Orderings_Oord @ SV1164 )
        = $false )
      | ( ( ! [SY2539: $i,SY2540: $i] :
              ( ~ ( c_lessequals @ SY2539 @ SY2540 @ SV1164 )
              | ( c_in @ SY2540 @ ( c_SetInterval_OatLeast @ SY2539 @ SV1164 ) @ SV1164 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6794]) ).

thf(8000,plain,
    ! [SV1165: $i] :
      ( ( ( class_Orderings_Oorder @ SV1165 )
        = $false )
      | ( ( ! [SY2541: $i,SY2542: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2541 @ SV1165 ) @ ( c_SetInterval_OatLeast @ SY2542 @ SV1165 ) @ ( tc_set @ SV1165 ) )
              | ( c_lessequals @ SY2542 @ SY2541 @ SV1165 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6795]) ).

thf(8001,plain,
    ! [SV1166: $i] :
      ( ( ( class_Orderings_Oorder @ SV1166 )
        = $false )
      | ( ( ! [SY2543: $i,SY2544: $i] :
              ( ~ ( c_lessequals @ SY2543 @ SY2544 @ SV1166 )
              | ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2544 @ SV1166 ) @ ( c_SetInterval_OatLeast @ SY2543 @ SV1166 ) @ ( tc_set @ SV1166 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6796]) ).

thf(8002,plain,
    ! [SV1167: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1167 )
        = $false )
      | ( ( ! [SY2545: $i,SY2546: $i] :
              ( ( ( c_SetInterval_OatMost @ SY2545 @ SV1167 )
               != ( c_SetInterval_OatMost @ SY2546 @ SV1167 ) )
              | ( SY2545 = SY2546 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6797]) ).

thf(8003,plain,
    ! [SV1168: $i] :
      ( ( ( class_Orderings_Oord @ SV1168 )
        = $false )
      | ( ( ! [SY2547: $i,SY2548: $i] :
              ( ~ ( c_in @ SY2547 @ ( c_SetInterval_OatMost @ SY2548 @ SV1168 ) @ SV1168 )
              | ( c_lessequals @ SY2547 @ SY2548 @ SV1168 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6798]) ).

thf(8004,plain,
    ! [SV1169: $i] :
      ( ( ( class_Orderings_Oord @ SV1169 )
        = $false )
      | ( ( ! [SY2549: $i,SY2550: $i] :
              ( ~ ( c_lessequals @ SY2549 @ SY2550 @ SV1169 )
              | ( c_in @ SY2549 @ ( c_SetInterval_OatMost @ SY2550 @ SV1169 ) @ SV1169 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6799]) ).

thf(8005,plain,
    ! [SV1170: $i] :
      ( ( ( class_Orderings_Oorder @ SV1170 )
        = $false )
      | ( ( ! [SY2551: $i,SY2552: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SY2551 @ SV1170 ) @ ( c_SetInterval_OatMost @ SY2552 @ SV1170 ) @ ( tc_set @ SV1170 ) )
              | ( c_lessequals @ SY2551 @ SY2552 @ SV1170 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6800]) ).

thf(8006,plain,
    ! [SV1171: $i] :
      ( ( ( class_Orderings_Oorder @ SV1171 )
        = $false )
      | ( ( ! [SY2553: $i,SY2554: $i] :
              ( ~ ( c_lessequals @ SY2553 @ SY2554 @ SV1171 )
              | ( c_lessequals @ ( c_SetInterval_OatMost @ SY2553 @ SV1171 ) @ ( c_SetInterval_OatMost @ SY2554 @ SV1171 ) @ ( tc_set @ SV1171 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6801]) ).

thf(8007,plain,
    ! [SV1172: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1172 )
        = $false )
      | ( ( ! [SY2555: $i,SY2556: $i] :
              ( ( ( c_SetInterval_OgreaterThan @ SY2555 @ SV1172 )
               != ( c_SetInterval_OgreaterThan @ SY2556 @ SV1172 ) )
              | ( SY2555 = SY2556 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6802]) ).

thf(8008,plain,
    ! [SV1173: $i] :
      ( ( ( class_Orderings_Oord @ SV1173 )
        = $false )
      | ( ( ! [SY2557: $i,SY2558: $i] :
              ( ~ ( c_in @ SY2557 @ ( c_SetInterval_OgreaterThan @ SY2558 @ SV1173 ) @ SV1173 )
              | ( c_less @ SY2558 @ SY2557 @ SV1173 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6803]) ).

thf(8009,plain,
    ! [SV1174: $i] :
      ( ( ( class_Orderings_Oord @ SV1174 )
        = $false )
      | ( ( ! [SY2559: $i,SY2560: $i] :
              ( ~ ( c_less @ SY2559 @ SY2560 @ SV1174 )
              | ( c_in @ SY2560 @ ( c_SetInterval_OgreaterThan @ SY2559 @ SV1174 ) @ SV1174 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6804]) ).

thf(8010,plain,
    ! [SV1175: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1175 )
        = $false )
      | ( ( ! [SY2561: $i,SY2562: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2561 @ SV1175 ) @ ( c_SetInterval_OgreaterThan @ SY2562 @ SV1175 ) @ ( tc_set @ SV1175 ) )
              | ( c_lessequals @ SY2562 @ SY2561 @ SV1175 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6805]) ).

thf(8011,plain,
    ! [SV1176: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1176 )
        = $false )
      | ( ( ! [SY2563: $i,SY2564: $i] :
              ( ~ ( c_lessequals @ SY2563 @ SY2564 @ SV1176 )
              | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2564 @ SV1176 ) @ ( c_SetInterval_OgreaterThan @ SY2563 @ SV1176 ) @ ( tc_set @ SV1176 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6806]) ).

thf(8012,plain,
    ! [SV1177: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1177 )
        = $false )
      | ( ( ! [SY2565: $i,SY2566: $i] :
              ( ( ( c_SetInterval_OlessThan @ SY2565 @ SV1177 )
               != ( c_SetInterval_OlessThan @ SY2566 @ SV1177 ) )
              | ( SY2565 = SY2566 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6807]) ).

thf(8013,plain,
    ! [SV1178: $i] :
      ( ( ( class_Orderings_Oord @ SV1178 )
        = $false )
      | ( ( ! [SY2567: $i,SY2568: $i] :
              ( ~ ( c_in @ SY2567 @ ( c_SetInterval_OlessThan @ SY2568 @ SV1178 ) @ SV1178 )
              | ( c_less @ SY2567 @ SY2568 @ SV1178 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6808]) ).

thf(8014,plain,
    ! [SV1179: $i] :
      ( ( ( class_Orderings_Oord @ SV1179 )
        = $false )
      | ( ( ! [SY2569: $i,SY2570: $i] :
              ( ~ ( c_less @ SY2569 @ SY2570 @ SV1179 )
              | ( c_in @ SY2569 @ ( c_SetInterval_OlessThan @ SY2570 @ SV1179 ) @ SV1179 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6809]) ).

thf(8015,plain,
    ! [SV1180: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1180 )
        = $false )
      | ( ( ! [SY2571: $i,SY2572: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2571 @ SV1180 ) @ ( c_SetInterval_OlessThan @ SY2572 @ SV1180 ) @ ( tc_set @ SV1180 ) )
              | ( c_lessequals @ SY2571 @ SY2572 @ SV1180 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6810]) ).

thf(8016,plain,
    ! [SV1181: $i] :
      ( ( ( class_Orderings_Olinorder @ SV1181 )
        = $false )
      | ( ( ! [SY2573: $i,SY2574: $i] :
              ( ~ ( c_lessequals @ SY2573 @ SY2574 @ SV1181 )
              | ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2573 @ SV1181 ) @ ( c_SetInterval_OlessThan @ SY2574 @ SV1181 ) @ ( tc_set @ SV1181 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6811]) ).

thf(8017,plain,
    ! [SV1682: $i,SV1467: $i,SV1182: $i] :
      ( ( ~ ( c_in @ SV1182 @ SV1467 @ SV1682 )
        | ~ ( c_in @ SV1182 @ ( c_uminus @ SV1467 @ ( tc_set @ SV1682 ) ) @ SV1682 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6812]) ).

thf(8018,plain,
    ! [SV1683: $i,SV1468: $i,SV1183: $i] :
      ( ( ( c_in @ SV1183 @ SV1468 @ SV1683 )
        | ( c_in @ SV1183 @ ( c_uminus @ SV1468 @ ( tc_set @ SV1683 ) ) @ SV1683 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6813]) ).

thf(8019,plain,
    ! [SV1684: $i,SV1469: $i,SV1184: $i] :
      ( ( ( ( c_uminus @ SV1184 @ ( tc_set @ SV1469 ) )
         != ( c_uminus @ SV1684 @ ( tc_set @ SV1469 ) ) )
        | ( SV1184 = SV1684 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6814]) ).

thf(8020,plain,
    ! [SV1685: $i,SV1470: $i,SV1185: $i] :
      ( ( ~ ( c_lessequals @ ( c_uminus @ SV1185 @ ( tc_set @ SV1470 ) ) @ ( c_uminus @ SV1685 @ ( tc_set @ SV1470 ) ) @ ( tc_set @ SV1470 ) )
        | ( c_lessequals @ SV1685 @ SV1185 @ ( tc_set @ SV1470 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6815]) ).

thf(8021,plain,
    ! [SV1686: $i,SV1471: $i,SV1186: $i] :
      ( ( ~ ( c_lessequals @ SV1186 @ SV1471 @ ( tc_set @ SV1686 ) )
        | ( c_lessequals @ ( c_uminus @ SV1471 @ ( tc_set @ SV1686 ) ) @ ( c_uminus @ SV1186 @ ( tc_set @ SV1686 ) ) @ ( tc_set @ SV1686 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6816]) ).

thf(8022,plain,
    ! [SV1687: $i,SV1472: $i,SV1187: $i] :
      ( ( ~ ( c_in @ SV1187 @ SV1472 @ SV1687 )
        | ! [SY3306: $i] :
            ~ ( c_in @ SV1187 @ ( c_minus @ SY3306 @ SV1472 @ ( tc_set @ SV1687 ) ) @ SV1687 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6817]) ).

thf(8023,plain,
    ! [SV1688: $i,SV1473: $i,SV1188: $i] :
      ( ( ! [SY3307: $i] :
            ( ~ ( c_in @ SV1188 @ ( c_minus @ SV1473 @ SV1688 @ ( tc_set @ SY3307 ) ) @ SY3307 )
            | ( c_in @ SV1188 @ SV1473 @ SY3307 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6818]) ).

thf(8024,plain,
    ! [SV1689: $i,SV1474: $i,SV1189: $i] :
      ( ( ~ ( c_in @ SV1189 @ SV1474 @ SV1689 )
        | ! [SY3308: $i] :
            ( ( c_in @ SV1189 @ SY3308 @ SV1689 )
            | ( c_in @ SV1189 @ ( c_minus @ SV1474 @ SY3308 @ ( tc_set @ SV1689 ) ) @ SV1689 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6819]) ).

thf(8025,plain,
    ! [SV1690: $i,SV1475: $i,SV1190: $i] :
      ( ( ! [SY3309: $i] :
            ( ~ ( c_in @ SV1190 @ ( c_inter @ SV1475 @ SV1690 @ SY3309 ) @ SY3309 )
            | ( c_in @ SV1190 @ SV1690 @ SY3309 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6820]) ).

thf(8026,plain,
    ! [SV1691: $i,SV1476: $i,SV1191: $i] :
      ( ( ! [SY3310: $i] :
            ( ~ ( c_in @ SV1191 @ ( c_inter @ SV1476 @ SV1691 @ SY3310 ) @ SY3310 )
            | ( c_in @ SV1191 @ SV1476 @ SY3310 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6821]) ).

thf(8027,plain,
    ! [SV1692: $i,SV1477: $i,SV1192: $i] :
      ( ( ~ ( c_in @ SV1192 @ SV1477 @ SV1692 )
        | ! [SY3311: $i] :
            ( ~ ( c_in @ SV1192 @ SY3311 @ SV1692 )
            | ( c_in @ SV1192 @ ( c_inter @ SY3311 @ SV1477 @ SV1692 ) @ SV1692 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6822]) ).

thf(8028,plain,
    ! [SV1693: $i,SV1478: $i,SV1193: $i] :
      ( ( ~ ( c_in @ SV1193 @ SV1478 @ ( tc_set @ SV1693 ) )
        | ! [SY3312: $i] :
            ( ~ ( c_in @ SY3312 @ ( c_Inter @ SV1478 @ SV1693 ) @ SV1693 )
            | ( c_in @ SY3312 @ SV1193 @ SV1693 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6823]) ).

thf(8029,plain,
    ! [SV1694: $i,SV1479: $i,SV1194: $i] :
      ( ( ~ ( c_in @ SV1194 @ ( c_Pow @ SV1479 @ SV1694 ) @ ( tc_set @ SV1694 ) )
        | ( c_lessequals @ SV1194 @ SV1479 @ ( tc_set @ SV1694 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6824]) ).

thf(8030,plain,
    ! [SV1695: $i,SV1480: $i,SV1195: $i] :
      ( ( ~ ( c_lessequals @ SV1195 @ SV1480 @ ( tc_set @ SV1695 ) )
        | ( c_in @ SV1195 @ ( c_Pow @ SV1480 @ SV1695 ) @ ( tc_set @ SV1695 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6825]) ).

thf(8031,plain,
    ! [SV1696: $i,SV1481: $i,SV1196: $i] :
      ( ( ~ ( c_in @ SV1196 @ SV1481 @ SV1696 )
        | ! [SY3313: $i] : ( c_in @ SV1196 @ ( c_union @ SY3313 @ SV1481 @ SV1696 ) @ SV1696 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6826]) ).

thf(8032,plain,
    ! [SV1697: $i,SV1482: $i,SV1197: $i] :
      ( ( ~ ( c_in @ SV1197 @ SV1482 @ SV1697 )
        | ! [SY3314: $i] : ( c_in @ SV1197 @ ( c_union @ SV1482 @ SY3314 @ SV1697 ) @ SV1697 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6827]) ).

thf(8033,plain,
    ! [SV1698: $i,SV1483: $i,SV1198: $i] :
      ( ( ! [SY3315: $i] :
            ( ~ ( c_in @ SV1198 @ ( c_union @ SV1483 @ SV1698 @ SY3315 ) @ SY3315 )
            | ( c_in @ SV1198 @ SV1698 @ SY3315 )
            | ( c_in @ SV1198 @ SV1483 @ SY3315 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6828]) ).

thf(8034,plain,
    ! [SV1699: $i,SV1199: $i] :
      ( ( ( ! [SY3316: $i] :
              ( ( c_union @ SV1199 @ SV1699 @ SY3316 )
             != c_emptyset ) )
        = $true )
      | ( ( SV1199 = c_emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6829]) ).

thf(8035,plain,
    ! [SV1484: $i,SV1200: $i] :
      ( ( ( ! [SY3074: $i] :
              ( ( c_union @ SV1200 @ SV1484 @ SY3074 )
             != c_emptyset ) )
        = $true )
      | ( ( SV1484 = c_emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6830]) ).

thf(8036,plain,
    ! [SV1700: $i,SV1485: $i,SV1202: $i] :
      ( ( ~ ( c_in @ SV1202 @ SV1485 @ SV1700 )
        | ! [SY3317: $i] :
            ( ~ ( c_in @ SV1485 @ SY3317 @ ( tc_set @ SV1700 ) )
            | ( c_in @ SV1202 @ ( c_Union @ SY3317 @ SV1700 ) @ SV1700 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6831]) ).

thf(8037,plain,
    ! [SV1486: $i,SV1203: $i] :
      ( ( c_in @ SV1203 @ c_emptyset @ SV1486 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6832]) ).

thf(8038,plain,
    ! [SV1701: $i,SV1487: $i,SV1204: $i] :
      ( ( ~ ( c_in @ SV1204 @ SV1487 @ SV1701 )
        | ! [SY3318: $i] : ( c_in @ SV1204 @ ( c_insert @ SY3318 @ SV1487 @ SV1701 ) @ SV1701 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6833]) ).

thf(8039,plain,
    ! [SV1702: $i,SV1488: $i,SV1205: $i] :
      ( ( c_in @ SV1205 @ ( c_insert @ SV1205 @ SV1488 @ SV1702 ) @ SV1702 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6834]) ).

thf(8040,plain,
    ! [SV1703: $i,SV1489: $i,SV1206: $i] :
      ( ( ! [SY3319: $i] :
            ( ~ ( c_in @ SV1206 @ ( c_insert @ SV1489 @ SV1703 @ SY3319 ) @ SY3319 )
            | ( SV1206 = SV1489 )
            | ( c_in @ SV1206 @ SV1703 @ SY3319 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6835]) ).

thf(8041,plain,
    ! [SV1490: $i,SV1207: $i] :
      ( ( c_less @ SV1207 @ c_emptyset @ ( tc_set @ SV1490 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6836]) ).

thf(8042,plain,
    ! [SV1704: $i,SV1491: $i,SV1208: $i] :
      ( ( ! [SY3320: $i] :
            ( ( ( c_insert @ SV1208 @ SV1491 @ SV1704 )
             != ( c_insert @ SY3320 @ c_emptyset @ SV1704 ) )
            | ( SV1208 = SY3320 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6837]) ).

thf(8043,plain,
    ! [SV1705: $i,SV1492: $i,SV1209: $i] :
      ( ( ! [SY3321: $i] :
            ( ( ( c_insert @ SV1209 @ SV1492 @ SV1705 )
             != ( c_insert @ SY3321 @ c_emptyset @ SV1705 ) )
            | ( c_lessequals @ SV1492 @ ( c_insert @ SY3321 @ c_emptyset @ SV1705 ) @ ( tc_set @ SV1705 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6838]) ).

thf(8044,plain,
    ! [SV1706: $i,SV1493: $i,SV1210: $i] :
      ( ( ~ ( c_lessequals @ SV1210 @ ( c_insert @ SV1493 @ c_emptyset @ SV1706 ) @ ( tc_set @ SV1706 ) )
        | ( ( c_insert @ SV1493 @ SV1210 @ SV1706 )
          = ( c_insert @ SV1493 @ c_emptyset @ SV1706 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6839]) ).

thf(8045,plain,
    ! [SV1707: $i,SV1494: $i,SV1211: $i] :
      ( ( ! [SY3322: $i] :
            ( ( c_insert @ SV1211 @ c_emptyset @ SV1494 )
           != ( c_insert @ SV1707 @ SY3322 @ SV1494 ) )
        | ( SV1707 = SV1211 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6840]) ).

thf(8046,plain,
    ! [SV1708: $i,SV1495: $i,SV1212: $i] :
      ( ( ! [SY3323: $i] :
            ( ( ( c_insert @ SV1212 @ c_emptyset @ SV1495 )
             != ( c_insert @ SV1708 @ SY3323 @ SV1495 ) )
            | ( c_lessequals @ SY3323 @ ( c_insert @ SV1212 @ c_emptyset @ SV1495 ) @ ( tc_set @ SV1495 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6841]) ).

thf(8047,plain,
    ! [SV1709: $i,SV1496: $i,SV1213: $i] :
      ( ( ~ ( c_lessequals @ SV1213 @ ( c_insert @ SV1496 @ c_emptyset @ SV1709 ) @ ( tc_set @ SV1709 ) )
        | ( ( c_insert @ SV1496 @ c_emptyset @ SV1709 )
          = ( c_insert @ SV1496 @ SV1213 @ SV1709 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6842]) ).

thf(8048,plain,
    ! [SV1710: $i,SV1497: $i,SV1214: $i] :
      ( ( ! [SY3324: $i] :
            ( ( ( c_Sum__Type_OInl @ SV1214 @ SV1497 @ SV1710 )
             != ( c_Sum__Type_OInl @ SY3324 @ SV1497 @ SV1710 ) )
            | ( SV1214 = SY3324 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6843]) ).

thf(8049,plain,
    ! [SV1711: $i,SV1498: $i,SV1215: $i] :
      ( ( ! [SY3325: $i] :
            ( ( c_Sum__Type_OInl @ SV1215 @ SV1498 @ SV1711 )
           != ( c_Sum__Type_OInr @ SY3325 @ SV1711 @ SV1498 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6844]) ).

thf(8050,plain,
    ! [SV1712: $i,SV1499: $i,SV1216: $i] :
      ( ( ! [SY3326: $i] :
            ( ( ( c_Sum__Type_OInr @ SV1216 @ SV1499 @ SV1712 )
             != ( c_Sum__Type_OInr @ SY3326 @ SV1499 @ SV1712 ) )
            | ( SV1216 = SY3326 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6845]) ).

thf(8051,plain,
    ! [SV1713: $i,SV1500: $i,SV1217: $i] :
      ( ( ! [SY3327: $i] :
            ( ( c_Sum__Type_OInr @ SV1217 @ SV1500 @ SV1713 )
           != ( c_Sum__Type_OInl @ SY3327 @ SV1713 @ SV1500 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6846]) ).

thf(8052,plain,
    ! [SV1501: $i,SV1218: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1218 @ SV1501 @ SV1501 ) @ SV1501 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ SV1218 @ SV1501 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6847]) ).

thf(8053,plain,
    ! [SV1502: $i,SV1219: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1219 @ SV1502 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1219 @ SV1502 @ SV1502 ) @ SV1502 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6848]) ).

thf(8054,plain,
    ! [SV1714: $i,SV1503: $i,SV1220: $i] :
      ( ( ! [SY3328: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1220 @ SV1503 @ SV1714 @ SV1714 ) @ SY3328 @ ( tc_prod @ SV1714 @ SV1714 ) ) @ SV1714 )
            | ( c_Wellfounded__Recursion_Oacyclic @ SY3328 @ SV1714 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6849]) ).

thf(8055,plain,
    ! [SV1715: $i,SV1504: $i,SV1221: $i] :
      ( ( ! [SY3329: $i] :
            ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1221 @ SV1504 @ SV1715 @ SV1715 ) @ SY3329 @ ( tc_prod @ SV1715 @ SV1715 ) ) @ SV1715 )
            | ~ ( c_in @ ( c_Pair @ SV1504 @ SV1221 @ SV1715 @ SV1715 ) @ ( c_Transitive__Closure_Ortrancl @ SY3329 @ SV1715 ) @ ( tc_prod @ SV1715 @ SV1715 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6850]) ).

thf(8056,plain,
    ! [SV1505: $i,SV1222: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1222 @ SV1505 ) )
        = $true )
      | ( ( ! [SY3104: $i,SY3105: $i] :
              ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SY3104 @ SY3105 @ SV1505 @ SV1505 ) @ SV1222 @ ( tc_prod @ SV1505 @ SV1505 ) ) @ SV1505 )
              | ( c_in @ ( c_Pair @ SY3105 @ SY3104 @ SV1505 @ SV1505 ) @ ( c_Transitive__Closure_Ortrancl @ SV1222 @ SV1505 ) @ ( tc_prod @ SV1505 @ SV1505 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6851]) ).

thf(8057,plain,
    ! [SV1716: $i,SV1506: $i,SV1223: $i] :
      ( ( ! [SY3330: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1223 @ SV1506 @ SV1716 @ SV1716 ) @ SY3330 @ ( tc_prod @ SV1716 @ SV1716 ) ) @ SV1716 )
            | ( c_Wellfounded__Recursion_Owf @ SY3330 @ SV1716 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6852]) ).

thf(8058,plain,
    ! [SV1717: $i,SV1507: $i,SV1224: $i] :
      ( ( ! [SY3331: $i] :
            ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1224 @ SV1507 @ SV1717 @ SV1717 ) @ SY3331 @ ( tc_prod @ SV1717 @ SV1717 ) ) @ SV1717 )
            | ~ ( c_in @ ( c_Pair @ SV1507 @ SV1224 @ SV1717 @ SV1717 ) @ ( c_Transitive__Closure_Ortrancl @ SY3331 @ SV1717 ) @ ( tc_prod @ SV1717 @ SV1717 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6853]) ).

thf(8059,plain,
    ! [SV1508: $i,SV1225: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1225 @ SV1508 ) )
        = $true )
      | ( ( ! [SY3110: $i,SY3111: $i] :
              ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SY3110 @ SY3111 @ SV1508 @ SV1508 ) @ SV1225 @ ( tc_prod @ SV1508 @ SV1508 ) ) @ SV1508 )
              | ( c_in @ ( c_Pair @ SY3111 @ SY3110 @ SV1508 @ SV1508 ) @ ( c_Transitive__Closure_Ortrancl @ SV1225 @ SV1508 ) @ ( tc_prod @ SV1508 @ SV1508 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6854]) ).

thf(8060,plain,
    ! [SV1509: $i,SV1226: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1226 @ SV1509 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) )
        = $true )
      | ( ( c_less @ SV1226 @ SV1509 @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6855]) ).

thf(8061,plain,
    ! [SV1510: $i,SV1227: $i] :
      ( ( ( ~ ( c_less @ SV1227 @ SV1510 @ tc_nat ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1227 @ SV1510 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6856]) ).

thf(8062,plain,
    ! [SV1718: $i,SV1511: $i,SV1228: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ ( c_Message_Osynth @ SV1718 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ SV1718 @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OKey @ SV1228 ) @ SV1718 @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6857]) ).

thf(8063,plain,
    ! [SV1719: $i,SV1512: $i,SV1229: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg )
        | ( c_in @ SV1512 @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ SV1719 @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6858]) ).

thf(8064,plain,
    ! [SV1513: $i,SV1230: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ( c_in @ SV1230 @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ SV1513 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6859]) ).

thf(8065,plain,
    ! [SV1514: $i,SV1231: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ ( c_Message_Osynth @ SV1514 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ SV1514 @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6860]) ).

thf(8066,plain,
    ! [SV1720: $i,SV1515: $i,SV1232: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1232 @ SV1515 ) @ ( c_Message_Oanalz @ SV1720 ) @ tc_Message_Omsg )
        | ( c_in @ SV1515 @ ( c_Message_Oanalz @ SV1720 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6861]) ).

thf(8067,plain,
    ! [SV1721: $i,SV1516: $i,SV1233: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1233 @ SV1516 ) @ ( c_Message_Oanalz @ SV1721 ) @ tc_Message_Omsg )
        | ( c_in @ SV1233 @ ( c_Message_Oanalz @ SV1721 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6862]) ).

thf(8068,plain,
    ! [SV1722: $i,SV1517: $i,SV1234: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1234 @ SV1517 ) @ ( c_Message_Oparts @ SV1722 ) @ tc_Message_Omsg )
        | ( c_in @ SV1517 @ ( c_Message_Oparts @ SV1722 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6863]) ).

thf(8069,plain,
    ! [SV1723: $i,SV1518: $i,SV1235: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1235 @ SV1518 ) @ ( c_Message_Oparts @ SV1723 ) @ tc_Message_Omsg )
        | ( c_in @ SV1235 @ ( c_Message_Oparts @ SV1723 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6864]) ).

thf(8070,plain,
    ! [SV1724: $i,SV1519: $i,SV1236: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg )
        | ( c_in @ SV1519 @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ SV1724 @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6865]) ).

thf(8071,plain,
    ! [SV1725: $i,SV1520: $i,SV1237: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg )
        | ( c_in @ SV1237 @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ SV1725 @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6866]) ).

thf(8072,plain,
    ! [SV1521: $i,SV1238: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ ( c_Message_Osynth @ SV1521 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ SV1521 @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6867]) ).

thf(8073,plain,
    ! [SV1522: $i,SV1243: $i] :
      ( ( ( ( c_Message_Oagent_OFriend @ SV1243 )
         != ( c_Message_Oagent_OFriend @ SV1522 ) )
        = $true )
      | ( ( SV1243 = SV1522 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6872]) ).

thf(8074,plain,
    ! [SV1726: $i,SV1523: $i,SV1244: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1244 @ SV1523 ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1244 ) ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        | ( c_in @ SV1523 @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6873]) ).

thf(8075,plain,
    ! [SV1524: $i,SV1245: $i] :
      ( ( ( ~ ( c_in @ SV1245 @ SV1524 @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1245 @ ( c_Message_Oanalz @ SV1524 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6874]) ).

thf(8076,plain,
    ! [SV1525: $i,SV1246: $i] :
      ( ( ( ~ ( c_in @ SV1246 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SV1525 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1246 @ ( c_Message_Oanalz @ SV1525 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6875]) ).

thf(8077,plain,
    ! [SV1727: $i,SV1526: $i,SV1247: $i] :
      ( ( ~ ( c_in @ SV1247 @ ( c_Message_Oparts @ ( c_union @ SV1526 @ SV1727 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
        | ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1727 ) @ tc_Message_Omsg )
        | ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1526 ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6876]) ).

thf(8078,plain,
    ! [SV1527: $i,SV1248: $i] :
      ( ( ( ( c_Message_Omsg_OAgent @ SV1248 )
         != ( c_Message_Omsg_OAgent @ SV1527 ) )
        = $true )
      | ( ( SV1248 = SV1527 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6877]) ).

thf(8079,plain,
    ! [SV1528: $i,SV1249: $i] :
      ( ( ( ( c_Message_Omsg_ONumber @ SV1249 )
         != ( c_Message_Omsg_ONumber @ SV1528 ) )
        = $true )
      | ( ( SV1249 = SV1528 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6878]) ).

thf(8080,plain,
    ! [SV1529: $i,SV1250: $i] :
      ( ( ( ( c_Message_Omsg_ONonce @ SV1250 )
         != ( c_Message_Omsg_ONonce @ SV1529 ) )
        = $true )
      | ( ( SV1250 = SV1529 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6879]) ).

thf(8081,plain,
    ! [SV1530: $i,SV1251: $i] :
      ( ( ( ( c_Message_Omsg_OKey @ SV1251 )
         != ( c_Message_Omsg_OKey @ SV1530 ) )
        = $true )
      | ( ( SV1251 = SV1530 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6880]) ).

thf(8082,plain,
    ! [SV1531: $i,SV1252: $i] :
      ( ( ( ( c_Message_Omsg_OHash @ SV1252 )
         != ( c_Message_Omsg_OHash @ SV1531 ) )
        = $true )
      | ( ( SV1252 = SV1531 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6881]) ).

thf(8083,plain,
    ! [SV1728: $i,SV1532: $i,SV1253: $i] :
      ( ( ! [SY3332: $i] :
            ( ( c_Message_Omsg_OMPair @ SV1253 @ SV1532 )
           != ( c_Message_Omsg_OMPair @ SV1728 @ SY3332 ) )
        | ( SV1253 = SV1728 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6882]) ).

thf(8084,plain,
    ! [SV1729: $i,SV1533: $i,SV1254: $i] :
      ( ( ! [SY3333: $i] :
            ( ( ( c_Message_Omsg_OMPair @ SV1254 @ SV1533 )
             != ( c_Message_Omsg_OMPair @ SV1729 @ SY3333 ) )
            | ( SV1533 = SY3333 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6883]) ).

thf(8085,plain,
    ! [SV1730: $i,SV1534: $i,SV1255: $i] :
      ( ( ! [SY3334: $i] :
            ( ( c_Message_Omsg_OCrypt @ SV1255 @ SV1534 )
           != ( c_Message_Omsg_OCrypt @ SV1730 @ SY3334 ) )
        | ( SV1255 = SV1730 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6884]) ).

thf(8086,plain,
    ! [SV1731: $i,SV1535: $i,SV1256: $i] :
      ( ( ! [SY3335: $i] :
            ( ( ( c_Message_Omsg_OCrypt @ SV1256 @ SV1535 )
             != ( c_Message_Omsg_OCrypt @ SV1731 @ SY3335 ) )
            | ( SV1535 = SY3335 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6885]) ).

thf(8087,plain,
    ! [SV1536: $i,SV1257: $i] :
      ( ( ( ~ ( c_in @ SV1257 @ SV1536 @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1257 @ ( c_Message_Oparts @ SV1536 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6886]) ).

thf(8088,plain,
    ! [SV1537: $i,SV1259: $i] :
      ( ( ( ~ ( c_in @ SV1259 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SV1537 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1259 @ ( c_Message_Oparts @ SV1537 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6888]) ).

thf(8089,plain,
    ! [SV1539: $i,SV1261: $i] :
      ( ( ( ~ ( c_in @ SV1261 @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ! [SY3130: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SY3130 ) @ SV1539 @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OCrypt @ SY3130 @ SV1261 ) @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6890]) ).

thf(8090,plain,
    ! [SV1540: $i,SV1262: $i] :
      ( ( ( ~ ( c_in @ SV1262 @ ( c_Message_Osynth @ SV1540 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OHash @ SV1262 ) @ ( c_Message_Osynth @ SV1540 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6891]) ).

thf(8091,plain,
    ! [SV1541: $i,SV1263: $i] :
      ( ( ( ~ ( c_in @ SV1263 @ SV1541 @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1263 @ ( c_Message_Osynth @ SV1541 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6892]) ).

thf(8092,plain,
    ! [SV1542: $i,SV1264: $i] :
      ( ( ( ~ ( c_in @ SV1264 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ! [SY3131: $i] :
              ( ~ ( c_in @ SY3131 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OMPair @ SY3131 @ SV1264 ) @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6893]) ).

thf(8093,plain,
    ! [SV1544: $i,SV1266: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SV1544 ) @ ( tc_set @ tc_Message_Omsg ) ) )
        = $true )
      | ( ( ! [SY3132: $i,SY3133: $i] :
              ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SY3132 ) @ ( c_Message_Oanalz @ SY3133 ) @ ( tc_set @ tc_Message_Omsg ) )
              | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SY3132 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SY3133 @ SV1544 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6895]) ).

thf(8094,plain,
    ! [SV1545: $i,SV1267: $i] :
      ( ( ( ~ ( c_in @ SV1267 @ ( c_Message_Osynth @ ( c_Message_Osynth @ SV1545 ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1267 @ ( c_Message_Osynth @ SV1545 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6896]) ).

thf(8095,plain,
    ! [SV1732: $i,SV1546: $i,SV1268: $i,SV1: $i] :
      ( ( ( ( c_Datatype__Universe_OLeaf @ SV1 @ SV1268 @ SV1546 )
         != ( c_Datatype__Universe_OLeaf @ SV1732 @ SV1268 @ SV1546 ) )
        | ( SV1 = SV1732 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6897]) ).

thf(8096,plain,
    ! [SV1733: $i,SV1547: $i,SV1269: $i,SV2: $i] :
      ( ( ( ( c_Datatype__Universe_ONumb @ SV2 @ SV1269 @ SV1547 )
         != ( c_Datatype__Universe_ONumb @ SV1733 @ SV1269 @ SV1547 ) )
        | ( SV2 = SV1733 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6898]) ).

thf(8097,plain,
    ! [SV1734: $i,SV1548: $i,SV1270: $i,SV3: $i] :
      ( ( ! [SY3336: $i] :
            ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1270 @ SV1548 @ SV1734 @ SY3336 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SY3336 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SY3336 ) ) ) )
            | ( SV3
              = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SY3336 ) @ ( c_Main_OdprodE__2 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SY3336 ) @ SV1734 @ SY3336 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SY3336 ) @ ( c_Main_OdprodE__4 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SY3336 ) @ SV1734 @ SY3336 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SY3336 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SY3336 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6899]) ).

thf(8098,plain,
    ! [SV1735: $i,SV1549: $i,SV1271: $i,SV4: $i] :
      ( ( ! [SY3337: $i] :
            ( ~ ( c_in @ SV4 @ ( c_Datatype__Universe_Odprod @ SV1271 @ SV1549 @ SV1735 @ SY3337 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SY3337 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SY3337 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SY3337 ) @ ( c_Main_OdprodE__4 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SY3337 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SY3337 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SY3337 ) ) ) @ SV1549 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SY3337 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SY3337 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6900]) ).

thf(8099,plain,
    ! [SV1736: $i,SV1550: $i,SV1272: $i,SV5: $i] :
      ( ( ! [SY3338: $i] :
            ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odprod @ SV1272 @ SV1550 @ SV1736 @ SY3338 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SY3338 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SY3338 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SY3338 ) @ ( c_Main_OdprodE__3 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SY3338 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SY3338 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SY3338 ) ) ) @ SV1272 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SY3338 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SY3338 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6901]) ).

thf(8100,plain,
    ! [SV1737: $i,SV1551: $i,SV1273: $i,SV6: $i] :
      ( ( ! [SY3339: $i,SY3340: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SY3339 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
            | ! [SY3341: $i,SY3342: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY3340 @ SY3341 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SY3342 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
                | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY3340 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SY3341 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3342 @ SY3339 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6902]) ).

thf(8101,plain,
    ! [SV1738: $i,SV1552: $i,SV1274: $i,SV7: $i] :
      ( ( ! [SY3343: $i] :
            ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1274 @ SV1552 @ SV1738 @ SY3343 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SY3343 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SY3343 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1274 @ SV7 @ SV1738 @ SY3343 ) @ SV1738 @ SY3343 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1274 @ SV7 @ SV1738 @ SY3343 ) @ SV1738 @ SY3343 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SY3343 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SY3343 ) ) ) )
            | ( SV7
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1552 @ SV7 @ SV1738 @ SY3343 ) @ SV1738 @ SY3343 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1552 @ SV7 @ SV1738 @ SY3343 ) @ SV1738 @ SY3343 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SY3343 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SY3343 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6903]) ).

thf(8102,plain,
    ! [SV1739: $i,SV1553: $i,SV1275: $i,SV8: $i] :
      ( ( ! [SY3344: $i] :
            ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1275 @ SV1553 @ SV1739 @ SY3344 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) ) )
            | ( SV8
              = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1275 @ SV8 @ SV1739 @ SY3344 ) @ SV1739 @ SY3344 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1275 @ SV8 @ SV1739 @ SY3344 ) @ SV1739 @ SY3344 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1553 @ SV8 @ SV1739 @ SY3344 ) @ ( c_Main_OdsumE__4 @ SV1553 @ SV8 @ SV1739 @ SY3344 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) ) @ SV1553 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SY3344 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6904]) ).

thf(8103,plain,
    ! [SV1740: $i,SV1554: $i,SV1276: $i,SV9: $i] :
      ( ( ! [SY3345: $i] :
            ( ~ ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SV1276 @ SV1554 @ SV1740 @ SY3345 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) ) )
            | ( SV9
              = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1554 @ SV9 @ SV1740 @ SY3345 ) @ SV1740 @ SY3345 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1554 @ SV9 @ SV1740 @ SY3345 ) @ SV1740 @ SY3345 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1276 @ SV9 @ SV1740 @ SY3345 ) @ ( c_Main_OdsumE__2 @ SV1276 @ SV9 @ SV1740 @ SY3345 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) ) @ SV1276 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SY3345 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6905]) ).

thf(8104,plain,
    ! [SV1741: $i,SV1555: $i,SV1277: $i,SV10: $i] :
      ( ( ! [SY3346: $i] :
            ( ~ ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SV1277 @ SV1555 @ SV1741 @ SY3346 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1277 @ SV10 @ SV1741 @ SY3346 ) @ ( c_Main_OdsumE__2 @ SV1277 @ SV10 @ SV1741 @ SY3346 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) ) @ SV1277 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1555 @ SV10 @ SV1741 @ SY3346 ) @ ( c_Main_OdsumE__4 @ SV1555 @ SV10 @ SV1741 @ SY3346 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) ) @ SV1555 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SY3346 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6906]) ).

thf(8105,plain,
    ! [SV1742: $i,SV1556: $i,SV1278: $i,SV11: $i] :
      ( ( ! [SY3347: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV11 @ SV1278 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ SY3347 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) )
            | ! [SY3348: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SV1556 @ SV1742 ) @ ( c_Datatype__Universe_OIn0 @ SV1278 @ SV1556 @ SV1742 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3347 @ SY3348 @ SV1556 @ SV1742 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6907]) ).

thf(8106,plain,
    ! [SV1743: $i,SV1557: $i,SV1279: $i,SV12: $i] :
      ( ( ! [SY3349: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV12 @ SV1279 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ SY3349 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) )
            | ! [SY3350: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SV1557 @ SV1743 ) @ ( c_Datatype__Universe_OIn1 @ SV1279 @ SV1557 @ SV1743 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3350 @ SY3349 @ SV1557 @ SV1743 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6908]) ).

thf(8107,plain,
    ! [SV1744: $i,SV1558: $i,SV1280: $i,SV13: $i] :
      ( ( ! [SY3351: $i] :
            ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1280 @ SV1558 @ SV1744 @ SY3351 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1744 @ SY3351 ) ) )
            | ( SV13
              = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SY3351 ) @ ( c_Main_OuprodE__2 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SY3351 ) @ SV1744 @ SY3351 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6909]) ).

thf(8108,plain,
    ! [SV1745: $i,SV1559: $i,SV1281: $i,SV14: $i] :
      ( ( ! [SY3352: $i] :
            ( ~ ( c_in @ SV14 @ ( c_Datatype__Universe_Ouprod @ SV1281 @ SV1559 @ SV1745 @ SY3352 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SY3352 ) ) )
            | ( c_in @ ( c_Main_OuprodE__2 @ SV1281 @ SV1559 @ SV14 @ SV1745 @ SY3352 ) @ SV1559 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SY3352 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6910]) ).

thf(8109,plain,
    ! [SV1746: $i,SV1560: $i,SV1282: $i,SV15: $i] :
      ( ( ! [SY3353: $i] :
            ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ouprod @ SV1282 @ SV1560 @ SV1746 @ SY3353 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SY3353 ) ) )
            | ( c_in @ ( c_Main_OuprodE__1 @ SV1282 @ SV1560 @ SV15 @ SV1746 @ SY3353 ) @ SV1282 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SY3353 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6911]) ).

thf(8110,plain,
    ! [SV1747: $i,SV1561: $i,SV1283: $i,SV16: $i] :
      ( ( ~ ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        | ! [SY3354: $i,SY3355: $i] :
            ( ~ ( c_in @ SY3354 @ SY3355 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
            | ( c_in @ ( c_Datatype__Universe_OScons @ SY3354 @ SV16 @ SV1561 @ SV1747 ) @ ( c_Datatype__Universe_Ouprod @ SY3355 @ SV1283 @ SV1561 @ SV1747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6912]) ).

thf(8111,plain,
    ! [SV1748: $i,SV1562: $i,SV1284: $i,SV17: $i] :
      ( ( ! [SY3356: $i] :
            ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1284 @ SV1562 @ SV1748 @ SY3356 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1748 @ SY3356 ) ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1284 @ SV17 @ SV1748 @ SY3356 ) @ SV1748 @ SY3356 ) )
            | ( SV17
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1562 @ SV17 @ SV1748 @ SY3356 ) @ SV1748 @ SY3356 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6913]) ).

thf(8112,plain,
    ! [SV1749: $i,SV1563: $i,SV1285: $i,SV18: $i] :
      ( ( ! [SY3357: $i] :
            ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1285 @ SV1563 @ SV1749 @ SY3357 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SY3357 ) ) )
            | ( SV18
              = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1285 @ SV18 @ SV1749 @ SY3357 ) @ SV1749 @ SY3357 ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SV1563 @ SV18 @ SV1749 @ SY3357 ) @ SV1563 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SY3357 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6914]) ).

thf(8113,plain,
    ! [SV1750: $i,SV1564: $i,SV1286: $i,SV19: $i] :
      ( ( ! [SY3358: $i] :
            ( ~ ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SV1286 @ SV1564 @ SV1750 @ SY3358 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SY3358 ) ) )
            | ( SV19
              = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1564 @ SV19 @ SV1750 @ SY3358 ) @ SV1750 @ SY3358 ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SV1286 @ SV19 @ SV1750 @ SY3358 ) @ SV1286 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SY3358 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6915]) ).

thf(8114,plain,
    ! [SV1751: $i,SV1565: $i,SV1287: $i,SV20: $i] :
      ( ( ! [SY3359: $i] :
            ( ~ ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SV1287 @ SV1565 @ SV1751 @ SY3359 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SY3359 ) ) )
            | ( c_in @ ( c_Main_OusumE__1 @ SV1287 @ SV20 @ SV1751 @ SY3359 ) @ SV1287 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SY3359 ) ) )
            | ( c_in @ ( c_Main_OusumE__2 @ SV1565 @ SV20 @ SV1751 @ SY3359 ) @ SV1565 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SY3359 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6916]) ).

thf(8115,plain,
    ! [SV1752: $i,SV1566: $i,SV1288: $i,SV21: $i] :
      ( ( ~ ( c_in @ SV21 @ SV1288 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) )
        | ! [SY3360: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ SV21 @ SV1566 @ SV1752 ) @ ( c_Datatype__Universe_Ousum @ SV1288 @ SY3360 @ SV1566 @ SV1752 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6917]) ).

thf(8116,plain,
    ! [SV1753: $i,SV1567: $i,SV1289: $i,SV22: $i] :
      ( ( ~ ( c_in @ SV22 @ SV1289 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) )
        | ! [SY3361: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ SV22 @ SV1567 @ SV1753 ) @ ( c_Datatype__Universe_Ousum @ SY3361 @ SV1289 @ SV1567 @ SV1753 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6918]) ).

thf(8117,plain,
    ! [SV1292: $i,SV27: $i] :
      ( ( ( ( c_Divides_Oop_Amod @ SV27 @ SV1292 @ tc_nat )
          = c_0 )
        = $false )
      | ( ( SV27
          = ( c_times @ SV1292 @ ( c_Main_Omod__eq__0D__dest__1 @ SV1292 @ SV27 ) @ tc_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6919]) ).

thf(8118,plain,
    ! [SV1293: $i,SV29: $i] :
      ( ( ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) )
        = $false )
      | ( ( ! [SY2813: $i] : ( c_in @ ( c_insert @ SY2813 @ SV29 @ SV1293 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6920]) ).

thf(8119,plain,
    ! [SV1294: $i,SV30: $i] :
      ( ( ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) )
        = $false )
      | ( ( ! [SY2814: $i] : ( c_in @ ( c_inter @ SV30 @ SY2814 @ SV1294 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6921]) ).

thf(8120,plain,
    ! [SV1295: $i,SV31: $i] :
      ( ( ( c_in @ SV31 @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) )
        = $false )
      | ( ( ! [SY2815: $i] : ( c_in @ ( c_inter @ SY2815 @ SV31 @ SV1295 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6922]) ).

thf(8121,plain,
    ! [SV1296: $i,SV32: $i] :
      ( ( ( c_in @ SV32 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1296 ) ) )
        = $false )
      | ( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV32 @ SV1296 ) @ SV32 @ ( tc_set @ SV1296 ) )
          | ( c_in @ ( c_Union @ SV32 @ SV1296 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1296 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6923]) ).

thf(8122,plain,
    ! [SV1297: $i,SV33: $i] :
      ( ( ( c_in @ SV33 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1297 ) ) )
        = $false )
      | ( ( ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) )
          | ( c_in @ ( c_Union @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6924]) ).

thf(8123,plain,
    ! [SV1300: $i,SV36: $i] :
      ( ( ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        = $false )
      | ( ( ! [SY2816: $i] :
              ( ~ ( c_in @ SY2816 @ SV36 @ SV1300 )
              | ! [SY2817: $i] :
                  ( ~ ( c_in @ SY2817 @ SV36 @ SV1300 )
                  | ( SY2816 = SY2817 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6925]) ).

thf(8124,plain,
    ! [SV1305: $i,SV43: $i] :
      ( ( ( ( c_Divides_Oop_Amod @ SV43 @ SV1305 @ tc_IntDef_Oint )
          = c_0 )
        = $false )
      | ( ( SV43
          = ( c_times @ SV1305 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SV1305 @ SV43 ) @ tc_IntDef_Oint ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6926]) ).

thf(8125,plain,
    ! [SV1568: $i,SV1308: $i,SV46: $i] :
      ( ( ( ~ ( c_in @ SV46 @ ( c_List_Olists @ SV1308 @ SV1568 ) @ ( tc_List_Olist @ SV1568 ) ) )
        = $true )
      | ( ( ! [SY3182: $i] :
              ( ~ ( c_in @ SY3182 @ ( c_List_Oset @ SV46 @ SV1568 ) @ SV1568 )
              | ( c_in @ SY3182 @ SV1308 @ SV1568 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6927]) ).

thf(8126,plain,
    ! [SV1569: $i,SV1309: $i,SV47: $i] :
      ( ( ( c_in @ SV47 @ ( c_List_Olists @ SV1309 @ SV1569 ) @ ( tc_List_Olist @ SV1569 ) )
        = $true )
      | ( ( c_in @ ( c_Main_Oin__listsI__1 @ SV1309 @ SV47 @ SV1569 ) @ ( c_List_Oset @ SV47 @ SV1569 ) @ SV1569 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6928]) ).

thf(8127,plain,
    ! [SV1570: $i,SV1310: $i,SV48: $i] :
      ( ( ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV48 @ SV1310 @ SV1570 ) @ SV48 @ SV1570 ) )
        = $true )
      | ( ( c_in @ SV1310 @ ( c_List_Olists @ SV48 @ SV1570 ) @ ( tc_List_Olist @ SV1570 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6929]) ).

thf(8128,plain,
    ! [SV1754: $i,SV1571: $i,SV1312: $i,SV50: $i] :
      ( ( ! [SY3362: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV50 @ SV1312 @ SV1571 ) @ SV1754 @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) @ ( c_List_Olistrel @ SY3362 @ SV1571 ) @ ( tc_prod @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) )
            | ( SV1754
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY3362 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ ( c_Main_Olistrel__Cons1__2 @ SY3362 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ SV1571 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6930]) ).

thf(8129,plain,
    ! [SV1755: $i,SV1572: $i,SV1313: $i,SV51: $i] :
      ( ( ! [SY3363: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV51 @ SV1313 @ SV1572 ) @ SV1755 @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SY3363 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) )
            | ( c_in @ ( c_Pair @ SV1313 @ ( c_Main_Olistrel__Cons1__2 @ SY3363 @ SV1755 @ SV51 @ SV1313 @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SY3363 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6931]) ).

thf(8130,plain,
    ! [SV1756: $i,SV1573: $i,SV1314: $i,SV52: $i] :
      ( ( ! [SY3364: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV52 @ SV1314 @ SV1573 ) @ SV1756 @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) @ ( c_List_Olistrel @ SY3364 @ SV1573 ) @ ( tc_prod @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) )
            | ( c_in @ ( c_Pair @ SV52 @ ( c_Main_Olistrel__Cons1__1 @ SY3364 @ SV1756 @ SV52 @ SV1314 @ SV1573 ) @ SV1573 @ SV1573 ) @ SY3364 @ ( tc_prod @ SV1573 @ SV1573 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6932]) ).

thf(8131,plain,
    ! [SV1757: $i,SV1574: $i,SV1315: $i,SV53: $i] :
      ( ( ! [SY3365: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV53 @ ( c_List_Olist_OCons @ SV1315 @ SV1574 @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) @ ( c_List_Olistrel @ SY3365 @ SV1757 ) @ ( tc_prod @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) )
            | ( SV53
              = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY3365 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ ( c_Main_Olistrel__Cons2__2 @ SY3365 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ SV1757 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6933]) ).

thf(8132,plain,
    ! [SV1758: $i,SV1575: $i,SV1316: $i,SV54: $i] :
      ( ( ! [SY3366: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV54 @ ( c_List_Olist_OCons @ SV1316 @ SV1575 @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SY3366 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY3366 @ SV54 @ SV1316 @ SV1575 @ SV1758 ) @ SV1575 @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SY3366 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6934]) ).

thf(8133,plain,
    ! [SV1759: $i,SV1576: $i,SV1317: $i,SV55: $i] :
      ( ( ! [SY3367: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV55 @ ( c_List_Olist_OCons @ SV1317 @ SV1576 @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) @ ( c_List_Olistrel @ SY3367 @ SV1759 ) @ ( tc_prod @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY3367 @ SV55 @ SV1317 @ SV1576 @ SV1759 ) @ SV1317 @ SV1759 @ SV1759 ) @ SY3367 @ ( tc_prod @ SV1759 @ SV1759 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6935]) ).

thf(8134,plain,
    ! [SV1760: $i,SV1577: $i,SV56: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV56 @ ( tc_List_Olist @ SV1577 ) @ ( tc_List_Olist @ SV1577 ) ) @ ( c_List_Olistrel @ SV1760 @ SV1577 ) @ ( tc_prod @ ( tc_List_Olist @ SV1577 ) @ ( tc_List_Olist @ SV1577 ) ) ) )
        = $true )
      | ( ( SV56 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6936]) ).

thf(8135,plain,
    ! [SV1761: $i,SV1578: $i,SV57: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV57 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1578 ) @ ( tc_List_Olist @ SV1578 ) ) @ ( c_List_Olistrel @ SV1761 @ SV1578 ) @ ( tc_prod @ ( tc_List_Olist @ SV1578 ) @ ( tc_List_Olist @ SV1578 ) ) ) )
        = $true )
      | ( ( SV57 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6937]) ).

thf(8136,plain,
    ! [SV1762: $i,SV1579: $i,SV1318: $i,SV58: $i] :
      ( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV58 @ SV1318 @ SV1579 ) @ ( c_List_Olists @ SV1762 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) )
        | ( c_in @ SV1318 @ ( c_List_Olists @ SV1762 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6938]) ).

thf(8137,plain,
    ! [SV1763: $i,SV1580: $i,SV1319: $i,SV59: $i] :
      ( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV59 @ SV1319 @ SV1580 ) @ ( c_List_Olists @ SV1763 @ SV1580 ) @ ( tc_List_Olist @ SV1580 ) )
        | ( c_in @ SV59 @ SV1763 @ SV1580 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6939]) ).

thf(8138,plain,
    ! [SV1581: $i,SV1320: $i,SV60: $i] :
      ( ( ( ~ ( c_in @ SV60 @ SV1320 @ SV1581 ) )
        = $true )
      | ( ( ! [SY3199: $i] :
              ( ~ ( c_in @ SY3199 @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) )
              | ( c_in @ ( c_List_Olist_OCons @ SV60 @ SY3199 @ SV1581 ) @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6940]) ).

thf(8139,plain,
    ! [SV1322: $i,SV62: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ SV62 @ SV1322 )
        = $false )
      | ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV62 @ SV1322 ) @ ( tc_List_Olist @ SV1322 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6941]) ).

thf(8140,plain,
    ! [SV1323: $i,SV63: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ SV63 @ SV1323 )
        = $false )
      | ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV63 @ SV1323 ) @ ( tc_List_Olist @ SV1323 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6942]) ).

thf(8141,plain,
    ! [SV68: $i,SV1764: $i] :
      ( ( ( c_lessequals @ SV1764 @ SV1764 @ SV68 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV68 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[6943]) ).

thf(8142,plain,
    ! [SV1765: $i,SV1582: $i,SV1324: $i,SV69: $i] :
      ( ( ~ ( c_in @ SV69 @ ( c_Relation_ODomain @ SV1324 @ SV1582 @ SV1765 ) @ SV1582 )
        | ( c_in @ ( c_Pair @ SV69 @ ( c_Main_ODomainE__1 @ SV69 @ SV1324 @ SV1582 @ SV1765 ) @ SV1582 @ SV1765 ) @ SV1324 @ ( tc_prod @ SV1582 @ SV1765 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6944]) ).

thf(8143,plain,
    ! [SV1766: $i,SV1583: $i,SV1325: $i,SV70: $i] :
      ( ( ! [SY3368: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1325 @ SV1583 @ SV1766 ) @ SY3368 @ ( tc_prod @ SV1583 @ SV1766 ) )
            | ( c_in @ SV70 @ ( c_Relation_ODomain @ SY3368 @ SV1583 @ SV1766 ) @ SV1583 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6945]) ).

thf(8144,plain,
    ! [SV1326: $i,SV71: $i] :
      ( ( ( c_in @ SV71 @ c_Relation_OId @ ( tc_prod @ SV1326 @ SV1326 ) )
        = $false )
      | ( ( SV71
          = ( c_Pair @ ( c_Main_OIdE__1 @ SV71 @ SV1326 ) @ ( c_Main_OIdE__1 @ SV71 @ SV1326 ) @ SV1326 @ SV1326 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6946]) ).

thf(8145,plain,
    ! [SV1767: $i,SV1584: $i,SV1327: $i,SV72: $i] :
      ( ( ! [SY3369: $i] :
            ( ~ ( c_in @ SV72 @ ( c_Relation_OImage @ SV1327 @ SV1584 @ SV1767 @ SY3369 ) @ SY3369 )
            | ( c_in @ ( c_Main_OImageE__1 @ SV1584 @ SV72 @ SV1327 @ SV1767 @ SY3369 ) @ SV1584 @ SV1767 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6947]) ).

thf(8146,plain,
    ! [SV1768: $i,SV1585: $i,SV1328: $i,SV73: $i] :
      ( ( ! [SY3370: $i] :
            ( ~ ( c_in @ SV73 @ ( c_Relation_OImage @ SV1328 @ SV1585 @ SV1768 @ SY3370 ) @ SY3370 )
            | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1585 @ SV73 @ SV1328 @ SV1768 @ SY3370 ) @ SV73 @ SV1768 @ SY3370 ) @ SV1328 @ ( tc_prod @ SV1768 @ SY3370 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6948]) ).

thf(8147,plain,
    ! [SV1769: $i,SV1586: $i,SV1329: $i,SV74: $i] :
      ( ( ~ ( c_in @ SV74 @ SV1329 @ SV1586 )
        | ! [SY3371: $i,SY3372: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV74 @ SV1769 @ SV1586 @ SY3371 ) @ SY3372 @ ( tc_prod @ SV1586 @ SY3371 ) )
            | ( c_in @ SV1769 @ ( c_Relation_OImage @ SY3372 @ SV1329 @ SV1586 @ SY3371 ) @ SY3371 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6949]) ).

thf(8148,plain,
    ! [SV1770: $i,SV1587: $i,SV1330: $i,SV75: $i] :
      ( ( ~ ( c_in @ SV75 @ ( c_Relation_ORange @ SV1330 @ SV1587 @ SV1770 ) @ SV1770 )
        | ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV75 @ SV1330 @ SV1770 @ SV1587 ) @ SV75 @ SV1587 @ SV1770 ) @ SV1330 @ ( tc_prod @ SV1587 @ SV1770 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6950]) ).

thf(8149,plain,
    ! [SV1771: $i,SV1588: $i,SV1331: $i,SV76: $i] :
      ( ( ! [SY3373: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV76 @ SV1331 @ SV1588 @ SV1771 ) @ SY3373 @ ( tc_prod @ SV1588 @ SV1771 ) )
            | ( c_in @ SV1331 @ ( c_Relation_ORange @ SY3373 @ SV1588 @ SV1771 ) @ SV1771 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6951]) ).

thf(8150,plain,
    ! [SV1772: $i,SV1589: $i,SV1332: $i,SV77: $i] :
      ( ( ~ ( c_in @ SV77 @ ( c_Relation_Oconverse @ SV1332 @ SV1589 @ SV1772 ) @ ( tc_prod @ SV1772 @ SV1589 ) )
        | ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1332 @ SV77 @ SV1589 @ SV1772 ) @ ( c_Main_OconverseE__2 @ SV1332 @ SV77 @ SV1589 @ SV1772 ) @ SV1589 @ SV1772 ) @ SV1332 @ ( tc_prod @ SV1589 @ SV1772 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6952]) ).

thf(8151,plain,
    ! [SV1773: $i,SV1590: $i,SV1333: $i,SV78: $i] :
      ( ( ~ ( c_in @ SV78 @ ( c_Relation_Oconverse @ SV1333 @ SV1590 @ SV1773 ) @ ( tc_prod @ SV1773 @ SV1590 ) )
        | ( SV78
          = ( c_Pair @ ( c_Main_OconverseE__2 @ SV1333 @ SV78 @ SV1590 @ SV1773 ) @ ( c_Main_OconverseE__1 @ SV1333 @ SV78 @ SV1590 @ SV1773 ) @ SV1773 @ SV1590 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6953]) ).

thf(8152,plain,
    ! [SV1591: $i,SV1334: $i,SV79: $i] :
      ( ( ( ~ ( c_in @ SV79 @ ( c_Relation_Odiag @ SV1334 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) ) )
        = $true )
      | ( ( SV79
          = ( c_Pair @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SV1591 ) @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SV1591 ) @ SV1591 @ SV1591 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6954]) ).

thf(8153,plain,
    ! [SV1592: $i,SV1335: $i,SV80: $i] :
      ( ( ( ~ ( c_in @ SV80 @ ( c_Relation_Odiag @ SV1335 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) ) )
        = $true )
      | ( ( c_in @ ( c_Main_OdiagE__1 @ SV1335 @ SV80 @ SV1592 ) @ SV1335 @ SV1592 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6955]) ).

thf(8154,plain,
    ! [SV1593: $i,SV1336: $i,SV81: $i] :
      ( ( ( ~ ( c_in @ SV81 @ SV1336 @ SV1593 ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV81 @ SV81 @ SV1593 @ SV1593 ) @ ( c_Relation_Odiag @ SV1336 @ SV1593 ) @ ( tc_prod @ SV1593 @ SV1593 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6956]) ).

thf(8155,plain,
    ! [SV1774: $i,SV1594: $i,SV1337: $i,SV82: $i] :
      ( ( ! [SY3374: $i,SY3375: $i] :
            ( ~ ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SV1337 @ SV1594 @ SV1774 @ SY3374 @ SY3375 ) @ ( tc_prod @ SY3375 @ SY3374 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SY3374 @ SY3375 ) @ ( c_Main_Orel__compE__3 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SY3374 @ SY3375 ) @ SV1774 @ SY3374 ) @ SV1337 @ ( tc_prod @ SV1774 @ SY3374 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6957]) ).

thf(8156,plain,
    ! [SV1775: $i,SV1595: $i,SV1338: $i,SV83: $i] :
      ( ( ! [SY3376: $i,SY3377: $i] :
            ( ~ ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SV1338 @ SV1595 @ SV1775 @ SY3376 @ SY3377 ) @ ( tc_prod @ SY3377 @ SY3376 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SY3376 @ SY3377 ) @ ( c_Main_Orel__compE__2 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SY3376 @ SY3377 ) @ SY3377 @ SV1775 ) @ SV1595 @ ( tc_prod @ SY3377 @ SV1775 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6958]) ).

thf(8157,plain,
    ! [SV1776: $i,SV1596: $i,SV1339: $i,SV84: $i] :
      ( ( ! [SY3378: $i,SY3379: $i] :
            ( ~ ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SV1339 @ SV1596 @ SV1776 @ SY3378 @ SY3379 ) @ ( tc_prod @ SY3379 @ SY3378 ) )
            | ( SV84
              = ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SY3378 @ SY3379 ) @ ( c_Main_Orel__compE__3 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SY3378 @ SY3379 ) @ SY3379 @ SY3378 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6959]) ).

thf(8158,plain,
    ! [SV1777: $i,SV1597: $i,SV1340: $i,SV85: $i] :
      ( ( ! [SY3380: $i,SY3381: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SY3380 @ ( tc_prod @ SV1597 @ SV1777 ) )
            | ! [SY3382: $i,SY3383: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY3381 @ SV85 @ SY3382 @ SV1597 ) @ SY3383 @ ( tc_prod @ SY3382 @ SV1597 ) )
                | ( c_in @ ( c_Pair @ SY3381 @ SV1340 @ SY3382 @ SV1777 ) @ ( c_Relation_Orel__comp @ SY3380 @ SY3383 @ SV1597 @ SV1777 @ SY3382 ) @ ( tc_prod @ SY3382 @ SV1777 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6960]) ).

thf(8159,plain,
    ! [SV1598: $i,SV1349: $i,SV96: $i] :
      ( ( ( c_in @ SV96 @ ( c_Inter @ SV1349 @ SV1598 ) @ SV1598 )
        = $true )
      | ( ( c_in @ ( c_Main_OInterI__1 @ SV96 @ SV1349 @ SV1598 ) @ SV1349 @ ( tc_set @ SV1598 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6961]) ).

thf(8160,plain,
    ! [SV1599: $i,SV1350: $i,SV97: $i] :
      ( ( ( ~ ( c_in @ SV97 @ ( c_Main_OInterI__1 @ SV97 @ SV1350 @ SV1599 ) @ SV1599 ) )
        = $true )
      | ( ( c_in @ SV97 @ ( c_Inter @ SV1350 @ SV1599 ) @ SV1599 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6962]) ).

thf(8161,plain,
    ! [SV1600: $i,SV1352: $i,SV99: $i] :
      ( ( ( ~ ( c_in @ SV99 @ ( c_Union @ SV1352 @ SV1600 ) @ SV1600 ) )
        = $true )
      | ( ( c_in @ ( c_Main_OUnionE__1 @ SV99 @ SV1352 @ SV1600 ) @ SV1352 @ ( tc_set @ SV1600 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6963]) ).

thf(8162,plain,
    ! [SV1601: $i,SV1353: $i,SV100: $i] :
      ( ( ( ~ ( c_in @ SV100 @ ( c_Union @ SV1353 @ SV1601 ) @ SV1601 ) )
        = $true )
      | ( ( c_in @ SV100 @ ( c_Main_OUnionE__1 @ SV100 @ SV1353 @ SV1601 ) @ SV1601 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6964]) ).

thf(8163,plain,
    ! [SV1602: $i,SV1355: $i,SV102: $i] :
      ( ( ( ~ ( c_less @ SV102 @ SV1355 @ ( tc_set @ SV1602 ) ) )
        = $true )
      | ( ( ~ ( c_lessequals @ SV1355 @ SV102 @ ( tc_set @ SV1602 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6965]) ).

thf(8164,plain,
    ! [SV1603: $i,SV1356: $i,SV103: $i] :
      ( ( ( ~ ( c_less @ SV103 @ SV1356 @ ( tc_set @ SV1603 ) ) )
        = $true )
      | ( ( c_lessequals @ SV103 @ SV1356 @ ( tc_set @ SV1603 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6966]) ).

thf(8165,plain,
    ! [SV1604: $i,SV1357: $i,SV104: $i] :
      ( ( ( ~ ( c_lessequals @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) ) )
        = $true )
      | ( ( ( SV104 = SV1357 )
          | ( c_less @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6967]) ).

thf(8166,plain,
    ! [SV1778: $i,SV1358: $i,SV105: $i] :
      ( ( ( ~ ( c_in @ SV105 @ ( c_insert @ SV1358 @ c_emptyset @ SV1778 ) @ SV1778 ) )
        = $true )
      | ( ( SV105 = SV1358 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[6968]) ).

thf(8167,plain,
    ! [SV1605: $i,SV1360: $i,SV107: $i] :
      ( ( ( ( c_insert @ SV107 @ c_emptyset @ SV1360 )
         != ( c_insert @ SV1605 @ c_emptyset @ SV1360 ) )
        = $true )
      | ( ( SV107 = SV1605 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6969]) ).

thf(8168,plain,
    ! [SV1606: $i,SV1361: $i,SV108: $i] :
      ( ( ( ~ ( c_in @ SV108 @ SV1361 @ SV1606 ) )
        = $true )
      | ( ( ! [SY3229: $i] :
              ( ~ ( c_lessequals @ SV1361 @ SY3229 @ ( tc_set @ SV1606 ) )
              | ( c_in @ SV108 @ SY3229 @ SV1606 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6970]) ).

thf(8169,plain,
    ! [SV1607: $i,SV1362: $i,SV109: $i] :
      ( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV109 @ SV1362 @ SV1607 ) @ SV109 @ SV1607 )
        = $true )
      | ( ( c_lessequals @ SV109 @ SV1362 @ ( tc_set @ SV1607 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6971]) ).

thf(8170,plain,
    ! [SV1608: $i,SV1363: $i,SV110: $i] :
      ( ( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV110 @ SV1363 @ SV1608 ) @ SV1363 @ SV1608 ) )
        = $true )
      | ( ( c_lessequals @ SV110 @ SV1363 @ ( tc_set @ SV1608 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6972]) ).

thf(8171,plain,
    ! [SV1609: $i,SV1364: $i,SV111: $i] :
      ( ( ( ~ ( c_lessequals @ SV111 @ SV1364 @ ( tc_set @ SV1609 ) ) )
        = $true )
      | ( ( ~ ( c_lessequals @ SV1364 @ SV111 @ ( tc_set @ SV1609 ) )
          | ( SV1364 = SV111 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6973]) ).

thf(8172,plain,
    ! [SV1610: $i,SV1366: $i,SV113: $i] :
      ( ( ( ~ ( c_in @ SV113 @ SV1366 @ SV1610 ) )
        = $true )
      | ( ( ! [SY3230: $i,SY3231: $i] : ( c_in @ ( c_Sum__Type_OInl @ SV113 @ SV1610 @ SY3230 ) @ ( c_Sum__Type_OPlus @ SV1366 @ SY3231 @ SV1610 @ SY3230 ) @ ( tc_sum @ SV1610 @ SY3230 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6974]) ).

thf(8173,plain,
    ! [SV1611: $i,SV1367: $i,SV114: $i] :
      ( ( ( ~ ( c_in @ SV114 @ SV1367 @ SV1611 ) )
        = $true )
      | ( ( ! [SY3232: $i,SY3233: $i] : ( c_in @ ( c_Sum__Type_OInr @ SV114 @ SV1611 @ SY3232 ) @ ( c_Sum__Type_OPlus @ SY3233 @ SV1367 @ SY3232 @ SV1611 ) @ ( tc_sum @ SY3232 @ SV1611 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6975]) ).

thf(8174,plain,
    ! [SV1779: $i,SV1612: $i,SV1368: $i,SV115: $i] :
      ( ( ! [SY3384: $i] :
            ( ~ ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SV1368 @ SV1612 @ SV1779 @ SY3384 ) @ ( tc_sum @ SV1779 @ SY3384 ) )
            | ( SV115
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1368 @ SV115 @ SV1779 @ SY3384 ) @ SV1779 @ SY3384 ) )
            | ( SV115
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1612 @ SV115 @ SY3384 @ SV1779 ) @ SY3384 @ SV1779 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6976]) ).

thf(8175,plain,
    ! [SV1780: $i,SV1613: $i,SV1369: $i,SV116: $i] :
      ( ( ! [SY3385: $i] :
            ( ~ ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SV1369 @ SV1613 @ SV1780 @ SY3385 ) @ ( tc_sum @ SV1780 @ SY3385 ) )
            | ( SV116
              = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1369 @ SV116 @ SV1780 @ SY3385 ) @ SV1780 @ SY3385 ) )
            | ( c_in @ ( c_Main_OPlusE__2 @ SV1613 @ SV116 @ SY3385 @ SV1780 ) @ SV1613 @ SY3385 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6977]) ).

thf(8176,plain,
    ! [SV1781: $i,SV1614: $i,SV1370: $i,SV117: $i] :
      ( ( ! [SY3386: $i] :
            ( ~ ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SV1370 @ SV1614 @ SV1781 @ SY3386 ) @ ( tc_sum @ SV1781 @ SY3386 ) )
            | ( SV117
              = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1614 @ SV117 @ SY3386 @ SV1781 ) @ SY3386 @ SV1781 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SV1370 @ SV117 @ SV1781 @ SY3386 ) @ SV1370 @ SV1781 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6978]) ).

thf(8177,plain,
    ! [SV1782: $i,SV1615: $i,SV1371: $i,SV118: $i] :
      ( ( ! [SY3387: $i] :
            ( ~ ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SV1371 @ SV1615 @ SV1782 @ SY3387 ) @ ( tc_sum @ SV1782 @ SY3387 ) )
            | ( c_in @ ( c_Main_OPlusE__1 @ SV1371 @ SV118 @ SV1782 @ SY3387 ) @ SV1371 @ SV1782 )
            | ( c_in @ ( c_Main_OPlusE__2 @ SV1615 @ SV118 @ SY3387 @ SV1782 ) @ SV1615 @ SY3387 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6979]) ).

thf(8178,plain,
    ! [SV1616: $i,SV1372: $i,SV119: $i] :
      ( ( ( ~ ( c_in @ SV119 @ SV1372 @ ( tc_prod @ SV1616 @ SV1616 ) ) )
        = $true )
      | ( ( c_in @ SV119 @ ( c_Transitive__Closure_Ortrancl @ SV1372 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6980]) ).

thf(8179,plain,
    ! [SV1783: $i,SV1618: $i,SV1374: $i,SV121: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ SV1783 @ ( tc_prod @ SV1618 @ SV1618 ) )
        | ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SV1783 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6982]) ).

thf(8180,plain,
    ! [SV1784: $i,SV1619: $i,SV1375: $i,SV122: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Otrancl @ SV1784 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
        | ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1784 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6983]) ).

thf(8181,plain,
    ! [SV1376: $i,SV124: $i] :
      ( ( ( c_Relation_Otrans @ SV124 @ SV1376 )
        = $false )
      | ( ( ! [SY2929: $i,SY2930: $i] :
              ( ~ ( c_Relation_Otrans @ SY2929 @ SY2930 )
              | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SY2929 @ SV124 @ SY2930 @ SV1376 ) @ ( tc_prod @ SY2930 @ SV1376 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6984]) ).

thf(8182,plain,
    ! [SV1377: $i,SV125: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ SV125 @ SV1377 )
        = $false )
      | ( ( ! [SY2931: $i,SY2932: $i] :
              ( ~ ( c_Wellfounded__Recursion_Owf @ SY2931 @ SY2932 )
              | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SY2931 @ SV125 @ SY2932 @ SV1377 ) @ ( tc_prod @ SY2932 @ SV1377 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[6985]) ).

thf(8183,plain,
    ! [SV127: $i,SV1378: $i] :
      ( ( ( ~ ( class_Finite__Set_Ofinite @ SV1378 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV127 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV127 @ SV1378 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6987]) ).

thf(8184,plain,
    ! [SV129: $i,SV1380: $i] :
      ( ( ( ~ ( class_Finite__Set_Ofinite @ SV1380 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV129 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV129 @ SV1380 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6988]) ).

thf(8185,plain,
    ! [SV135: $i,SV1381: $i] :
      ( ( ( ~ ( class_Finite__Set_Ofinite @ SV1381 ) )
        = $true )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV135 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV135 @ SV1381 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6990]) ).

thf(8186,plain,
    ! [SV1620: $i,SV1382: $i,SV1043: $i] :
      ( ( ( ~ ( c_in @ SV1043 @ ( c_Datatype_Oo2s @ SV1382 @ SV1620 ) @ SV1620 ) )
        = $true )
      | ( ( SV1382
          = ( c_Datatype_Ooption_OSome @ SV1043 @ SV1620 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7898]) ).

thf(8187,plain,
    ! [SV1623: $i,SV1386: $i,SV1049: $i] :
      ( ( ( ( c_Datatype_Ooption_OSome @ SV1049 @ SV1386 )
         != ( c_Datatype_Ooption_OSome @ SV1623 @ SV1386 ) )
        = $true )
      | ( ( SV1049 = SV1623 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7903]) ).

thf(8188,plain,
    ! [SV1785: $i,SV1624: $i,SV1387: $i,SV1050: $i] :
      ( ( ( ( c_Datatype__Universe_OAtom @ SV1050 @ SV1387 @ SV1624 )
         != ( c_Datatype__Universe_OAtom @ SV1785 @ SV1387 @ SV1624 ) )
        | ( SV1050 = SV1785 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7904]) ).

thf(8189,plain,
    ! [SV1786: $i,SV1625: $i,SV1388: $i,SV1051: $i] :
      ( ( ! [SY3388: $i] :
            ( ( c_Datatype__Universe_OAtom @ SV1051 @ SV1388 @ SV1625 )
           != ( c_Datatype__Universe_OScons @ SV1786 @ SY3388 @ SV1388 @ SV1625 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7905]) ).

thf(8190,plain,
    ! [SV1787: $i,SV1626: $i,SV1389: $i,SV1052: $i] :
      ( ( ( ( c_Datatype__Universe_OIn0 @ SV1052 @ SV1389 @ SV1626 )
         != ( c_Datatype__Universe_OIn0 @ SV1787 @ SV1389 @ SV1626 ) )
        | ( SV1052 = SV1787 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7906]) ).

thf(8191,plain,
    ! [SV1788: $i,SV1627: $i,SV1390: $i,SV1053: $i] :
      ( ( ( c_Datatype__Universe_OIn0 @ SV1053 @ SV1390 @ SV1627 )
       != ( c_Datatype__Universe_OIn1 @ SV1788 @ SV1390 @ SV1627 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7907]) ).

thf(8192,plain,
    ! [SV1789: $i,SV1628: $i,SV1391: $i,SV1054: $i] :
      ( ( ( ( c_Datatype__Universe_OIn1 @ SV1054 @ SV1391 @ SV1628 )
         != ( c_Datatype__Universe_OIn1 @ SV1789 @ SV1391 @ SV1628 ) )
        | ( SV1054 = SV1789 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7908]) ).

thf(8193,plain,
    ! [SV1790: $i,SV1629: $i,SV1392: $i,SV1055: $i] :
      ( ( ( c_Datatype__Universe_OIn1 @ SV1055 @ SV1392 @ SV1629 )
       != ( c_Datatype__Universe_OIn0 @ SV1790 @ SV1392 @ SV1629 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7909]) ).

thf(8194,plain,
    ! [SV1791: $i,SV1630: $i,SV1393: $i,SV1056: $i] :
      ( ( ( c_Datatype__Universe_OLeaf @ SV1056 @ SV1393 @ SV1630 )
       != ( c_Datatype__Universe_ONumb @ SV1791 @ SV1393 @ SV1630 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7910]) ).

thf(8195,plain,
    ! [SV1792: $i,SV1631: $i,SV1394: $i,SV1057: $i] :
      ( ( ! [SY3389: $i] :
            ( ( c_Datatype__Universe_OLeaf @ SV1057 @ SV1394 @ SV1631 )
           != ( c_Datatype__Universe_OScons @ SV1792 @ SY3389 @ SV1394 @ SV1631 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7911]) ).

thf(8196,plain,
    ! [SV1793: $i,SV1632: $i,SV1395: $i,SV1058: $i] :
      ( ( ( c_Datatype__Universe_ONumb @ SV1058 @ SV1395 @ SV1632 )
       != ( c_Datatype__Universe_OLeaf @ SV1793 @ SV1395 @ SV1632 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7912]) ).

thf(8197,plain,
    ! [SV1794: $i,SV1633: $i,SV1396: $i,SV1059: $i] :
      ( ( ! [SY3390: $i] :
            ( ( c_Datatype__Universe_ONumb @ SV1059 @ SV1396 @ SV1633 )
           != ( c_Datatype__Universe_OScons @ SV1794 @ SY3390 @ SV1396 @ SV1633 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7913]) ).

thf(8198,plain,
    ! [SV1795: $i,SV1634: $i,SV1397: $i,SV1060: $i] :
      ( ( ! [SY3391: $i] :
            ( ! [SY3392: $i] :
                ( ( c_Datatype__Universe_OScons @ SV1060 @ SV1397 @ SV1634 @ SV1795 )
               != ( c_Datatype__Universe_OScons @ SY3391 @ SY3392 @ SV1634 @ SV1795 ) )
            | ( SV1060 = SY3391 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7914]) ).

thf(8199,plain,
    ! [SV1796: $i,SV1635: $i,SV1398: $i,SV1061: $i] :
      ( ( ! [SY3393: $i,SY3394: $i] :
            ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SV1398 @ SV1635 @ SV1796 )
             != ( c_Datatype__Universe_OScons @ SY3393 @ SY3394 @ SV1635 @ SV1796 ) )
            | ( SV1398 = SY3394 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7915]) ).

thf(8200,plain,
    ! [SV1797: $i,SV1636: $i,SV1399: $i,SV1062: $i] :
      ( ( ! [SY3395: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1062 @ SV1399 @ SV1636 @ SV1797 )
           != ( c_Datatype__Universe_OAtom @ SY3395 @ SV1636 @ SV1797 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7916]) ).

thf(8201,plain,
    ! [SV1798: $i,SV1637: $i,SV1400: $i,SV1063: $i] :
      ( ( ! [SY3396: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1063 @ SV1400 @ SV1637 @ SV1798 )
           != ( c_Datatype__Universe_OLeaf @ SY3396 @ SV1637 @ SV1798 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7917]) ).

thf(8202,plain,
    ! [SV1799: $i,SV1638: $i,SV1401: $i,SV1064: $i] :
      ( ( ! [SY3397: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1064 @ SV1401 @ SV1638 @ SV1799 )
           != ( c_Datatype__Universe_ONumb @ SY3397 @ SV1638 @ SV1799 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7918]) ).

thf(8203,plain,
    ! [SV1800: $i,SV1639: $i,SV1066: $i] :
      ( ( ( c_emptyset
         != ( c_Equiv__Relations_Oquotient @ SV1066 @ SV1639 @ SV1800 ) )
        = $true )
      | ( ( SV1066 = c_emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7920]) ).

thf(8204,plain,
    ! [SV1801: $i,SV1640: $i,SV1068: $i] :
      ( ( ( ( c_Equiv__Relations_Oquotient @ SV1068 @ SV1640 @ SV1801 )
         != c_emptyset )
        = $true )
      | ( ( SV1068 = c_emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7921]) ).

thf(8205,plain,
    ! [SV1802: $i,SV1641: $i,SV1404: $i,SV1070: $i] :
      ( ( ~ ( c_in @ ( c_minus @ SV1070 @ ( c_insert @ SV1404 @ SV1641 @ SV1802 ) @ ( tc_set @ SV1802 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1802 ) )
        | ( c_in @ ( c_minus @ SV1070 @ SV1641 @ ( tc_set @ SV1802 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1802 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7922]) ).

thf(8206,plain,
    ! [SV1642: $i,SV1405: $i,SV1071: $i] :
      ( ( ( ~ ( c_in @ ( c_minus @ SV1071 @ SV1405 @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) ) )
        = $true )
      | ( ( ! [SY3272: $i] : ( c_in @ ( c_minus @ SV1071 @ ( c_insert @ SY3272 @ SV1405 @ SV1642 ) @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7923]) ).

thf(8207,plain,
    ! [SV1406: $i,SV1072: $i] :
      ( ( ( c_in @ ( c_Pow @ SV1072 @ SV1406 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1406 ) ) )
        = $false )
      | ( ( c_in @ SV1072 @ c_Finite__Set_OFinites @ ( tc_set @ SV1406 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7924]) ).

thf(8208,plain,
    ! [SV1407: $i,SV1073: $i] :
      ( ( ( c_in @ SV1073 @ c_Finite__Set_OFinites @ ( tc_set @ SV1407 ) )
        = $false )
      | ( ( c_in @ ( c_Pow @ SV1073 @ SV1407 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1407 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7925]) ).

thf(8209,plain,
    ! [SV1643: $i,SV1408: $i,SV1074: $i] :
      ( ( ( ~ ( c_in @ ( c_union @ SV1074 @ SV1408 @ SV1643 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1643 ) ) )
        = $true )
      | ( ( c_in @ SV1074 @ c_Finite__Set_OFinites @ ( tc_set @ SV1643 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7926]) ).

thf(8210,plain,
    ! [SV1644: $i,SV1409: $i,SV1075: $i] :
      ( ( ( ~ ( c_in @ ( c_union @ SV1075 @ SV1409 @ SV1644 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1644 ) ) )
        = $true )
      | ( ( c_in @ SV1409 @ c_Finite__Set_OFinites @ ( tc_set @ SV1644 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7927]) ).

thf(8211,plain,
    ! [SV1410: $i,SV1076: $i] :
      ( ( ( c_in @ SV1076 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        = $false )
      | ( ( ! [SY2981: $i] :
              ( ~ ( c_in @ SY2981 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
              | ( c_in @ ( c_union @ SY2981 @ SV1076 @ SV1410 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7928]) ).

thf(8212,plain,
    ! [SV1645: $i,SV1411: $i,SV1077: $i] :
      ( ( ( ~ ( c_in @ ( c_Relation_Oconverse @ SV1077 @ SV1411 @ SV1645 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1645 @ SV1411 ) ) ) )
        = $true )
      | ( ( c_in @ SV1077 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1411 @ SV1645 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7929]) ).

thf(8213,plain,
    ! [SV1646: $i,SV1412: $i,SV1078: $i] :
      ( ( ( ~ ( c_in @ SV1078 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1412 @ SV1646 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Relation_Oconverse @ SV1078 @ SV1412 @ SV1646 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1646 @ SV1412 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7930]) ).

thf(8214,plain,
    ! [SV1803: $i,SV1413: $i,SV1079: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1079 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1413 @ SV1803 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1079 @ SV1413 @ tc_nat )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7931]) ).

thf(8215,plain,
    ! [SV1647: $i,SV1414: $i,SV1080: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1080 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1414 @ SV1647 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1080 @ SV1647 @ tc_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7932]) ).

thf(8216,plain,
    ! [SV1415: $i,SV1081: $i] :
      ( ( ( c_Divides_Oop_Advd @ SV1081 @ SV1415 @ tc_nat )
        = $false )
      | ( ( ! [SY2986: $i] :
              ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SY2986 @ tc_nat )
              | ( c_Divides_Oop_Advd @ SV1081 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2986 @ SV1415 @ tc_nat @ tc_nat ) ) @ tc_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7933]) ).

thf(8217,plain,
    ! [SV1416: $i,SV1082: $i] :
      ( ( ( ( c_IntDef_Oint @ SV1082 )
          = ( c_IntDef_Oint @ SV1416 ) )
        = $false )
      | ( ( SV1082 = SV1416 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7934]) ).

thf(8218,plain,
    ! [SV1417: $i,SV1083: $i] :
      ( ( ( c_Divides_Oop_Advd @ SV1083 @ ( c_uminus @ SV1417 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = $false )
      | ( ( c_Divides_Oop_Advd @ SV1083 @ SV1417 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7935]) ).

thf(8219,plain,
    ! [SV1418: $i,SV1084: $i] :
      ( ( ( c_Divides_Oop_Advd @ SV1084 @ SV1418 @ tc_IntDef_Oint )
        = $false )
      | ( ( c_Divides_Oop_Advd @ SV1084 @ ( c_uminus @ SV1418 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7936]) ).

thf(8220,plain,
    ! [SV1419: $i,SV1086: $i] :
      ( ( ( c_Divides_Oop_Advd @ ( c_uminus @ SV1086 @ tc_IntDef_Oint ) @ SV1419 @ tc_IntDef_Oint )
        = $false )
      | ( ( c_Divides_Oop_Advd @ SV1086 @ SV1419 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7938]) ).

thf(8221,plain,
    ! [SV1420: $i,SV1087: $i] :
      ( ( ( c_Divides_Oop_Advd @ SV1087 @ SV1420 @ tc_IntDef_Oint )
        = $false )
      | ( ( c_Divides_Oop_Advd @ ( c_uminus @ SV1087 @ tc_IntDef_Oint ) @ SV1420 @ tc_IntDef_Oint )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7939]) ).

thf(8222,plain,
    ! [SV1648: $i,SV1421: $i,SV1088: $i] :
      ( ( c_in @ ( c_Pair @ SV1088 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1421 ) @ ( tc_List_Olist @ SV1421 ) ) @ ( c_List_Olex @ SV1648 @ SV1421 ) @ ( tc_prod @ ( tc_List_Olist @ SV1421 ) @ ( tc_List_Olist @ SV1421 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7940]) ).

thf(8223,plain,
    ! [SV1804: $i,SV1649: $i,SV1089: $i] :
      ( ( ( c_List_Olist_ONil
         != ( c_append @ SV1089 @ SV1649 @ SV1804 ) )
        = $true )
      | ( ( SV1089 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7941]) ).

thf(8224,plain,
    ! [SV1805: $i,SV1422: $i,SV1090: $i] :
      ( ( ( c_List_Olist_ONil
         != ( c_append @ SV1090 @ SV1422 @ SV1805 ) )
        = $true )
      | ( ( SV1422 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7942]) ).

thf(8225,plain,
    ! [SV1650: $i,SV1092: $i] :
      ( ( ( c_List_Olist_ONil
          = ( c_List_Orev @ SV1092 @ SV1650 ) )
        = $false )
      | ( ( SV1092 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7943]) ).

thf(8226,plain,
    ! [SV1651: $i,SV1423: $i,SV1094: $i] :
      ( ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1094 @ ( tc_List_Olist @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) @ ( c_List_Olex @ SV1651 @ SV1423 ) @ ( tc_prod @ ( tc_List_Olist @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7944]) ).

thf(8227,plain,
    ! [SV1806: $i,SV1652: $i,SV1424: $i,SV1095: $i] :
      ( ( ! [SY3398: $i] :
            ( ( c_append @ SV1095 @ ( c_List_Olist_OCons @ SV1424 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 )
           != ( c_append @ SV1806 @ ( c_List_Olist_OCons @ SY3398 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 ) )
        | ( SV1095 = SV1806 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7945]) ).

thf(8228,plain,
    ! [SV1807: $i,SV1653: $i,SV1425: $i,SV1096: $i] :
      ( ( ! [SY3399: $i] :
            ( ( ( c_append @ SV1096 @ ( c_List_Olist_OCons @ SV1425 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 )
             != ( c_append @ SV1807 @ ( c_List_Olist_OCons @ SY3399 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 ) )
            | ( SV1425 = SY3399 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7946]) ).

thf(8229,plain,
    ! [SV1808: $i,SV1654: $i,SV1426: $i,SV1097: $i] :
      ( ( ~ ( c_in @ ( c_append @ SV1097 @ SV1426 @ SV1654 ) @ ( c_List_Olists @ SV1808 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) )
        | ( c_in @ SV1097 @ ( c_List_Olists @ SV1808 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7947]) ).

thf(8230,plain,
    ! [SV1809: $i,SV1655: $i,SV1427: $i,SV1098: $i] :
      ( ( ~ ( c_in @ ( c_append @ SV1098 @ SV1427 @ SV1655 ) @ ( c_List_Olists @ SV1809 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) )
        | ( c_in @ SV1427 @ ( c_List_Olists @ SV1809 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7948]) ).

thf(8231,plain,
    ! [SV1656: $i,SV1428: $i,SV1099: $i] :
      ( ( ( ~ ( c_in @ SV1099 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) ) )
        = $true )
      | ( ( ! [SY3280: $i] :
              ( ~ ( c_in @ SY3280 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
              | ( c_in @ ( c_append @ SY3280 @ SV1099 @ SV1656 ) @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7949]) ).

thf(8232,plain,
    ! [SV1810: $i,SV1657: $i,SV1100: $i] :
      ( ( ( ( c_append @ SV1100 @ SV1657 @ SV1810 )
         != c_List_Olist_ONil )
        = $true )
      | ( ( SV1100 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7950]) ).

thf(8233,plain,
    ! [SV1811: $i,SV1429: $i,SV1101: $i] :
      ( ( ( ( c_append @ SV1101 @ SV1429 @ SV1811 )
         != c_List_Olist_ONil )
        = $true )
      | ( ( SV1429 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7951]) ).

thf(8234,plain,
    ! [SV1812: $i,SV1658: $i,SV1430: $i,SV1103: $i] :
      ( ( ( ( c_append @ SV1103 @ SV1430 @ SV1658 )
         != ( c_append @ SV1812 @ SV1430 @ SV1658 ) )
        | ( SV1103 = SV1812 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7952]) ).

thf(8235,plain,
    ! [SV1813: $i,SV1659: $i,SV1104: $i] :
      ( ( ( ( c_append @ SV1104 @ SV1659 @ SV1813 )
         != SV1659 )
        = $true )
      | ( ( SV1104 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7953]) ).

thf(8236,plain,
    ! [SV1814: $i,SV1432: $i,SV1106: $i] :
      ( ( ( ( c_append @ SV1106 @ SV1432 @ SV1814 )
         != SV1106 )
        = $true )
      | ( ( SV1432 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7954]) ).

thf(8237,plain,
    ! [SV1660: $i,SV1434: $i,SV1108: $i] :
      ( ( ( ! [SY3284: $i] :
              ( ( c_List_Ochar_OChar @ SV1108 @ SV1434 )
             != ( c_List_Ochar_OChar @ SV1660 @ SY3284 ) ) )
        = $true )
      | ( ( SV1108 = SV1660 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7955]) ).

thf(8238,plain,
    ! [SV1815: $i,SV1661: $i,SV1435: $i,SV1109: $i] :
      ( ( ( ( c_List_Ochar_OChar @ SV1109 @ SV1435 )
         != ( c_List_Ochar_OChar @ SV1661 @ SV1815 ) )
        | ( SV1435 = SV1815 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7956]) ).

thf(8239,plain,
    ! [SV1662: $i,SV1110: $i] :
      ( ( ( ( c_Nat_Osize @ SV1110 @ ( tc_List_Olist @ SV1662 ) )
          = c_0 )
        = $false )
      | ( ( SV1110 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7957]) ).

thf(8240,plain,
    ! [SV1436: $i,SV1114: $i] :
      ( ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1114 @ SV1436 ) @ ( tc_List_Olist @ SV1436 ) )
          = ( c_Nat_Osize @ SV1114 @ ( tc_List_Olist @ SV1436 ) ) )
        = $false )
      | ( ( ( c_List_Oremdups @ SV1114 @ SV1436 )
          = SV1114 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7959]) ).

thf(8241,plain,
    ! [SV1437: $i,SV1115: $i] :
      ( ( ( ( c_List_Oremdups @ SV1115 @ SV1437 )
          = SV1115 )
        = $false )
      | ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1115 @ SV1437 ) @ ( tc_List_Olist @ SV1437 ) )
          = ( c_Nat_Osize @ SV1115 @ ( tc_List_Olist @ SV1437 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7960]) ).

thf(8242,plain,
    ! [SV1664: $i,SV1438: $i,SV1116: $i] :
      ( ( c_List_Olist_ONil
        = ( c_List_Olist_OCons @ SV1116 @ SV1438 @ SV1664 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7961]) ).

thf(8243,plain,
    ! [SV1665: $i,SV1439: $i,SV1117: $i] :
      ( ( ( c_List_Olist_OCons @ SV1117 @ SV1439 @ SV1665 )
        = c_List_Olist_ONil )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7962]) ).

thf(8244,plain,
    ! [SV1816: $i,SV1666: $i,SV1440: $i,SV1118: $i] :
      ( ( ! [SY3400: $i] :
            ( ( c_List_Olist_OCons @ SV1118 @ SV1440 @ SV1666 )
           != ( c_List_Olist_OCons @ SV1816 @ SY3400 @ SV1666 ) )
        | ( SV1118 = SV1816 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7963]) ).

thf(8245,plain,
    ! [SV1817: $i,SV1667: $i,SV1441: $i,SV1119: $i] :
      ( ( ! [SY3401: $i] :
            ( ( ( c_List_Olist_OCons @ SV1119 @ SV1441 @ SV1667 )
             != ( c_List_Olist_OCons @ SV1817 @ SY3401 @ SV1667 ) )
            | ( SV1441 = SY3401 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7964]) ).

thf(8246,plain,
    ! [SV1818: $i,SV1668: $i,SV1442: $i,SV1120: $i] :
      ( ( ( ( c_List_Orev @ SV1120 @ SV1442 )
         != ( c_List_Olist_OCons @ SV1668 @ SV1818 @ SV1442 ) )
        | ( SV1120
          = ( c_append @ ( c_List_Orev @ SV1818 @ SV1442 ) @ ( c_List_Olist_OCons @ SV1668 @ c_List_Olist_ONil @ SV1442 ) @ SV1442 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7965]) ).

thf(8247,plain,
    ! [SV1670: $i,SV1122: $i] :
      ( ( ( ( c_List_Orev @ SV1122 @ SV1670 )
          = c_List_Olist_ONil )
        = $false )
      | ( ( SV1122 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7967]) ).

thf(8248,plain,
    ! [SV1671: $i,SV1444: $i,SV1124: $i] :
      ( ( ( ( c_List_Orev @ SV1124 @ SV1444 )
         != ( c_List_Orev @ SV1671 @ SV1444 ) )
        = $true )
      | ( ( SV1124 = SV1671 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7968]) ).

thf(8249,plain,
    ! [SV1819: $i,SV1672: $i,SV1445: $i,SV1125: $i] :
      ( ( ( ( c_append @ SV1125 @ SV1445 @ SV1672 )
         != ( c_append @ SV1125 @ SV1819 @ SV1672 ) )
        | ( SV1445 = SV1819 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7969]) ).

thf(8250,plain,
    ! [SV1820: $i,SV1446: $i,SV1126: $i] :
      ( ( ( SV1126
         != ( c_append @ SV1446 @ SV1126 @ SV1820 ) )
        = $true )
      | ( ( SV1446 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7970]) ).

thf(8251,plain,
    ! [SV1821: $i,SV1448: $i,SV1128: $i] :
      ( ( ( SV1128
         != ( c_append @ SV1128 @ SV1448 @ SV1821 ) )
        = $true )
      | ( ( SV1448 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7971]) ).

thf(8252,plain,
    ! [SV1673: $i,SV1130: $i] :
      ( ( ( c_emptyset
          = ( c_List_Oset @ SV1130 @ SV1673 ) )
        = $false )
      | ( ( SV1130 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7972]) ).

thf(8253,plain,
    ! [SV1674: $i,SV1132: $i] :
      ( ( ( ( c_List_Oset @ SV1132 @ SV1674 )
          = c_emptyset )
        = $false )
      | ( ( SV1132 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7973]) ).

thf(8254,plain,
    ! [SV1450: $i,SV1134: $i] :
      ( ( ( ( c_Suc @ SV1134 )
          = ( c_Suc @ SV1450 ) )
        = $false )
      | ( ( SV1134 = SV1450 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7974]) ).

thf(8255,plain,
    ! [SV1451: $i,SV1135: $i] :
      ( ( ( c_lessequals @ ( c_Suc @ SV1135 ) @ ( c_Suc @ SV1451 ) @ tc_nat )
        = $false )
      | ( ( c_lessequals @ SV1135 @ SV1451 @ tc_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7975]) ).

thf(8256,plain,
    ! [SV1452: $i,SV1136: $i] :
      ( ( ( c_lessequals @ SV1136 @ SV1452 @ tc_nat )
        = $false )
      | ( ( c_lessequals @ ( c_Suc @ SV1136 ) @ ( c_Suc @ SV1452 ) @ tc_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7976]) ).

thf(8257,plain,
    ! [SV1453: $i,SV1137: $i] :
      ( ( ( c_less @ ( c_Suc @ SV1137 ) @ ( c_Suc @ SV1453 ) @ tc_nat )
        = $false )
      | ( ( c_less @ SV1137 @ SV1453 @ tc_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7977]) ).

thf(8258,plain,
    ! [SV1454: $i,SV1138: $i] :
      ( ( ( c_less @ SV1138 @ SV1454 @ tc_nat )
        = $false )
      | ( ( c_less @ ( c_Suc @ SV1138 ) @ ( c_Suc @ SV1454 ) @ tc_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7978]) ).

thf(8259,plain,
    ! [SV1455: $i,SV1141: $i] :
      ( ( ( c_less @ c_0 @ ( c_plus @ SV1141 @ SV1455 @ tc_nat ) @ tc_nat )
        = $false )
      | ( ( ( c_less @ c_0 @ SV1455 @ tc_nat )
          | ( c_less @ c_0 @ SV1141 @ tc_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7979]) ).

thf(8260,plain,
    ! [SV1822: $i,SV1142: $i] :
      ( ( ( c_less @ c_0 @ ( c_plus @ SV1142 @ SV1822 @ tc_nat ) @ tc_nat )
        = $true )
      | ( ( c_less @ c_0 @ SV1142 @ tc_nat )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7980]) ).

thf(8261,plain,
    ! [SV1143: $i,SV1823: $i] :
      ( ( ( c_less @ c_0 @ ( c_plus @ SV1823 @ SV1143 @ tc_nat ) @ tc_nat )
        = $true )
      | ( ( c_less @ c_0 @ SV1143 @ tc_nat )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7981]) ).

thf(8262,plain,
    ! [SV1675: $i,SV1144: $i] :
      ( ( ( ( c_plus @ SV1144 @ SV1675 @ tc_nat )
          = c_0 )
        = $false )
      | ( ( SV1144 = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7982]) ).

thf(8263,plain,
    ! [SV1456: $i,SV1145: $i] :
      ( ( ( ( c_plus @ SV1145 @ SV1456 @ tc_nat )
          = c_0 )
        = $false )
      | ( ( SV1456 = c_0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7983]) ).

thf(8264,plain,
    ! [SV1153: $i,SV1824: $i] :
      ( ( ( ~ ( c_less @ SV1824 @ SV1824 @ SV1153 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1153 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7989]) ).

thf(8265,plain,
    ! [SV1825: $i,SV1676: $i,SV1459: $i,SV1154: $i] :
      ( ( ! [SY3402: $i] :
            ( ! [SY3403: $i] :
                ( ( c_Pair @ SV1154 @ SV1459 @ SV1676 @ SV1825 )
               != ( c_Pair @ SY3402 @ SY3403 @ SV1676 @ SV1825 ) )
            | ( SV1154 = SY3402 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7990]) ).

thf(8266,plain,
    ! [SV1826: $i,SV1677: $i,SV1460: $i,SV1155: $i] :
      ( ( ! [SY3404: $i,SY3405: $i] :
            ( ( ( c_Pair @ SV1155 @ SV1460 @ SV1677 @ SV1826 )
             != ( c_Pair @ SY3404 @ SY3405 @ SV1677 @ SV1826 ) )
            | ( SV1460 = SY3405 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7991]) ).

thf(8267,plain,
    ! [SV1827: $i,SV1678: $i,SV1462: $i,SV1157: $i] :
      ( ( ! [SY3406: $i] :
            ( ~ ( c_in @ SV1157 @ ( c_Relation_OImage @ SV1462 @ ( c_insert @ SV1678 @ c_emptyset @ SV1827 ) @ SV1827 @ SY3406 ) @ SY3406 )
            | ( c_in @ ( c_Pair @ SV1678 @ SV1157 @ SV1827 @ SY3406 ) @ SV1462 @ ( tc_prod @ SV1827 @ SY3406 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7992]) ).

thf(8268,plain,
    ! [SV1828: $i,SV1679: $i,SV1463: $i,SV1158: $i] :
      ( ( ! [SY3407: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1158 @ SV1463 @ SV1679 @ SV1828 ) @ SY3407 @ ( tc_prod @ SV1679 @ SV1828 ) )
            | ( c_in @ SV1463 @ ( c_Relation_OImage @ SY3407 @ ( c_insert @ SV1158 @ c_emptyset @ SV1679 ) @ SV1679 @ SV1828 ) @ SV1828 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7993]) ).

thf(8269,plain,
    ! [SV1829: $i,SV1680: $i,SV1464: $i,SV1159: $i] :
      ( ( ! [SY3408: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1159 @ SV1464 @ SV1680 @ SV1829 ) @ ( c_Relation_Oconverse @ SY3408 @ SV1829 @ SV1680 ) @ ( tc_prod @ SV1680 @ SV1829 ) )
            | ( c_in @ ( c_Pair @ SV1464 @ SV1159 @ SV1829 @ SV1680 ) @ SY3408 @ ( tc_prod @ SV1829 @ SV1680 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7994]) ).

thf(8270,plain,
    ! [SV1830: $i,SV1681: $i,SV1465: $i,SV1160: $i] :
      ( ( ! [SY3409: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1160 @ SV1465 @ SV1681 @ SV1830 ) @ SY3409 @ ( tc_prod @ SV1681 @ SV1830 ) )
            | ( c_in @ ( c_Pair @ SV1465 @ SV1160 @ SV1830 @ SV1681 ) @ ( c_Relation_Oconverse @ SY3409 @ SV1681 @ SV1830 ) @ ( tc_prod @ SV1830 @ SV1681 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7995]) ).

thf(8271,plain,
    ! [SV1831: $i,SV1466: $i,SV1161: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1161 @ SV1466 @ SV1831 @ SV1831 ) @ c_Relation_OId @ ( tc_prod @ SV1831 @ SV1831 ) ) )
        = $true )
      | ( ( SV1161 = SV1466 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7996]) ).

thf(8272,plain,
    ! [SV1162: $i,SV1832: $i] :
      ( ( ( ! [SY3410: $i] :
              ( ( ( c_SetInterval_OatLeast @ SV1832 @ SV1162 )
               != ( c_SetInterval_OatLeast @ SY3410 @ SV1162 ) )
              | ( SV1832 = SY3410 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1162 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7997]) ).

thf(8273,plain,
    ! [SV1163: $i,SV1833: $i] :
      ( ( ( ! [SY3411: $i] :
              ( ~ ( c_in @ SV1833 @ ( c_SetInterval_OatLeast @ SY3411 @ SV1163 ) @ SV1163 )
              | ( c_lessequals @ SY3411 @ SV1833 @ SV1163 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1163 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7998]) ).

thf(8274,plain,
    ! [SV1164: $i,SV1834: $i] :
      ( ( ( ! [SY3412: $i] :
              ( ~ ( c_lessequals @ SV1834 @ SY3412 @ SV1164 )
              | ( c_in @ SY3412 @ ( c_SetInterval_OatLeast @ SV1834 @ SV1164 ) @ SV1164 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1164 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7999]) ).

thf(8275,plain,
    ! [SV1165: $i,SV1835: $i] :
      ( ( ( ! [SY3413: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1835 @ SV1165 ) @ ( c_SetInterval_OatLeast @ SY3413 @ SV1165 ) @ ( tc_set @ SV1165 ) )
              | ( c_lessequals @ SY3413 @ SV1835 @ SV1165 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1165 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8000]) ).

thf(8276,plain,
    ! [SV1166: $i,SV1836: $i] :
      ( ( ( ! [SY3414: $i] :
              ( ~ ( c_lessequals @ SV1836 @ SY3414 @ SV1166 )
              | ( c_lessequals @ ( c_SetInterval_OatLeast @ SY3414 @ SV1166 ) @ ( c_SetInterval_OatLeast @ SV1836 @ SV1166 ) @ ( tc_set @ SV1166 ) ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1166 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8001]) ).

thf(8277,plain,
    ! [SV1167: $i,SV1837: $i] :
      ( ( ( ! [SY3415: $i] :
              ( ( ( c_SetInterval_OatMost @ SV1837 @ SV1167 )
               != ( c_SetInterval_OatMost @ SY3415 @ SV1167 ) )
              | ( SV1837 = SY3415 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1167 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8002]) ).

thf(8278,plain,
    ! [SV1168: $i,SV1838: $i] :
      ( ( ( ! [SY3416: $i] :
              ( ~ ( c_in @ SV1838 @ ( c_SetInterval_OatMost @ SY3416 @ SV1168 ) @ SV1168 )
              | ( c_lessequals @ SV1838 @ SY3416 @ SV1168 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1168 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8003]) ).

thf(8279,plain,
    ! [SV1169: $i,SV1839: $i] :
      ( ( ( ! [SY3417: $i] :
              ( ~ ( c_lessequals @ SV1839 @ SY3417 @ SV1169 )
              | ( c_in @ SV1839 @ ( c_SetInterval_OatMost @ SY3417 @ SV1169 ) @ SV1169 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1169 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8004]) ).

thf(8280,plain,
    ! [SV1170: $i,SV1840: $i] :
      ( ( ( ! [SY3418: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1840 @ SV1170 ) @ ( c_SetInterval_OatMost @ SY3418 @ SV1170 ) @ ( tc_set @ SV1170 ) )
              | ( c_lessequals @ SV1840 @ SY3418 @ SV1170 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1170 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8005]) ).

thf(8281,plain,
    ! [SV1171: $i,SV1841: $i] :
      ( ( ( ! [SY3419: $i] :
              ( ~ ( c_lessequals @ SV1841 @ SY3419 @ SV1171 )
              | ( c_lessequals @ ( c_SetInterval_OatMost @ SV1841 @ SV1171 ) @ ( c_SetInterval_OatMost @ SY3419 @ SV1171 ) @ ( tc_set @ SV1171 ) ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1171 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8006]) ).

thf(8282,plain,
    ! [SV1172: $i,SV1842: $i] :
      ( ( ( ! [SY3420: $i] :
              ( ( ( c_SetInterval_OgreaterThan @ SV1842 @ SV1172 )
               != ( c_SetInterval_OgreaterThan @ SY3420 @ SV1172 ) )
              | ( SV1842 = SY3420 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1172 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8007]) ).

thf(8283,plain,
    ! [SV1173: $i,SV1843: $i] :
      ( ( ( ! [SY3421: $i] :
              ( ~ ( c_in @ SV1843 @ ( c_SetInterval_OgreaterThan @ SY3421 @ SV1173 ) @ SV1173 )
              | ( c_less @ SY3421 @ SV1843 @ SV1173 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1173 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8008]) ).

thf(8284,plain,
    ! [SV1174: $i,SV1844: $i] :
      ( ( ( ! [SY3422: $i] :
              ( ~ ( c_less @ SV1844 @ SY3422 @ SV1174 )
              | ( c_in @ SY3422 @ ( c_SetInterval_OgreaterThan @ SV1844 @ SV1174 ) @ SV1174 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1174 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8009]) ).

thf(8285,plain,
    ! [SV1175: $i,SV1845: $i] :
      ( ( ( ! [SY3423: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1845 @ SV1175 ) @ ( c_SetInterval_OgreaterThan @ SY3423 @ SV1175 ) @ ( tc_set @ SV1175 ) )
              | ( c_lessequals @ SY3423 @ SV1845 @ SV1175 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1175 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8010]) ).

thf(8286,plain,
    ! [SV1176: $i,SV1846: $i] :
      ( ( ( ! [SY3424: $i] :
              ( ~ ( c_lessequals @ SV1846 @ SY3424 @ SV1176 )
              | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY3424 @ SV1176 ) @ ( c_SetInterval_OgreaterThan @ SV1846 @ SV1176 ) @ ( tc_set @ SV1176 ) ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1176 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8011]) ).

thf(8287,plain,
    ! [SV1177: $i,SV1847: $i] :
      ( ( ( ! [SY3425: $i] :
              ( ( ( c_SetInterval_OlessThan @ SV1847 @ SV1177 )
               != ( c_SetInterval_OlessThan @ SY3425 @ SV1177 ) )
              | ( SV1847 = SY3425 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1177 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8012]) ).

thf(8288,plain,
    ! [SV1178: $i,SV1848: $i] :
      ( ( ( ! [SY3426: $i] :
              ( ~ ( c_in @ SV1848 @ ( c_SetInterval_OlessThan @ SY3426 @ SV1178 ) @ SV1178 )
              | ( c_less @ SV1848 @ SY3426 @ SV1178 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1178 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8013]) ).

thf(8289,plain,
    ! [SV1179: $i,SV1849: $i] :
      ( ( ( ! [SY3427: $i] :
              ( ~ ( c_less @ SV1849 @ SY3427 @ SV1179 )
              | ( c_in @ SV1849 @ ( c_SetInterval_OlessThan @ SY3427 @ SV1179 ) @ SV1179 ) ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1179 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8014]) ).

thf(8290,plain,
    ! [SV1180: $i,SV1850: $i] :
      ( ( ( ! [SY3428: $i] :
              ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1850 @ SV1180 ) @ ( c_SetInterval_OlessThan @ SY3428 @ SV1180 ) @ ( tc_set @ SV1180 ) )
              | ( c_lessequals @ SV1850 @ SY3428 @ SV1180 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1180 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8015]) ).

thf(8291,plain,
    ! [SV1181: $i,SV1851: $i] :
      ( ( ( ! [SY3429: $i] :
              ( ~ ( c_lessequals @ SV1851 @ SY3429 @ SV1181 )
              | ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1851 @ SV1181 ) @ ( c_SetInterval_OlessThan @ SY3429 @ SV1181 ) @ ( tc_set @ SV1181 ) ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1181 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8016]) ).

thf(8292,plain,
    ! [SV1682: $i,SV1467: $i,SV1182: $i] :
      ( ( ( ~ ( c_in @ SV1182 @ SV1467 @ SV1682 ) )
        = $true )
      | ( ( ~ ( c_in @ SV1182 @ ( c_uminus @ SV1467 @ ( tc_set @ SV1682 ) ) @ SV1682 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8017]) ).

thf(8293,plain,
    ! [SV1683: $i,SV1468: $i,SV1183: $i] :
      ( ( ( c_in @ SV1183 @ SV1468 @ SV1683 )
        = $true )
      | ( ( c_in @ SV1183 @ ( c_uminus @ SV1468 @ ( tc_set @ SV1683 ) ) @ SV1683 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8018]) ).

thf(8294,plain,
    ! [SV1684: $i,SV1469: $i,SV1184: $i] :
      ( ( ( ( c_uminus @ SV1184 @ ( tc_set @ SV1469 ) )
         != ( c_uminus @ SV1684 @ ( tc_set @ SV1469 ) ) )
        = $true )
      | ( ( SV1184 = SV1684 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8019]) ).

thf(8295,plain,
    ! [SV1685: $i,SV1470: $i,SV1185: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_uminus @ SV1185 @ ( tc_set @ SV1470 ) ) @ ( c_uminus @ SV1685 @ ( tc_set @ SV1470 ) ) @ ( tc_set @ SV1470 ) ) )
        = $true )
      | ( ( c_lessequals @ SV1685 @ SV1185 @ ( tc_set @ SV1470 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8020]) ).

thf(8296,plain,
    ! [SV1686: $i,SV1471: $i,SV1186: $i] :
      ( ( ( ~ ( c_lessequals @ SV1186 @ SV1471 @ ( tc_set @ SV1686 ) ) )
        = $true )
      | ( ( c_lessequals @ ( c_uminus @ SV1471 @ ( tc_set @ SV1686 ) ) @ ( c_uminus @ SV1186 @ ( tc_set @ SV1686 ) ) @ ( tc_set @ SV1686 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8021]) ).

thf(8297,plain,
    ! [SV1687: $i,SV1472: $i,SV1187: $i] :
      ( ( ( ~ ( c_in @ SV1187 @ SV1472 @ SV1687 ) )
        = $true )
      | ( ( ! [SY3306: $i] :
              ~ ( c_in @ SV1187 @ ( c_minus @ SY3306 @ SV1472 @ ( tc_set @ SV1687 ) ) @ SV1687 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8022]) ).

thf(8298,plain,
    ! [SV1852: $i,SV1688: $i,SV1473: $i,SV1188: $i] :
      ( ( ~ ( c_in @ SV1188 @ ( c_minus @ SV1473 @ SV1688 @ ( tc_set @ SV1852 ) ) @ SV1852 )
        | ( c_in @ SV1188 @ SV1473 @ SV1852 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8023]) ).

thf(8299,plain,
    ! [SV1689: $i,SV1474: $i,SV1189: $i] :
      ( ( ( ~ ( c_in @ SV1189 @ SV1474 @ SV1689 ) )
        = $true )
      | ( ( ! [SY3308: $i] :
              ( ( c_in @ SV1189 @ SY3308 @ SV1689 )
              | ( c_in @ SV1189 @ ( c_minus @ SV1474 @ SY3308 @ ( tc_set @ SV1689 ) ) @ SV1689 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8024]) ).

thf(8300,plain,
    ! [SV1853: $i,SV1690: $i,SV1475: $i,SV1190: $i] :
      ( ( ~ ( c_in @ SV1190 @ ( c_inter @ SV1475 @ SV1690 @ SV1853 ) @ SV1853 )
        | ( c_in @ SV1190 @ SV1690 @ SV1853 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8025]) ).

thf(8301,plain,
    ! [SV1854: $i,SV1691: $i,SV1476: $i,SV1191: $i] :
      ( ( ~ ( c_in @ SV1191 @ ( c_inter @ SV1476 @ SV1691 @ SV1854 ) @ SV1854 )
        | ( c_in @ SV1191 @ SV1476 @ SV1854 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8026]) ).

thf(8302,plain,
    ! [SV1692: $i,SV1477: $i,SV1192: $i] :
      ( ( ( ~ ( c_in @ SV1192 @ SV1477 @ SV1692 ) )
        = $true )
      | ( ( ! [SY3311: $i] :
              ( ~ ( c_in @ SV1192 @ SY3311 @ SV1692 )
              | ( c_in @ SV1192 @ ( c_inter @ SY3311 @ SV1477 @ SV1692 ) @ SV1692 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8027]) ).

thf(8303,plain,
    ! [SV1693: $i,SV1478: $i,SV1193: $i] :
      ( ( ( ~ ( c_in @ SV1193 @ SV1478 @ ( tc_set @ SV1693 ) ) )
        = $true )
      | ( ( ! [SY3312: $i] :
              ( ~ ( c_in @ SY3312 @ ( c_Inter @ SV1478 @ SV1693 ) @ SV1693 )
              | ( c_in @ SY3312 @ SV1193 @ SV1693 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8028]) ).

thf(8304,plain,
    ! [SV1694: $i,SV1479: $i,SV1194: $i] :
      ( ( ( ~ ( c_in @ SV1194 @ ( c_Pow @ SV1479 @ SV1694 ) @ ( tc_set @ SV1694 ) ) )
        = $true )
      | ( ( c_lessequals @ SV1194 @ SV1479 @ ( tc_set @ SV1694 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8029]) ).

thf(8305,plain,
    ! [SV1695: $i,SV1480: $i,SV1195: $i] :
      ( ( ( ~ ( c_lessequals @ SV1195 @ SV1480 @ ( tc_set @ SV1695 ) ) )
        = $true )
      | ( ( c_in @ SV1195 @ ( c_Pow @ SV1480 @ SV1695 ) @ ( tc_set @ SV1695 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8030]) ).

thf(8306,plain,
    ! [SV1696: $i,SV1481: $i,SV1196: $i] :
      ( ( ( ~ ( c_in @ SV1196 @ SV1481 @ SV1696 ) )
        = $true )
      | ( ( ! [SY3313: $i] : ( c_in @ SV1196 @ ( c_union @ SY3313 @ SV1481 @ SV1696 ) @ SV1696 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8031]) ).

thf(8307,plain,
    ! [SV1697: $i,SV1482: $i,SV1197: $i] :
      ( ( ( ~ ( c_in @ SV1197 @ SV1482 @ SV1697 ) )
        = $true )
      | ( ( ! [SY3314: $i] : ( c_in @ SV1197 @ ( c_union @ SV1482 @ SY3314 @ SV1697 ) @ SV1697 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8032]) ).

thf(8308,plain,
    ! [SV1855: $i,SV1698: $i,SV1483: $i,SV1198: $i] :
      ( ( ~ ( c_in @ SV1198 @ ( c_union @ SV1483 @ SV1698 @ SV1855 ) @ SV1855 )
        | ( c_in @ SV1198 @ SV1698 @ SV1855 )
        | ( c_in @ SV1198 @ SV1483 @ SV1855 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8033]) ).

thf(8309,plain,
    ! [SV1856: $i,SV1699: $i,SV1199: $i] :
      ( ( ( ( c_union @ SV1199 @ SV1699 @ SV1856 )
         != c_emptyset )
        = $true )
      | ( ( SV1199 = c_emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8034]) ).

thf(8310,plain,
    ! [SV1857: $i,SV1484: $i,SV1200: $i] :
      ( ( ( ( c_union @ SV1200 @ SV1484 @ SV1857 )
         != c_emptyset )
        = $true )
      | ( ( SV1484 = c_emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8035]) ).

thf(8311,plain,
    ! [SV1700: $i,SV1485: $i,SV1202: $i] :
      ( ( ( ~ ( c_in @ SV1202 @ SV1485 @ SV1700 ) )
        = $true )
      | ( ( ! [SY3317: $i] :
              ( ~ ( c_in @ SV1485 @ SY3317 @ ( tc_set @ SV1700 ) )
              | ( c_in @ SV1202 @ ( c_Union @ SY3317 @ SV1700 ) @ SV1700 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8036]) ).

thf(8312,plain,
    ! [SV1701: $i,SV1487: $i,SV1204: $i] :
      ( ( ( ~ ( c_in @ SV1204 @ SV1487 @ SV1701 ) )
        = $true )
      | ( ( ! [SY3318: $i] : ( c_in @ SV1204 @ ( c_insert @ SY3318 @ SV1487 @ SV1701 ) @ SV1701 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8038]) ).

thf(8313,plain,
    ! [SV1858: $i,SV1703: $i,SV1489: $i,SV1206: $i] :
      ( ( ~ ( c_in @ SV1206 @ ( c_insert @ SV1489 @ SV1703 @ SV1858 ) @ SV1858 )
        | ( SV1206 = SV1489 )
        | ( c_in @ SV1206 @ SV1703 @ SV1858 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8040]) ).

thf(8314,plain,
    ! [SV1859: $i,SV1704: $i,SV1491: $i,SV1208: $i] :
      ( ( ( ( c_insert @ SV1208 @ SV1491 @ SV1704 )
         != ( c_insert @ SV1859 @ c_emptyset @ SV1704 ) )
        | ( SV1208 = SV1859 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8042]) ).

thf(8315,plain,
    ! [SV1860: $i,SV1705: $i,SV1492: $i,SV1209: $i] :
      ( ( ( ( c_insert @ SV1209 @ SV1492 @ SV1705 )
         != ( c_insert @ SV1860 @ c_emptyset @ SV1705 ) )
        | ( c_lessequals @ SV1492 @ ( c_insert @ SV1860 @ c_emptyset @ SV1705 ) @ ( tc_set @ SV1705 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8043]) ).

thf(8316,plain,
    ! [SV1706: $i,SV1493: $i,SV1210: $i] :
      ( ( ( ~ ( c_lessequals @ SV1210 @ ( c_insert @ SV1493 @ c_emptyset @ SV1706 ) @ ( tc_set @ SV1706 ) ) )
        = $true )
      | ( ( ( c_insert @ SV1493 @ SV1210 @ SV1706 )
          = ( c_insert @ SV1493 @ c_emptyset @ SV1706 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8044]) ).

thf(8317,plain,
    ! [SV1707: $i,SV1494: $i,SV1211: $i] :
      ( ( ( ! [SY3322: $i] :
              ( ( c_insert @ SV1211 @ c_emptyset @ SV1494 )
             != ( c_insert @ SV1707 @ SY3322 @ SV1494 ) ) )
        = $true )
      | ( ( SV1707 = SV1211 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8045]) ).

thf(8318,plain,
    ! [SV1861: $i,SV1708: $i,SV1495: $i,SV1212: $i] :
      ( ( ( ( c_insert @ SV1212 @ c_emptyset @ SV1495 )
         != ( c_insert @ SV1708 @ SV1861 @ SV1495 ) )
        | ( c_lessequals @ SV1861 @ ( c_insert @ SV1212 @ c_emptyset @ SV1495 ) @ ( tc_set @ SV1495 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8046]) ).

thf(8319,plain,
    ! [SV1709: $i,SV1496: $i,SV1213: $i] :
      ( ( ( ~ ( c_lessequals @ SV1213 @ ( c_insert @ SV1496 @ c_emptyset @ SV1709 ) @ ( tc_set @ SV1709 ) ) )
        = $true )
      | ( ( ( c_insert @ SV1496 @ c_emptyset @ SV1709 )
          = ( c_insert @ SV1496 @ SV1213 @ SV1709 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8047]) ).

thf(8320,plain,
    ! [SV1862: $i,SV1710: $i,SV1497: $i,SV1214: $i] :
      ( ( ( ( c_Sum__Type_OInl @ SV1214 @ SV1497 @ SV1710 )
         != ( c_Sum__Type_OInl @ SV1862 @ SV1497 @ SV1710 ) )
        | ( SV1214 = SV1862 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8048]) ).

thf(8321,plain,
    ! [SV1863: $i,SV1711: $i,SV1498: $i,SV1215: $i] :
      ( ( ( c_Sum__Type_OInl @ SV1215 @ SV1498 @ SV1711 )
       != ( c_Sum__Type_OInr @ SV1863 @ SV1711 @ SV1498 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8049]) ).

thf(8322,plain,
    ! [SV1864: $i,SV1712: $i,SV1499: $i,SV1216: $i] :
      ( ( ( ( c_Sum__Type_OInr @ SV1216 @ SV1499 @ SV1712 )
         != ( c_Sum__Type_OInr @ SV1864 @ SV1499 @ SV1712 ) )
        | ( SV1216 = SV1864 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8050]) ).

thf(8323,plain,
    ! [SV1865: $i,SV1713: $i,SV1500: $i,SV1217: $i] :
      ( ( ( c_Sum__Type_OInr @ SV1217 @ SV1500 @ SV1713 )
       != ( c_Sum__Type_OInl @ SV1865 @ SV1713 @ SV1500 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8051]) ).

thf(8324,plain,
    ! [SV1501: $i,SV1218: $i] :
      ( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1218 @ SV1501 @ SV1501 ) @ SV1501 )
        = $false )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ SV1218 @ SV1501 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8052]) ).

thf(8325,plain,
    ! [SV1502: $i,SV1219: $i] :
      ( ( ( c_Wellfounded__Recursion_Oacyclic @ SV1219 @ SV1502 )
        = $false )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1219 @ SV1502 @ SV1502 ) @ SV1502 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8053]) ).

thf(8326,plain,
    ! [SV1866: $i,SV1714: $i,SV1503: $i,SV1220: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1220 @ SV1503 @ SV1714 @ SV1714 ) @ SV1866 @ ( tc_prod @ SV1714 @ SV1714 ) ) @ SV1714 )
        | ( c_Wellfounded__Recursion_Oacyclic @ SV1866 @ SV1714 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8054]) ).

thf(8327,plain,
    ! [SV1867: $i,SV1715: $i,SV1504: $i,SV1221: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1221 @ SV1504 @ SV1715 @ SV1715 ) @ SV1867 @ ( tc_prod @ SV1715 @ SV1715 ) ) @ SV1715 )
        | ~ ( c_in @ ( c_Pair @ SV1504 @ SV1221 @ SV1715 @ SV1715 ) @ ( c_Transitive__Closure_Ortrancl @ SV1867 @ SV1715 ) @ ( tc_prod @ SV1715 @ SV1715 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8055]) ).

thf(8328,plain,
    ! [SV1505: $i,SV1222: $i] :
      ( ( ( c_Wellfounded__Recursion_Oacyclic @ SV1222 @ SV1505 )
        = $false )
      | ( ( ! [SY3104: $i,SY3105: $i] :
              ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SY3104 @ SY3105 @ SV1505 @ SV1505 ) @ SV1222 @ ( tc_prod @ SV1505 @ SV1505 ) ) @ SV1505 )
              | ( c_in @ ( c_Pair @ SY3105 @ SY3104 @ SV1505 @ SV1505 ) @ ( c_Transitive__Closure_Ortrancl @ SV1222 @ SV1505 ) @ ( tc_prod @ SV1505 @ SV1505 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8056]) ).

thf(8329,plain,
    ! [SV1868: $i,SV1716: $i,SV1506: $i,SV1223: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1223 @ SV1506 @ SV1716 @ SV1716 ) @ SV1868 @ ( tc_prod @ SV1716 @ SV1716 ) ) @ SV1716 )
        | ( c_Wellfounded__Recursion_Owf @ SV1868 @ SV1716 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8057]) ).

thf(8330,plain,
    ! [SV1869: $i,SV1717: $i,SV1507: $i,SV1224: $i] :
      ( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1224 @ SV1507 @ SV1717 @ SV1717 ) @ SV1869 @ ( tc_prod @ SV1717 @ SV1717 ) ) @ SV1717 )
        | ~ ( c_in @ ( c_Pair @ SV1507 @ SV1224 @ SV1717 @ SV1717 ) @ ( c_Transitive__Closure_Ortrancl @ SV1869 @ SV1717 ) @ ( tc_prod @ SV1717 @ SV1717 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8058]) ).

thf(8331,plain,
    ! [SV1508: $i,SV1225: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ SV1225 @ SV1508 )
        = $false )
      | ( ( ! [SY3110: $i,SY3111: $i] :
              ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SY3110 @ SY3111 @ SV1508 @ SV1508 ) @ SV1225 @ ( tc_prod @ SV1508 @ SV1508 ) ) @ SV1508 )
              | ( c_in @ ( c_Pair @ SY3111 @ SY3110 @ SV1508 @ SV1508 ) @ ( c_Transitive__Closure_Ortrancl @ SV1225 @ SV1508 ) @ ( tc_prod @ SV1508 @ SV1508 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8059]) ).

thf(8332,plain,
    ! [SV1509: $i,SV1226: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1226 @ SV1509 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
        = $false )
      | ( ( c_less @ SV1226 @ SV1509 @ tc_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8060]) ).

thf(8333,plain,
    ! [SV1510: $i,SV1227: $i] :
      ( ( ( c_less @ SV1227 @ SV1510 @ tc_nat )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1227 @ SV1510 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8061]) ).

thf(8334,plain,
    ! [SV1718: $i,SV1511: $i,SV1228: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ ( c_Message_Osynth @ SV1718 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ SV1718 @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OKey @ SV1228 ) @ SV1718 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8062]) ).

thf(8335,plain,
    ! [SV1719: $i,SV1512: $i,SV1229: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ( c_in @ SV1512 @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ SV1719 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8063]) ).

thf(8336,plain,
    ! [SV1513: $i,SV1230: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ( c_in @ SV1230 @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ SV1513 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8064]) ).

thf(8337,plain,
    ! [SV1514: $i,SV1231: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ ( c_Message_Osynth @ SV1514 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ ( c_Message_Omsg_OKey @ SV1231 ) @ SV1514 @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8065]) ).

thf(8338,plain,
    ! [SV1720: $i,SV1515: $i,SV1232: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1232 @ SV1515 ) @ ( c_Message_Oanalz @ SV1720 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1515 @ ( c_Message_Oanalz @ SV1720 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8066]) ).

thf(8339,plain,
    ! [SV1721: $i,SV1516: $i,SV1233: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1233 @ SV1516 ) @ ( c_Message_Oanalz @ SV1721 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1233 @ ( c_Message_Oanalz @ SV1721 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8067]) ).

thf(8340,plain,
    ! [SV1722: $i,SV1517: $i,SV1234: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1234 @ SV1517 ) @ ( c_Message_Oparts @ SV1722 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1517 @ ( c_Message_Oparts @ SV1722 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8068]) ).

thf(8341,plain,
    ! [SV1723: $i,SV1518: $i,SV1235: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1235 @ SV1518 ) @ ( c_Message_Oparts @ SV1723 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1235 @ ( c_Message_Oparts @ SV1723 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8069]) ).

thf(8342,plain,
    ! [SV1724: $i,SV1519: $i,SV1236: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ( c_in @ SV1519 @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ SV1724 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8070]) ).

thf(8343,plain,
    ! [SV1725: $i,SV1520: $i,SV1237: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ( c_in @ SV1237 @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ SV1725 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8071]) ).

thf(8344,plain,
    ! [SV1521: $i,SV1238: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ ( c_Message_Osynth @ SV1521 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ ( c_Message_Omsg_ONonce @ SV1238 ) @ SV1521 @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8072]) ).

thf(8345,plain,
    ! [SV1522: $i,SV1243: $i] :
      ( ( ( ( c_Message_Oagent_OFriend @ SV1243 )
          = ( c_Message_Oagent_OFriend @ SV1522 ) )
        = $false )
      | ( ( SV1243 = SV1522 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8073]) ).

thf(8346,plain,
    ! [SV1726: $i,SV1523: $i,SV1244: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1244 @ SV1523 ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1244 ) ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
          | ( c_in @ SV1523 @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8074]) ).

thf(8347,plain,
    ! [SV1524: $i,SV1245: $i] :
      ( ( ( c_in @ SV1245 @ SV1524 @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1245 @ ( c_Message_Oanalz @ SV1524 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8075]) ).

thf(8348,plain,
    ! [SV1525: $i,SV1246: $i] :
      ( ( ( c_in @ SV1246 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SV1525 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1246 @ ( c_Message_Oanalz @ SV1525 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8076]) ).

thf(8349,plain,
    ! [SV1727: $i,SV1526: $i,SV1247: $i] :
      ( ( ( ~ ( c_in @ SV1247 @ ( c_Message_Oparts @ ( c_union @ SV1526 @ SV1727 @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1727 ) @ tc_Message_Omsg )
          | ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1526 ) @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8077]) ).

thf(8350,plain,
    ! [SV1527: $i,SV1248: $i] :
      ( ( ( ( c_Message_Omsg_OAgent @ SV1248 )
          = ( c_Message_Omsg_OAgent @ SV1527 ) )
        = $false )
      | ( ( SV1248 = SV1527 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8078]) ).

thf(8351,plain,
    ! [SV1528: $i,SV1249: $i] :
      ( ( ( ( c_Message_Omsg_ONumber @ SV1249 )
          = ( c_Message_Omsg_ONumber @ SV1528 ) )
        = $false )
      | ( ( SV1249 = SV1528 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8079]) ).

thf(8352,plain,
    ! [SV1529: $i,SV1250: $i] :
      ( ( ( ( c_Message_Omsg_ONonce @ SV1250 )
          = ( c_Message_Omsg_ONonce @ SV1529 ) )
        = $false )
      | ( ( SV1250 = SV1529 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8080]) ).

thf(8353,plain,
    ! [SV1530: $i,SV1251: $i] :
      ( ( ( ( c_Message_Omsg_OKey @ SV1251 )
          = ( c_Message_Omsg_OKey @ SV1530 ) )
        = $false )
      | ( ( SV1251 = SV1530 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8081]) ).

thf(8354,plain,
    ! [SV1531: $i,SV1252: $i] :
      ( ( ( ( c_Message_Omsg_OHash @ SV1252 )
          = ( c_Message_Omsg_OHash @ SV1531 ) )
        = $false )
      | ( ( SV1252 = SV1531 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8082]) ).

thf(8355,plain,
    ! [SV1728: $i,SV1532: $i,SV1253: $i] :
      ( ( ( ! [SY3332: $i] :
              ( ( c_Message_Omsg_OMPair @ SV1253 @ SV1532 )
             != ( c_Message_Omsg_OMPair @ SV1728 @ SY3332 ) ) )
        = $true )
      | ( ( SV1253 = SV1728 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8083]) ).

thf(8356,plain,
    ! [SV1870: $i,SV1729: $i,SV1533: $i,SV1254: $i] :
      ( ( ( ( c_Message_Omsg_OMPair @ SV1254 @ SV1533 )
         != ( c_Message_Omsg_OMPair @ SV1729 @ SV1870 ) )
        | ( SV1533 = SV1870 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8084]) ).

thf(8357,plain,
    ! [SV1730: $i,SV1534: $i,SV1255: $i] :
      ( ( ( ! [SY3334: $i] :
              ( ( c_Message_Omsg_OCrypt @ SV1255 @ SV1534 )
             != ( c_Message_Omsg_OCrypt @ SV1730 @ SY3334 ) ) )
        = $true )
      | ( ( SV1255 = SV1730 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8085]) ).

thf(8358,plain,
    ! [SV1871: $i,SV1731: $i,SV1535: $i,SV1256: $i] :
      ( ( ( ( c_Message_Omsg_OCrypt @ SV1256 @ SV1535 )
         != ( c_Message_Omsg_OCrypt @ SV1731 @ SV1871 ) )
        | ( SV1535 = SV1871 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8086]) ).

thf(8359,plain,
    ! [SV1536: $i,SV1257: $i] :
      ( ( ( c_in @ SV1257 @ SV1536 @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1257 @ ( c_Message_Oparts @ SV1536 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8087]) ).

thf(8360,plain,
    ! [SV1537: $i,SV1259: $i] :
      ( ( ( c_in @ SV1259 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SV1537 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1259 @ ( c_Message_Oparts @ SV1537 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8088]) ).

thf(8361,plain,
    ! [SV1539: $i,SV1261: $i] :
      ( ( ( c_in @ SV1261 @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ! [SY3130: $i] :
              ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SY3130 ) @ SV1539 @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OCrypt @ SY3130 @ SV1261 ) @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8089]) ).

thf(8362,plain,
    ! [SV1540: $i,SV1262: $i] :
      ( ( ( c_in @ SV1262 @ ( c_Message_Osynth @ SV1540 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ ( c_Message_Omsg_OHash @ SV1262 ) @ ( c_Message_Osynth @ SV1540 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8090]) ).

thf(8363,plain,
    ! [SV1541: $i,SV1263: $i] :
      ( ( ( c_in @ SV1263 @ SV1541 @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1263 @ ( c_Message_Osynth @ SV1541 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8091]) ).

thf(8364,plain,
    ! [SV1542: $i,SV1264: $i] :
      ( ( ( c_in @ SV1264 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ! [SY3131: $i] :
              ( ~ ( c_in @ SY3131 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
              | ( c_in @ ( c_Message_Omsg_OMPair @ SY3131 @ SV1264 ) @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8092]) ).

thf(8365,plain,
    ! [SV1544: $i,SV1266: $i] :
      ( ( ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SV1544 ) @ ( tc_set @ tc_Message_Omsg ) )
        = $false )
      | ( ( ! [SY3132: $i,SY3133: $i] :
              ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SY3132 ) @ ( c_Message_Oanalz @ SY3133 ) @ ( tc_set @ tc_Message_Omsg ) )
              | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SY3132 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SY3133 @ SV1544 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8093]) ).

thf(8366,plain,
    ! [SV1545: $i,SV1267: $i] :
      ( ( ( c_in @ SV1267 @ ( c_Message_Osynth @ ( c_Message_Osynth @ SV1545 ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1267 @ ( c_Message_Osynth @ SV1545 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8094]) ).

thf(8367,plain,
    ! [SV1732: $i,SV1546: $i,SV1268: $i,SV1: $i] :
      ( ( ( ( c_Datatype__Universe_OLeaf @ SV1 @ SV1268 @ SV1546 )
         != ( c_Datatype__Universe_OLeaf @ SV1732 @ SV1268 @ SV1546 ) )
        = $true )
      | ( ( SV1 = SV1732 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8095]) ).

thf(8368,plain,
    ! [SV1733: $i,SV1547: $i,SV1269: $i,SV2: $i] :
      ( ( ( ( c_Datatype__Universe_ONumb @ SV2 @ SV1269 @ SV1547 )
         != ( c_Datatype__Universe_ONumb @ SV1733 @ SV1269 @ SV1547 ) )
        = $true )
      | ( ( SV2 = SV1733 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8096]) ).

thf(8369,plain,
    ! [SV1872: $i,SV1734: $i,SV1548: $i,SV1270: $i,SV3: $i] :
      ( ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) ) )
        | ( SV3
          = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( c_Main_OdprodE__2 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ SV1734 @ SV1872 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( c_Main_OdprodE__4 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ SV1734 @ SV1872 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8097]) ).

thf(8370,plain,
    ! [SV1873: $i,SV1735: $i,SV1549: $i,SV1271: $i,SV4: $i] :
      ( ( ~ ( c_in @ SV4 @ ( c_Datatype__Universe_Odprod @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( c_Main_OdprodE__4 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) @ SV1549 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8098]) ).

thf(8371,plain,
    ! [SV1874: $i,SV1736: $i,SV1550: $i,SV1272: $i,SV5: $i] :
      ( ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odprod @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( c_Main_OdprodE__3 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) @ SV1272 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8099]) ).

thf(8372,plain,
    ! [SV1875: $i,SV1737: $i,SV1551: $i,SV1273: $i,SV6: $i] :
      ( ( ! [SY3430: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
            | ! [SY3431: $i,SY3432: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY3430 @ SY3431 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SY3432 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
                | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY3430 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SY3431 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3432 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8100]) ).

thf(8373,plain,
    ! [SV1876: $i,SV1738: $i,SV1552: $i,SV1274: $i,SV7: $i] :
      ( ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1274 @ SV1552 @ SV1738 @ SV1876 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
        | ( SV7
          = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
        | ( SV7
          = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8101]) ).

thf(8374,plain,
    ! [SV1877: $i,SV1739: $i,SV1553: $i,SV1275: $i,SV8: $i] :
      ( ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1275 @ SV1553 @ SV1739 @ SV1877 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
        | ( SV8
          = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( c_Main_OdsumE__4 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) @ SV1553 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8102]) ).

thf(8375,plain,
    ! [SV1878: $i,SV1740: $i,SV1554: $i,SV1276: $i,SV9: $i] :
      ( ( ~ ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SV1276 @ SV1554 @ SV1740 @ SV1878 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
        | ( SV9
          = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( c_Main_OdsumE__2 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) @ SV1276 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8103]) ).

thf(8376,plain,
    ! [SV1879: $i,SV1741: $i,SV1555: $i,SV1277: $i,SV10: $i] :
      ( ( ~ ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SV1277 @ SV1555 @ SV1741 @ SV1879 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__2 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1277 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__4 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1555 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8104]) ).

thf(8377,plain,
    ! [SV1880: $i,SV1742: $i,SV1556: $i,SV1278: $i,SV11: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV11 @ SV1278 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ SV1880 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) )
        | ! [SY3433: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SV1556 @ SV1742 ) @ ( c_Datatype__Universe_OIn0 @ SV1278 @ SV1556 @ SV1742 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1880 @ SY3433 @ SV1556 @ SV1742 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8105]) ).

thf(8378,plain,
    ! [SV1881: $i,SV1743: $i,SV1557: $i,SV1279: $i,SV12: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV12 @ SV1279 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ SV1881 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) )
        | ! [SY3434: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SV1557 @ SV1743 ) @ ( c_Datatype__Universe_OIn1 @ SV1279 @ SV1557 @ SV1743 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3434 @ SV1881 @ SV1557 @ SV1743 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8106]) ).

thf(8379,plain,
    ! [SV1882: $i,SV1744: $i,SV1558: $i,SV1280: $i,SV13: $i] :
      ( ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1280 @ SV1558 @ SV1744 @ SV1882 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1744 @ SV1882 ) ) )
        | ( SV13
          = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SV1882 ) @ ( c_Main_OuprodE__2 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SV1882 ) @ SV1744 @ SV1882 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8107]) ).

thf(8380,plain,
    ! [SV1883: $i,SV1745: $i,SV1559: $i,SV1281: $i,SV14: $i] :
      ( ( ~ ( c_in @ SV14 @ ( c_Datatype__Universe_Ouprod @ SV1281 @ SV1559 @ SV1745 @ SV1883 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SV1883 ) ) )
        | ( c_in @ ( c_Main_OuprodE__2 @ SV1281 @ SV1559 @ SV14 @ SV1745 @ SV1883 ) @ SV1559 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SV1883 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8108]) ).

thf(8381,plain,
    ! [SV1884: $i,SV1746: $i,SV1560: $i,SV1282: $i,SV15: $i] :
      ( ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ouprod @ SV1282 @ SV1560 @ SV1746 @ SV1884 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SV1884 ) ) )
        | ( c_in @ ( c_Main_OuprodE__1 @ SV1282 @ SV1560 @ SV15 @ SV1746 @ SV1884 ) @ SV1282 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SV1884 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8109]) ).

thf(8382,plain,
    ! [SV1747: $i,SV1561: $i,SV1283: $i,SV16: $i] :
      ( ( ( ~ ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) ) )
        = $true )
      | ( ( ! [SY3354: $i,SY3355: $i] :
              ( ~ ( c_in @ SY3354 @ SY3355 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
              | ( c_in @ ( c_Datatype__Universe_OScons @ SY3354 @ SV16 @ SV1561 @ SV1747 ) @ ( c_Datatype__Universe_Ouprod @ SY3355 @ SV1283 @ SV1561 @ SV1747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8110]) ).

thf(8383,plain,
    ! [SV1885: $i,SV1748: $i,SV1562: $i,SV1284: $i,SV17: $i] :
      ( ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1284 @ SV1562 @ SV1748 @ SV1885 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1748 @ SV1885 ) ) )
        | ( SV17
          = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1284 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) )
        | ( SV17
          = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1562 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8111]) ).

thf(8384,plain,
    ! [SV1886: $i,SV1749: $i,SV1563: $i,SV1285: $i,SV18: $i] :
      ( ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1285 @ SV1563 @ SV1749 @ SV1886 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) )
        | ( SV18
          = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1285 @ SV18 @ SV1749 @ SV1886 ) @ SV1749 @ SV1886 ) )
        | ( c_in @ ( c_Main_OusumE__2 @ SV1563 @ SV18 @ SV1749 @ SV1886 ) @ SV1563 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8112]) ).

thf(8385,plain,
    ! [SV1887: $i,SV1750: $i,SV1564: $i,SV1286: $i,SV19: $i] :
      ( ( ~ ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SV1286 @ SV1564 @ SV1750 @ SV1887 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) )
        | ( SV19
          = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1564 @ SV19 @ SV1750 @ SV1887 ) @ SV1750 @ SV1887 ) )
        | ( c_in @ ( c_Main_OusumE__1 @ SV1286 @ SV19 @ SV1750 @ SV1887 ) @ SV1286 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8113]) ).

thf(8386,plain,
    ! [SV1888: $i,SV1751: $i,SV1565: $i,SV1287: $i,SV20: $i] :
      ( ( ~ ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SV1287 @ SV1565 @ SV1751 @ SV1888 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
        | ( c_in @ ( c_Main_OusumE__1 @ SV1287 @ SV20 @ SV1751 @ SV1888 ) @ SV1287 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
        | ( c_in @ ( c_Main_OusumE__2 @ SV1565 @ SV20 @ SV1751 @ SV1888 ) @ SV1565 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8114]) ).

thf(8387,plain,
    ! [SV1752: $i,SV1566: $i,SV1288: $i,SV21: $i] :
      ( ( ( ~ ( c_in @ SV21 @ SV1288 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) ) )
        = $true )
      | ( ( ! [SY3360: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ SV21 @ SV1566 @ SV1752 ) @ ( c_Datatype__Universe_Ousum @ SV1288 @ SY3360 @ SV1566 @ SV1752 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8115]) ).

thf(8388,plain,
    ! [SV1753: $i,SV1567: $i,SV1289: $i,SV22: $i] :
      ( ( ( ~ ( c_in @ SV22 @ SV1289 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) ) )
        = $true )
      | ( ( ! [SY3361: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ SV22 @ SV1567 @ SV1753 ) @ ( c_Datatype__Universe_Ousum @ SY3361 @ SV1289 @ SV1567 @ SV1753 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8116]) ).

thf(8389,plain,
    ! [SV1293: $i,SV29: $i,SV1889: $i] :
      ( ( ( c_in @ ( c_insert @ SV1889 @ SV29 @ SV1293 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) )
        = $true )
      | ( ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8118]) ).

thf(8390,plain,
    ! [SV1294: $i,SV1890: $i,SV30: $i] :
      ( ( ( c_in @ ( c_inter @ SV30 @ SV1890 @ SV1294 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) )
        = $true )
      | ( ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ SV1294 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8119]) ).

thf(8391,plain,
    ! [SV1295: $i,SV31: $i,SV1891: $i] :
      ( ( ( c_in @ ( c_inter @ SV1891 @ SV31 @ SV1295 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) )
        = $true )
      | ( ( c_in @ SV31 @ c_Finite__Set_OFinites @ ( tc_set @ SV1295 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8120]) ).

thf(8392,plain,
    ! [SV1296: $i,SV32: $i] :
      ( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV32 @ SV1296 ) @ SV32 @ ( tc_set @ SV1296 ) )
        = $true )
      | ( ( c_in @ ( c_Union @ SV32 @ SV1296 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1296 ) )
        = $true )
      | ( ( c_in @ SV32 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1296 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8121]) ).

thf(8393,plain,
    ! [SV1297: $i,SV33: $i] :
      ( ( ( ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) ) )
        = $true )
      | ( ( c_in @ ( c_Union @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) )
        = $true )
      | ( ( c_in @ SV33 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1297 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8122]) ).

thf(8394,plain,
    ! [SV1300: $i,SV36: $i,SV1892: $i] :
      ( ( ( ~ ( c_in @ SV1892 @ SV36 @ SV1300 )
          | ! [SY3435: $i] :
              ( ~ ( c_in @ SY3435 @ SV36 @ SV1300 )
              | ( SV1892 = SY3435 ) ) )
        = $true )
      | ( ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8123]) ).

thf(8395,plain,
    ! [SV1568: $i,SV1308: $i,SV46: $i] :
      ( ( ( c_in @ SV46 @ ( c_List_Olists @ SV1308 @ SV1568 ) @ ( tc_List_Olist @ SV1568 ) )
        = $false )
      | ( ( ! [SY3182: $i] :
              ( ~ ( c_in @ SY3182 @ ( c_List_Oset @ SV46 @ SV1568 ) @ SV1568 )
              | ( c_in @ SY3182 @ SV1308 @ SV1568 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8125]) ).

thf(8396,plain,
    ! [SV1570: $i,SV1310: $i,SV48: $i] :
      ( ( ( c_in @ ( c_Main_Oin__listsI__1 @ SV48 @ SV1310 @ SV1570 ) @ SV48 @ SV1570 )
        = $false )
      | ( ( c_in @ SV1310 @ ( c_List_Olists @ SV48 @ SV1570 ) @ ( tc_List_Olist @ SV1570 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8127]) ).

thf(8397,plain,
    ! [SV1893: $i,SV1754: $i,SV1571: $i,SV1312: $i,SV50: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV50 @ SV1312 @ SV1571 ) @ SV1754 @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) @ ( c_List_Olistrel @ SV1893 @ SV1571 ) @ ( tc_prod @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) )
        | ( SV1754
          = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SV1893 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ ( c_Main_Olistrel__Cons1__2 @ SV1893 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ SV1571 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8128]) ).

thf(8398,plain,
    ! [SV1894: $i,SV1755: $i,SV1572: $i,SV1313: $i,SV51: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV51 @ SV1313 @ SV1572 ) @ SV1755 @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SV1894 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) )
        | ( c_in @ ( c_Pair @ SV1313 @ ( c_Main_Olistrel__Cons1__2 @ SV1894 @ SV1755 @ SV51 @ SV1313 @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SV1894 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8129]) ).

thf(8399,plain,
    ! [SV1895: $i,SV1756: $i,SV1573: $i,SV1314: $i,SV52: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV52 @ SV1314 @ SV1573 ) @ SV1756 @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) @ ( c_List_Olistrel @ SV1895 @ SV1573 ) @ ( tc_prod @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) )
        | ( c_in @ ( c_Pair @ SV52 @ ( c_Main_Olistrel__Cons1__1 @ SV1895 @ SV1756 @ SV52 @ SV1314 @ SV1573 ) @ SV1573 @ SV1573 ) @ SV1895 @ ( tc_prod @ SV1573 @ SV1573 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8130]) ).

thf(8400,plain,
    ! [SV1896: $i,SV1757: $i,SV1574: $i,SV1315: $i,SV53: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV53 @ ( c_List_Olist_OCons @ SV1315 @ SV1574 @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) @ ( c_List_Olistrel @ SV1896 @ SV1757 ) @ ( tc_prod @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) )
        | ( SV53
          = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SV1896 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ ( c_Main_Olistrel__Cons2__2 @ SV1896 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ SV1757 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8131]) ).

thf(8401,plain,
    ! [SV1897: $i,SV1758: $i,SV1575: $i,SV1316: $i,SV54: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV54 @ ( c_List_Olist_OCons @ SV1316 @ SV1575 @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SV1897 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SV1897 @ SV54 @ SV1316 @ SV1575 @ SV1758 ) @ SV1575 @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SV1897 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8132]) ).

thf(8402,plain,
    ! [SV1898: $i,SV1759: $i,SV1576: $i,SV1317: $i,SV55: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV55 @ ( c_List_Olist_OCons @ SV1317 @ SV1576 @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) @ ( c_List_Olistrel @ SV1898 @ SV1759 ) @ ( tc_prod @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) )
        | ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SV1898 @ SV55 @ SV1317 @ SV1576 @ SV1759 ) @ SV1317 @ SV1759 @ SV1759 ) @ SV1898 @ ( tc_prod @ SV1759 @ SV1759 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8133]) ).

thf(8403,plain,
    ! [SV1760: $i,SV1577: $i,SV56: $i] :
      ( ( ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV56 @ ( tc_List_Olist @ SV1577 ) @ ( tc_List_Olist @ SV1577 ) ) @ ( c_List_Olistrel @ SV1760 @ SV1577 ) @ ( tc_prod @ ( tc_List_Olist @ SV1577 ) @ ( tc_List_Olist @ SV1577 ) ) )
        = $false )
      | ( ( SV56 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8134]) ).

thf(8404,plain,
    ! [SV1761: $i,SV1578: $i,SV57: $i] :
      ( ( ( c_in @ ( c_Pair @ SV57 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1578 ) @ ( tc_List_Olist @ SV1578 ) ) @ ( c_List_Olistrel @ SV1761 @ SV1578 ) @ ( tc_prod @ ( tc_List_Olist @ SV1578 ) @ ( tc_List_Olist @ SV1578 ) ) )
        = $false )
      | ( ( SV57 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8135]) ).

thf(8405,plain,
    ! [SV1762: $i,SV1579: $i,SV1318: $i,SV58: $i] :
      ( ( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV58 @ SV1318 @ SV1579 ) @ ( c_List_Olists @ SV1762 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) ) )
        = $true )
      | ( ( c_in @ SV1318 @ ( c_List_Olists @ SV1762 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8136]) ).

thf(8406,plain,
    ! [SV1763: $i,SV1580: $i,SV1319: $i,SV59: $i] :
      ( ( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV59 @ SV1319 @ SV1580 ) @ ( c_List_Olists @ SV1763 @ SV1580 ) @ ( tc_List_Olist @ SV1580 ) ) )
        = $true )
      | ( ( c_in @ SV59 @ SV1763 @ SV1580 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8137]) ).

thf(8407,plain,
    ! [SV1581: $i,SV1320: $i,SV60: $i] :
      ( ( ( c_in @ SV60 @ SV1320 @ SV1581 )
        = $false )
      | ( ( ! [SY3199: $i] :
              ( ~ ( c_in @ SY3199 @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) )
              | ( c_in @ ( c_List_Olist_OCons @ SV60 @ SY3199 @ SV1581 ) @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8138]) ).

thf(8408,plain,
    ! [SV1765: $i,SV1582: $i,SV1324: $i,SV69: $i] :
      ( ( ( ~ ( c_in @ SV69 @ ( c_Relation_ODomain @ SV1324 @ SV1582 @ SV1765 ) @ SV1582 ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV69 @ ( c_Main_ODomainE__1 @ SV69 @ SV1324 @ SV1582 @ SV1765 ) @ SV1582 @ SV1765 ) @ SV1324 @ ( tc_prod @ SV1582 @ SV1765 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8142]) ).

thf(8409,plain,
    ! [SV1899: $i,SV1766: $i,SV1583: $i,SV1325: $i,SV70: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1325 @ SV1583 @ SV1766 ) @ SV1899 @ ( tc_prod @ SV1583 @ SV1766 ) )
        | ( c_in @ SV70 @ ( c_Relation_ODomain @ SV1899 @ SV1583 @ SV1766 ) @ SV1583 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8143]) ).

thf(8410,plain,
    ! [SV1900: $i,SV1767: $i,SV1584: $i,SV1327: $i,SV72: $i] :
      ( ( ~ ( c_in @ SV72 @ ( c_Relation_OImage @ SV1327 @ SV1584 @ SV1767 @ SV1900 ) @ SV1900 )
        | ( c_in @ ( c_Main_OImageE__1 @ SV1584 @ SV72 @ SV1327 @ SV1767 @ SV1900 ) @ SV1584 @ SV1767 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8145]) ).

thf(8411,plain,
    ! [SV1901: $i,SV1768: $i,SV1585: $i,SV1328: $i,SV73: $i] :
      ( ( ~ ( c_in @ SV73 @ ( c_Relation_OImage @ SV1328 @ SV1585 @ SV1768 @ SV1901 ) @ SV1901 )
        | ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1585 @ SV73 @ SV1328 @ SV1768 @ SV1901 ) @ SV73 @ SV1768 @ SV1901 ) @ SV1328 @ ( tc_prod @ SV1768 @ SV1901 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8146]) ).

thf(8412,plain,
    ! [SV1769: $i,SV1586: $i,SV1329: $i,SV74: $i] :
      ( ( ( ~ ( c_in @ SV74 @ SV1329 @ SV1586 ) )
        = $true )
      | ( ( ! [SY3371: $i,SY3372: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV74 @ SV1769 @ SV1586 @ SY3371 ) @ SY3372 @ ( tc_prod @ SV1586 @ SY3371 ) )
              | ( c_in @ SV1769 @ ( c_Relation_OImage @ SY3372 @ SV1329 @ SV1586 @ SY3371 ) @ SY3371 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8147]) ).

thf(8413,plain,
    ! [SV1770: $i,SV1587: $i,SV1330: $i,SV75: $i] :
      ( ( ( ~ ( c_in @ SV75 @ ( c_Relation_ORange @ SV1330 @ SV1587 @ SV1770 ) @ SV1770 ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV75 @ SV1330 @ SV1770 @ SV1587 ) @ SV75 @ SV1587 @ SV1770 ) @ SV1330 @ ( tc_prod @ SV1587 @ SV1770 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8148]) ).

thf(8414,plain,
    ! [SV1902: $i,SV1771: $i,SV1588: $i,SV1331: $i,SV76: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV76 @ SV1331 @ SV1588 @ SV1771 ) @ SV1902 @ ( tc_prod @ SV1588 @ SV1771 ) )
        | ( c_in @ SV1331 @ ( c_Relation_ORange @ SV1902 @ SV1588 @ SV1771 ) @ SV1771 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8149]) ).

thf(8415,plain,
    ! [SV1772: $i,SV1589: $i,SV1332: $i,SV77: $i] :
      ( ( ( ~ ( c_in @ SV77 @ ( c_Relation_Oconverse @ SV1332 @ SV1589 @ SV1772 ) @ ( tc_prod @ SV1772 @ SV1589 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1332 @ SV77 @ SV1589 @ SV1772 ) @ ( c_Main_OconverseE__2 @ SV1332 @ SV77 @ SV1589 @ SV1772 ) @ SV1589 @ SV1772 ) @ SV1332 @ ( tc_prod @ SV1589 @ SV1772 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8150]) ).

thf(8416,plain,
    ! [SV1773: $i,SV1590: $i,SV1333: $i,SV78: $i] :
      ( ( ( ~ ( c_in @ SV78 @ ( c_Relation_Oconverse @ SV1333 @ SV1590 @ SV1773 ) @ ( tc_prod @ SV1773 @ SV1590 ) ) )
        = $true )
      | ( ( SV78
          = ( c_Pair @ ( c_Main_OconverseE__2 @ SV1333 @ SV78 @ SV1590 @ SV1773 ) @ ( c_Main_OconverseE__1 @ SV1333 @ SV78 @ SV1590 @ SV1773 ) @ SV1773 @ SV1590 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8151]) ).

thf(8417,plain,
    ! [SV1591: $i,SV1334: $i,SV79: $i] :
      ( ( ( c_in @ SV79 @ ( c_Relation_Odiag @ SV1334 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) )
        = $false )
      | ( ( SV79
          = ( c_Pair @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SV1591 ) @ ( c_Main_OdiagE__1 @ SV1334 @ SV79 @ SV1591 ) @ SV1591 @ SV1591 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8152]) ).

thf(8418,plain,
    ! [SV1592: $i,SV1335: $i,SV80: $i] :
      ( ( ( c_in @ SV80 @ ( c_Relation_Odiag @ SV1335 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) )
        = $false )
      | ( ( c_in @ ( c_Main_OdiagE__1 @ SV1335 @ SV80 @ SV1592 ) @ SV1335 @ SV1592 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8153]) ).

thf(8419,plain,
    ! [SV1593: $i,SV1336: $i,SV81: $i] :
      ( ( ( c_in @ SV81 @ SV1336 @ SV1593 )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV81 @ SV81 @ SV1593 @ SV1593 ) @ ( c_Relation_Odiag @ SV1336 @ SV1593 ) @ ( tc_prod @ SV1593 @ SV1593 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8154]) ).

thf(8420,plain,
    ! [SV1903: $i,SV1774: $i,SV1594: $i,SV1337: $i,SV82: $i] :
      ( ( ! [SY3436: $i] :
            ( ~ ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SV1337 @ SV1594 @ SV1774 @ SV1903 @ SY3436 ) @ ( tc_prod @ SY3436 @ SV1903 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SY3436 ) @ ( c_Main_Orel__compE__3 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SY3436 ) @ SV1774 @ SV1903 ) @ SV1337 @ ( tc_prod @ SV1774 @ SV1903 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8155]) ).

thf(8421,plain,
    ! [SV1904: $i,SV1775: $i,SV1595: $i,SV1338: $i,SV83: $i] :
      ( ( ! [SY3437: $i] :
            ( ~ ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SV1338 @ SV1595 @ SV1775 @ SV1904 @ SY3437 ) @ ( tc_prod @ SY3437 @ SV1904 ) )
            | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SY3437 ) @ ( c_Main_Orel__compE__2 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SY3437 ) @ SY3437 @ SV1775 ) @ SV1595 @ ( tc_prod @ SY3437 @ SV1775 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8156]) ).

thf(8422,plain,
    ! [SV1905: $i,SV1776: $i,SV1596: $i,SV1339: $i,SV84: $i] :
      ( ( ! [SY3438: $i] :
            ( ~ ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SV1339 @ SV1596 @ SV1776 @ SV1905 @ SY3438 ) @ ( tc_prod @ SY3438 @ SV1905 ) )
            | ( SV84
              = ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SY3438 ) @ ( c_Main_Orel__compE__3 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SY3438 ) @ SY3438 @ SV1905 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8157]) ).

thf(8423,plain,
    ! [SV1906: $i,SV1777: $i,SV1597: $i,SV1340: $i,SV85: $i] :
      ( ( ! [SY3439: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) )
            | ! [SY3440: $i,SY3441: $i] :
                ( ~ ( c_in @ ( c_Pair @ SY3439 @ SV85 @ SY3440 @ SV1597 ) @ SY3441 @ ( tc_prod @ SY3440 @ SV1597 ) )
                | ( c_in @ ( c_Pair @ SY3439 @ SV1340 @ SY3440 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SY3441 @ SV1597 @ SV1777 @ SY3440 ) @ ( tc_prod @ SY3440 @ SV1777 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8158]) ).

thf(8424,plain,
    ! [SV1599: $i,SV1350: $i,SV97: $i] :
      ( ( ( c_in @ SV97 @ ( c_Main_OInterI__1 @ SV97 @ SV1350 @ SV1599 ) @ SV1599 )
        = $false )
      | ( ( c_in @ SV97 @ ( c_Inter @ SV1350 @ SV1599 ) @ SV1599 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8160]) ).

thf(8425,plain,
    ! [SV1600: $i,SV1352: $i,SV99: $i] :
      ( ( ( c_in @ SV99 @ ( c_Union @ SV1352 @ SV1600 ) @ SV1600 )
        = $false )
      | ( ( c_in @ ( c_Main_OUnionE__1 @ SV99 @ SV1352 @ SV1600 ) @ SV1352 @ ( tc_set @ SV1600 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8161]) ).

thf(8426,plain,
    ! [SV1601: $i,SV1353: $i,SV100: $i] :
      ( ( ( c_in @ SV100 @ ( c_Union @ SV1353 @ SV1601 ) @ SV1601 )
        = $false )
      | ( ( c_in @ SV100 @ ( c_Main_OUnionE__1 @ SV100 @ SV1353 @ SV1601 ) @ SV1601 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8162]) ).

thf(8427,plain,
    ! [SV1602: $i,SV1355: $i,SV102: $i] :
      ( ( ( c_less @ SV102 @ SV1355 @ ( tc_set @ SV1602 ) )
        = $false )
      | ( ( ~ ( c_lessequals @ SV1355 @ SV102 @ ( tc_set @ SV1602 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8163]) ).

thf(8428,plain,
    ! [SV1603: $i,SV1356: $i,SV103: $i] :
      ( ( ( c_less @ SV103 @ SV1356 @ ( tc_set @ SV1603 ) )
        = $false )
      | ( ( c_lessequals @ SV103 @ SV1356 @ ( tc_set @ SV1603 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8164]) ).

thf(8429,plain,
    ! [SV1604: $i,SV1357: $i,SV104: $i] :
      ( ( ( c_lessequals @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) )
        = $false )
      | ( ( ( SV104 = SV1357 )
          | ( c_less @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8165]) ).

thf(8430,plain,
    ! [SV1778: $i,SV1358: $i,SV105: $i] :
      ( ( ( c_in @ SV105 @ ( c_insert @ SV1358 @ c_emptyset @ SV1778 ) @ SV1778 )
        = $false )
      | ( ( SV105 = SV1358 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8166]) ).

thf(8431,plain,
    ! [SV1605: $i,SV1360: $i,SV107: $i] :
      ( ( ( ( c_insert @ SV107 @ c_emptyset @ SV1360 )
          = ( c_insert @ SV1605 @ c_emptyset @ SV1360 ) )
        = $false )
      | ( ( SV107 = SV1605 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8167]) ).

thf(8432,plain,
    ! [SV1606: $i,SV1361: $i,SV108: $i] :
      ( ( ( c_in @ SV108 @ SV1361 @ SV1606 )
        = $false )
      | ( ( ! [SY3229: $i] :
              ( ~ ( c_lessequals @ SV1361 @ SY3229 @ ( tc_set @ SV1606 ) )
              | ( c_in @ SV108 @ SY3229 @ SV1606 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8168]) ).

thf(8433,plain,
    ! [SV1608: $i,SV1363: $i,SV110: $i] :
      ( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV110 @ SV1363 @ SV1608 ) @ SV1363 @ SV1608 )
        = $false )
      | ( ( c_lessequals @ SV110 @ SV1363 @ ( tc_set @ SV1608 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8170]) ).

thf(8434,plain,
    ! [SV1609: $i,SV1364: $i,SV111: $i] :
      ( ( ( c_lessequals @ SV111 @ SV1364 @ ( tc_set @ SV1609 ) )
        = $false )
      | ( ( ~ ( c_lessequals @ SV1364 @ SV111 @ ( tc_set @ SV1609 ) )
          | ( SV1364 = SV111 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8171]) ).

thf(8435,plain,
    ! [SV1610: $i,SV1366: $i,SV113: $i] :
      ( ( ( c_in @ SV113 @ SV1366 @ SV1610 )
        = $false )
      | ( ( ! [SY3230: $i,SY3231: $i] : ( c_in @ ( c_Sum__Type_OInl @ SV113 @ SV1610 @ SY3230 ) @ ( c_Sum__Type_OPlus @ SV1366 @ SY3231 @ SV1610 @ SY3230 ) @ ( tc_sum @ SV1610 @ SY3230 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8172]) ).

thf(8436,plain,
    ! [SV1611: $i,SV1367: $i,SV114: $i] :
      ( ( ( c_in @ SV114 @ SV1367 @ SV1611 )
        = $false )
      | ( ( ! [SY3232: $i,SY3233: $i] : ( c_in @ ( c_Sum__Type_OInr @ SV114 @ SV1611 @ SY3232 ) @ ( c_Sum__Type_OPlus @ SY3233 @ SV1367 @ SY3232 @ SV1611 ) @ ( tc_sum @ SY3232 @ SV1611 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8173]) ).

thf(8437,plain,
    ! [SV1907: $i,SV1779: $i,SV1612: $i,SV1368: $i,SV115: $i] :
      ( ( ~ ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SV1368 @ SV1612 @ SV1779 @ SV1907 ) @ ( tc_sum @ SV1779 @ SV1907 ) )
        | ( SV115
          = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1368 @ SV115 @ SV1779 @ SV1907 ) @ SV1779 @ SV1907 ) )
        | ( SV115
          = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1612 @ SV115 @ SV1907 @ SV1779 ) @ SV1907 @ SV1779 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8174]) ).

thf(8438,plain,
    ! [SV1908: $i,SV1780: $i,SV1613: $i,SV1369: $i,SV116: $i] :
      ( ( ~ ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SV1369 @ SV1613 @ SV1780 @ SV1908 ) @ ( tc_sum @ SV1780 @ SV1908 ) )
        | ( SV116
          = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1369 @ SV116 @ SV1780 @ SV1908 ) @ SV1780 @ SV1908 ) )
        | ( c_in @ ( c_Main_OPlusE__2 @ SV1613 @ SV116 @ SV1908 @ SV1780 ) @ SV1613 @ SV1908 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8175]) ).

thf(8439,plain,
    ! [SV1909: $i,SV1781: $i,SV1614: $i,SV1370: $i,SV117: $i] :
      ( ( ~ ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SV1370 @ SV1614 @ SV1781 @ SV1909 ) @ ( tc_sum @ SV1781 @ SV1909 ) )
        | ( SV117
          = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1614 @ SV117 @ SV1909 @ SV1781 ) @ SV1909 @ SV1781 ) )
        | ( c_in @ ( c_Main_OPlusE__1 @ SV1370 @ SV117 @ SV1781 @ SV1909 ) @ SV1370 @ SV1781 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8176]) ).

thf(8440,plain,
    ! [SV1910: $i,SV1782: $i,SV1615: $i,SV1371: $i,SV118: $i] :
      ( ( ~ ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SV1371 @ SV1615 @ SV1782 @ SV1910 ) @ ( tc_sum @ SV1782 @ SV1910 ) )
        | ( c_in @ ( c_Main_OPlusE__1 @ SV1371 @ SV118 @ SV1782 @ SV1910 ) @ SV1371 @ SV1782 )
        | ( c_in @ ( c_Main_OPlusE__2 @ SV1615 @ SV118 @ SV1910 @ SV1782 ) @ SV1615 @ SV1910 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8177]) ).

thf(8441,plain,
    ! [SV1616: $i,SV1372: $i,SV119: $i] :
      ( ( ( c_in @ SV119 @ SV1372 @ ( tc_prod @ SV1616 @ SV1616 ) )
        = $false )
      | ( ( c_in @ SV119 @ ( c_Transitive__Closure_Ortrancl @ SV1372 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8178]) ).

thf(8442,plain,
    ! [SV1783: $i,SV1618: $i,SV1374: $i,SV121: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ SV1783 @ ( tc_prod @ SV1618 @ SV1618 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SV1783 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8179]) ).

thf(8443,plain,
    ! [SV1784: $i,SV1619: $i,SV1375: $i,SV122: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Otrancl @ SV1784 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1784 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8180]) ).

thf(8444,plain,
    ! [SV1376: $i,SV124: $i,SV1911: $i] :
      ( ( ( ! [SY3442: $i] :
              ( ~ ( c_Relation_Otrans @ SV1911 @ SY3442 )
              | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1911 @ SV124 @ SY3442 @ SV1376 ) @ ( tc_prod @ SY3442 @ SV1376 ) ) ) )
        = $true )
      | ( ( c_Relation_Otrans @ SV124 @ SV1376 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8181]) ).

thf(8445,plain,
    ! [SV1377: $i,SV125: $i,SV1912: $i] :
      ( ( ( ! [SY3443: $i] :
              ( ~ ( c_Wellfounded__Recursion_Owf @ SV1912 @ SY3443 )
              | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1912 @ SV125 @ SY3443 @ SV1377 ) @ ( tc_prod @ SY3443 @ SV1377 ) ) ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV125 @ SV1377 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8182]) ).

thf(8446,plain,
    ! [SV127: $i,SV1378: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV1378 )
        = $false )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV127 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV127 @ SV1378 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8183]) ).

thf(8447,plain,
    ! [SV129: $i,SV1380: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV1380 )
        = $false )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV129 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV129 @ SV1380 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8184]) ).

thf(8448,plain,
    ! [SV135: $i,SV1381: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV1381 )
        = $false )
      | ( ( ~ ( class_Finite__Set_Ofinite @ SV135 ) )
        = $true )
      | ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV135 @ SV1381 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8185]) ).

thf(8449,plain,
    ! [SV1620: $i,SV1382: $i,SV1043: $i] :
      ( ( ( c_in @ SV1043 @ ( c_Datatype_Oo2s @ SV1382 @ SV1620 ) @ SV1620 )
        = $false )
      | ( ( SV1382
          = ( c_Datatype_Ooption_OSome @ SV1043 @ SV1620 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8186]) ).

thf(8450,plain,
    ! [SV1623: $i,SV1386: $i,SV1049: $i] :
      ( ( ( ( c_Datatype_Ooption_OSome @ SV1049 @ SV1386 )
          = ( c_Datatype_Ooption_OSome @ SV1623 @ SV1386 ) )
        = $false )
      | ( ( SV1049 = SV1623 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8187]) ).

thf(8451,plain,
    ! [SV1785: $i,SV1624: $i,SV1387: $i,SV1050: $i] :
      ( ( ( ( c_Datatype__Universe_OAtom @ SV1050 @ SV1387 @ SV1624 )
         != ( c_Datatype__Universe_OAtom @ SV1785 @ SV1387 @ SV1624 ) )
        = $true )
      | ( ( SV1050 = SV1785 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8188]) ).

thf(8452,plain,
    ! [SV1913: $i,SV1786: $i,SV1625: $i,SV1388: $i,SV1051: $i] :
      ( ( ( c_Datatype__Universe_OAtom @ SV1051 @ SV1388 @ SV1625 )
       != ( c_Datatype__Universe_OScons @ SV1786 @ SV1913 @ SV1388 @ SV1625 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8189]) ).

thf(8453,plain,
    ! [SV1787: $i,SV1626: $i,SV1389: $i,SV1052: $i] :
      ( ( ( ( c_Datatype__Universe_OIn0 @ SV1052 @ SV1389 @ SV1626 )
         != ( c_Datatype__Universe_OIn0 @ SV1787 @ SV1389 @ SV1626 ) )
        = $true )
      | ( ( SV1052 = SV1787 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8190]) ).

thf(8454,plain,
    ! [SV1788: $i,SV1627: $i,SV1390: $i,SV1053: $i] :
      ( ( ( c_Datatype__Universe_OIn0 @ SV1053 @ SV1390 @ SV1627 )
        = ( c_Datatype__Universe_OIn1 @ SV1788 @ SV1390 @ SV1627 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8191]) ).

thf(8455,plain,
    ! [SV1789: $i,SV1628: $i,SV1391: $i,SV1054: $i] :
      ( ( ( ( c_Datatype__Universe_OIn1 @ SV1054 @ SV1391 @ SV1628 )
         != ( c_Datatype__Universe_OIn1 @ SV1789 @ SV1391 @ SV1628 ) )
        = $true )
      | ( ( SV1054 = SV1789 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8192]) ).

thf(8456,plain,
    ! [SV1790: $i,SV1629: $i,SV1392: $i,SV1055: $i] :
      ( ( ( c_Datatype__Universe_OIn1 @ SV1055 @ SV1392 @ SV1629 )
        = ( c_Datatype__Universe_OIn0 @ SV1790 @ SV1392 @ SV1629 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8193]) ).

thf(8457,plain,
    ! [SV1791: $i,SV1630: $i,SV1393: $i,SV1056: $i] :
      ( ( ( c_Datatype__Universe_OLeaf @ SV1056 @ SV1393 @ SV1630 )
        = ( c_Datatype__Universe_ONumb @ SV1791 @ SV1393 @ SV1630 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8194]) ).

thf(8458,plain,
    ! [SV1914: $i,SV1792: $i,SV1631: $i,SV1394: $i,SV1057: $i] :
      ( ( ( c_Datatype__Universe_OLeaf @ SV1057 @ SV1394 @ SV1631 )
       != ( c_Datatype__Universe_OScons @ SV1792 @ SV1914 @ SV1394 @ SV1631 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8195]) ).

thf(8459,plain,
    ! [SV1793: $i,SV1632: $i,SV1395: $i,SV1058: $i] :
      ( ( ( c_Datatype__Universe_ONumb @ SV1058 @ SV1395 @ SV1632 )
        = ( c_Datatype__Universe_OLeaf @ SV1793 @ SV1395 @ SV1632 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8196]) ).

thf(8460,plain,
    ! [SV1915: $i,SV1794: $i,SV1633: $i,SV1396: $i,SV1059: $i] :
      ( ( ( c_Datatype__Universe_ONumb @ SV1059 @ SV1396 @ SV1633 )
       != ( c_Datatype__Universe_OScons @ SV1794 @ SV1915 @ SV1396 @ SV1633 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8197]) ).

thf(8461,plain,
    ! [SV1916: $i,SV1795: $i,SV1634: $i,SV1397: $i,SV1060: $i] :
      ( ( ! [SY3444: $i] :
            ( ( c_Datatype__Universe_OScons @ SV1060 @ SV1397 @ SV1634 @ SV1795 )
           != ( c_Datatype__Universe_OScons @ SV1916 @ SY3444 @ SV1634 @ SV1795 ) )
        | ( SV1060 = SV1916 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8198]) ).

thf(8462,plain,
    ! [SV1917: $i,SV1796: $i,SV1635: $i,SV1398: $i,SV1061: $i] :
      ( ( ! [SY3445: $i] :
            ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SV1398 @ SV1635 @ SV1796 )
             != ( c_Datatype__Universe_OScons @ SV1917 @ SY3445 @ SV1635 @ SV1796 ) )
            | ( SV1398 = SY3445 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8199]) ).

thf(8463,plain,
    ! [SV1918: $i,SV1797: $i,SV1636: $i,SV1399: $i,SV1062: $i] :
      ( ( ( c_Datatype__Universe_OScons @ SV1062 @ SV1399 @ SV1636 @ SV1797 )
       != ( c_Datatype__Universe_OAtom @ SV1918 @ SV1636 @ SV1797 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8200]) ).

thf(8464,plain,
    ! [SV1919: $i,SV1798: $i,SV1637: $i,SV1400: $i,SV1063: $i] :
      ( ( ( c_Datatype__Universe_OScons @ SV1063 @ SV1400 @ SV1637 @ SV1798 )
       != ( c_Datatype__Universe_OLeaf @ SV1919 @ SV1637 @ SV1798 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8201]) ).

thf(8465,plain,
    ! [SV1920: $i,SV1799: $i,SV1638: $i,SV1401: $i,SV1064: $i] :
      ( ( ( c_Datatype__Universe_OScons @ SV1064 @ SV1401 @ SV1638 @ SV1799 )
       != ( c_Datatype__Universe_ONumb @ SV1920 @ SV1638 @ SV1799 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8202]) ).

thf(8466,plain,
    ! [SV1800: $i,SV1639: $i,SV1066: $i] :
      ( ( ( c_emptyset
          = ( c_Equiv__Relations_Oquotient @ SV1066 @ SV1639 @ SV1800 ) )
        = $false )
      | ( ( SV1066 = c_emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8203]) ).

thf(8467,plain,
    ! [SV1801: $i,SV1640: $i,SV1068: $i] :
      ( ( ( ( c_Equiv__Relations_Oquotient @ SV1068 @ SV1640 @ SV1801 )
          = c_emptyset )
        = $false )
      | ( ( SV1068 = c_emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8204]) ).

thf(8468,plain,
    ! [SV1802: $i,SV1641: $i,SV1404: $i,SV1070: $i] :
      ( ( ( ~ ( c_in @ ( c_minus @ SV1070 @ ( c_insert @ SV1404 @ SV1641 @ SV1802 ) @ ( tc_set @ SV1802 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1802 ) ) )
        = $true )
      | ( ( c_in @ ( c_minus @ SV1070 @ SV1641 @ ( tc_set @ SV1802 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1802 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8205]) ).

thf(8469,plain,
    ! [SV1642: $i,SV1405: $i,SV1071: $i] :
      ( ( ( c_in @ ( c_minus @ SV1071 @ SV1405 @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) )
        = $false )
      | ( ( ! [SY3272: $i] : ( c_in @ ( c_minus @ SV1071 @ ( c_insert @ SY3272 @ SV1405 @ SV1642 ) @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8206]) ).

thf(8470,plain,
    ! [SV1643: $i,SV1408: $i,SV1074: $i] :
      ( ( ( c_in @ ( c_union @ SV1074 @ SV1408 @ SV1643 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1643 ) )
        = $false )
      | ( ( c_in @ SV1074 @ c_Finite__Set_OFinites @ ( tc_set @ SV1643 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8209]) ).

thf(8471,plain,
    ! [SV1644: $i,SV1409: $i,SV1075: $i] :
      ( ( ( c_in @ ( c_union @ SV1075 @ SV1409 @ SV1644 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1644 ) )
        = $false )
      | ( ( c_in @ SV1409 @ c_Finite__Set_OFinites @ ( tc_set @ SV1644 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8210]) ).

thf(8472,plain,
    ! [SV1076: $i,SV1410: $i,SV1921: $i] :
      ( ( ( ~ ( c_in @ SV1921 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
          | ( c_in @ ( c_union @ SV1921 @ SV1076 @ SV1410 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) ) )
        = $true )
      | ( ( c_in @ SV1076 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8211]) ).

thf(8473,plain,
    ! [SV1645: $i,SV1411: $i,SV1077: $i] :
      ( ( ( c_in @ ( c_Relation_Oconverse @ SV1077 @ SV1411 @ SV1645 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1645 @ SV1411 ) ) )
        = $false )
      | ( ( c_in @ SV1077 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1411 @ SV1645 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8212]) ).

thf(8474,plain,
    ! [SV1646: $i,SV1412: $i,SV1078: $i] :
      ( ( ( c_in @ SV1078 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1412 @ SV1646 ) ) )
        = $false )
      | ( ( c_in @ ( c_Relation_Oconverse @ SV1078 @ SV1412 @ SV1646 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1646 @ SV1412 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8213]) ).

thf(8475,plain,
    ! [SV1803: $i,SV1413: $i,SV1079: $i] :
      ( ( ( c_Divides_Oop_Advd @ SV1079 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1413 @ SV1803 @ tc_nat @ tc_nat ) ) @ tc_nat )
        = $false )
      | ( ( c_Divides_Oop_Advd @ SV1079 @ SV1413 @ tc_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8214]) ).

thf(8476,plain,
    ! [SV1647: $i,SV1414: $i,SV1080: $i] :
      ( ( ( c_Divides_Oop_Advd @ SV1080 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1414 @ SV1647 @ tc_nat @ tc_nat ) ) @ tc_nat )
        = $false )
      | ( ( c_Divides_Oop_Advd @ SV1080 @ SV1647 @ tc_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8215]) ).

thf(8477,plain,
    ! [SV1415: $i,SV1922: $i,SV1081: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SV1922 @ tc_nat )
          | ( c_Divides_Oop_Advd @ SV1081 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1922 @ SV1415 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1081 @ SV1415 @ tc_nat )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8216]) ).

thf(8478,plain,
    ! [SV1804: $i,SV1649: $i,SV1089: $i] :
      ( ( ( c_List_Olist_ONil
          = ( c_append @ SV1089 @ SV1649 @ SV1804 ) )
        = $false )
      | ( ( SV1089 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8223]) ).

thf(8479,plain,
    ! [SV1805: $i,SV1422: $i,SV1090: $i] :
      ( ( ( c_List_Olist_ONil
          = ( c_append @ SV1090 @ SV1422 @ SV1805 ) )
        = $false )
      | ( ( SV1422 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8224]) ).

thf(8480,plain,
    ! [SV1806: $i,SV1652: $i,SV1424: $i,SV1095: $i] :
      ( ( ( ! [SY3398: $i] :
              ( ( c_append @ SV1095 @ ( c_List_Olist_OCons @ SV1424 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 )
             != ( c_append @ SV1806 @ ( c_List_Olist_OCons @ SY3398 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 ) ) )
        = $true )
      | ( ( SV1095 = SV1806 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8227]) ).

thf(8481,plain,
    ! [SV1923: $i,SV1807: $i,SV1653: $i,SV1425: $i,SV1096: $i] :
      ( ( ( ( c_append @ SV1096 @ ( c_List_Olist_OCons @ SV1425 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 )
         != ( c_append @ SV1807 @ ( c_List_Olist_OCons @ SV1923 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 ) )
        | ( SV1425 = SV1923 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8228]) ).

thf(8482,plain,
    ! [SV1808: $i,SV1654: $i,SV1426: $i,SV1097: $i] :
      ( ( ( ~ ( c_in @ ( c_append @ SV1097 @ SV1426 @ SV1654 ) @ ( c_List_Olists @ SV1808 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) ) )
        = $true )
      | ( ( c_in @ SV1097 @ ( c_List_Olists @ SV1808 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8229]) ).

thf(8483,plain,
    ! [SV1809: $i,SV1655: $i,SV1427: $i,SV1098: $i] :
      ( ( ( ~ ( c_in @ ( c_append @ SV1098 @ SV1427 @ SV1655 ) @ ( c_List_Olists @ SV1809 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) ) )
        = $true )
      | ( ( c_in @ SV1427 @ ( c_List_Olists @ SV1809 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8230]) ).

thf(8484,plain,
    ! [SV1656: $i,SV1428: $i,SV1099: $i] :
      ( ( ( c_in @ SV1099 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        = $false )
      | ( ( ! [SY3280: $i] :
              ( ~ ( c_in @ SY3280 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
              | ( c_in @ ( c_append @ SY3280 @ SV1099 @ SV1656 ) @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8231]) ).

thf(8485,plain,
    ! [SV1810: $i,SV1657: $i,SV1100: $i] :
      ( ( ( ( c_append @ SV1100 @ SV1657 @ SV1810 )
          = c_List_Olist_ONil )
        = $false )
      | ( ( SV1100 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8232]) ).

thf(8486,plain,
    ! [SV1811: $i,SV1429: $i,SV1101: $i] :
      ( ( ( ( c_append @ SV1101 @ SV1429 @ SV1811 )
          = c_List_Olist_ONil )
        = $false )
      | ( ( SV1429 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8233]) ).

thf(8487,plain,
    ! [SV1812: $i,SV1658: $i,SV1430: $i,SV1103: $i] :
      ( ( ( ( c_append @ SV1103 @ SV1430 @ SV1658 )
         != ( c_append @ SV1812 @ SV1430 @ SV1658 ) )
        = $true )
      | ( ( SV1103 = SV1812 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8234]) ).

thf(8488,plain,
    ! [SV1813: $i,SV1659: $i,SV1104: $i] :
      ( ( ( ( c_append @ SV1104 @ SV1659 @ SV1813 )
          = SV1659 )
        = $false )
      | ( ( SV1104 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8235]) ).

thf(8489,plain,
    ! [SV1814: $i,SV1432: $i,SV1106: $i] :
      ( ( ( ( c_append @ SV1106 @ SV1432 @ SV1814 )
          = SV1106 )
        = $false )
      | ( ( SV1432 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8236]) ).

thf(8490,plain,
    ! [SV1924: $i,SV1660: $i,SV1434: $i,SV1108: $i] :
      ( ( ( ( c_List_Ochar_OChar @ SV1108 @ SV1434 )
         != ( c_List_Ochar_OChar @ SV1660 @ SV1924 ) )
        = $true )
      | ( ( SV1108 = SV1660 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8237]) ).

thf(8491,plain,
    ! [SV1815: $i,SV1661: $i,SV1435: $i,SV1109: $i] :
      ( ( ( ( c_List_Ochar_OChar @ SV1109 @ SV1435 )
         != ( c_List_Ochar_OChar @ SV1661 @ SV1815 ) )
        = $true )
      | ( ( SV1435 = SV1815 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8238]) ).

thf(8492,plain,
    ! [SV1816: $i,SV1666: $i,SV1440: $i,SV1118: $i] :
      ( ( ( ! [SY3400: $i] :
              ( ( c_List_Olist_OCons @ SV1118 @ SV1440 @ SV1666 )
             != ( c_List_Olist_OCons @ SV1816 @ SY3400 @ SV1666 ) ) )
        = $true )
      | ( ( SV1118 = SV1816 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8244]) ).

thf(8493,plain,
    ! [SV1925: $i,SV1817: $i,SV1667: $i,SV1441: $i,SV1119: $i] :
      ( ( ( ( c_List_Olist_OCons @ SV1119 @ SV1441 @ SV1667 )
         != ( c_List_Olist_OCons @ SV1817 @ SV1925 @ SV1667 ) )
        | ( SV1441 = SV1925 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8245]) ).

thf(8494,plain,
    ! [SV1818: $i,SV1668: $i,SV1442: $i,SV1120: $i] :
      ( ( ( ( c_List_Orev @ SV1120 @ SV1442 )
         != ( c_List_Olist_OCons @ SV1668 @ SV1818 @ SV1442 ) )
        = $true )
      | ( ( SV1120
          = ( c_append @ ( c_List_Orev @ SV1818 @ SV1442 ) @ ( c_List_Olist_OCons @ SV1668 @ c_List_Olist_ONil @ SV1442 ) @ SV1442 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8246]) ).

thf(8495,plain,
    ! [SV1671: $i,SV1444: $i,SV1124: $i] :
      ( ( ( ( c_List_Orev @ SV1124 @ SV1444 )
          = ( c_List_Orev @ SV1671 @ SV1444 ) )
        = $false )
      | ( ( SV1124 = SV1671 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8248]) ).

thf(8496,plain,
    ! [SV1819: $i,SV1672: $i,SV1445: $i,SV1125: $i] :
      ( ( ( ( c_append @ SV1125 @ SV1445 @ SV1672 )
         != ( c_append @ SV1125 @ SV1819 @ SV1672 ) )
        = $true )
      | ( ( SV1445 = SV1819 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8249]) ).

thf(8497,plain,
    ! [SV1820: $i,SV1446: $i,SV1126: $i] :
      ( ( ( SV1126
          = ( c_append @ SV1446 @ SV1126 @ SV1820 ) )
        = $false )
      | ( ( SV1446 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8250]) ).

thf(8498,plain,
    ! [SV1821: $i,SV1448: $i,SV1128: $i] :
      ( ( ( SV1128
          = ( c_append @ SV1128 @ SV1448 @ SV1821 ) )
        = $false )
      | ( ( SV1448 = c_List_Olist_ONil )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8251]) ).

thf(8499,plain,
    ! [SV1141: $i,SV1455: $i] :
      ( ( ( c_less @ c_0 @ SV1455 @ tc_nat )
        = $true )
      | ( ( c_less @ c_0 @ SV1141 @ tc_nat )
        = $true )
      | ( ( c_less @ c_0 @ ( c_plus @ SV1141 @ SV1455 @ tc_nat ) @ tc_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8259]) ).

thf(8500,plain,
    ! [SV1153: $i,SV1824: $i] :
      ( ( ( c_less @ SV1824 @ SV1824 @ SV1153 )
        = $false )
      | ( ( class_Orderings_Oorder @ SV1153 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8264]) ).

thf(8501,plain,
    ! [SV1926: $i,SV1825: $i,SV1676: $i,SV1459: $i,SV1154: $i] :
      ( ( ! [SY3446: $i] :
            ( ( c_Pair @ SV1154 @ SV1459 @ SV1676 @ SV1825 )
           != ( c_Pair @ SV1926 @ SY3446 @ SV1676 @ SV1825 ) )
        | ( SV1154 = SV1926 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8265]) ).

thf(8502,plain,
    ! [SV1927: $i,SV1826: $i,SV1677: $i,SV1460: $i,SV1155: $i] :
      ( ( ! [SY3447: $i] :
            ( ( ( c_Pair @ SV1155 @ SV1460 @ SV1677 @ SV1826 )
             != ( c_Pair @ SV1927 @ SY3447 @ SV1677 @ SV1826 ) )
            | ( SV1460 = SY3447 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8266]) ).

thf(8503,plain,
    ! [SV1928: $i,SV1827: $i,SV1678: $i,SV1462: $i,SV1157: $i] :
      ( ( ~ ( c_in @ SV1157 @ ( c_Relation_OImage @ SV1462 @ ( c_insert @ SV1678 @ c_emptyset @ SV1827 ) @ SV1827 @ SV1928 ) @ SV1928 )
        | ( c_in @ ( c_Pair @ SV1678 @ SV1157 @ SV1827 @ SV1928 ) @ SV1462 @ ( tc_prod @ SV1827 @ SV1928 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8267]) ).

thf(8504,plain,
    ! [SV1929: $i,SV1828: $i,SV1679: $i,SV1463: $i,SV1158: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV1158 @ SV1463 @ SV1679 @ SV1828 ) @ SV1929 @ ( tc_prod @ SV1679 @ SV1828 ) )
        | ( c_in @ SV1463 @ ( c_Relation_OImage @ SV1929 @ ( c_insert @ SV1158 @ c_emptyset @ SV1679 ) @ SV1679 @ SV1828 ) @ SV1828 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8268]) ).

thf(8505,plain,
    ! [SV1930: $i,SV1829: $i,SV1680: $i,SV1464: $i,SV1159: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV1159 @ SV1464 @ SV1680 @ SV1829 ) @ ( c_Relation_Oconverse @ SV1930 @ SV1829 @ SV1680 ) @ ( tc_prod @ SV1680 @ SV1829 ) )
        | ( c_in @ ( c_Pair @ SV1464 @ SV1159 @ SV1829 @ SV1680 ) @ SV1930 @ ( tc_prod @ SV1829 @ SV1680 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8269]) ).

thf(8506,plain,
    ! [SV1931: $i,SV1830: $i,SV1681: $i,SV1465: $i,SV1160: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV1160 @ SV1465 @ SV1681 @ SV1830 ) @ SV1931 @ ( tc_prod @ SV1681 @ SV1830 ) )
        | ( c_in @ ( c_Pair @ SV1465 @ SV1160 @ SV1830 @ SV1681 ) @ ( c_Relation_Oconverse @ SV1931 @ SV1681 @ SV1830 ) @ ( tc_prod @ SV1830 @ SV1681 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8270]) ).

thf(8507,plain,
    ! [SV1831: $i,SV1466: $i,SV1161: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1161 @ SV1466 @ SV1831 @ SV1831 ) @ c_Relation_OId @ ( tc_prod @ SV1831 @ SV1831 ) )
        = $false )
      | ( ( SV1161 = SV1466 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8271]) ).

thf(8508,plain,
    ! [SV1932: $i,SV1162: $i,SV1832: $i] :
      ( ( ( ( ( c_SetInterval_OatLeast @ SV1832 @ SV1162 )
           != ( c_SetInterval_OatLeast @ SV1932 @ SV1162 ) )
          | ( SV1832 = SV1932 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1162 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8272]) ).

thf(8509,plain,
    ! [SV1163: $i,SV1933: $i,SV1833: $i] :
      ( ( ( ~ ( c_in @ SV1833 @ ( c_SetInterval_OatLeast @ SV1933 @ SV1163 ) @ SV1163 )
          | ( c_lessequals @ SV1933 @ SV1833 @ SV1163 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1163 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8273]) ).

thf(8510,plain,
    ! [SV1164: $i,SV1934: $i,SV1834: $i] :
      ( ( ( ~ ( c_lessequals @ SV1834 @ SV1934 @ SV1164 )
          | ( c_in @ SV1934 @ ( c_SetInterval_OatLeast @ SV1834 @ SV1164 ) @ SV1164 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1164 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8274]) ).

thf(8511,plain,
    ! [SV1935: $i,SV1165: $i,SV1835: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1835 @ SV1165 ) @ ( c_SetInterval_OatLeast @ SV1935 @ SV1165 ) @ ( tc_set @ SV1165 ) )
          | ( c_lessequals @ SV1935 @ SV1835 @ SV1165 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1165 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8275]) ).

thf(8512,plain,
    ! [SV1166: $i,SV1936: $i,SV1836: $i] :
      ( ( ( ~ ( c_lessequals @ SV1836 @ SV1936 @ SV1166 )
          | ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1936 @ SV1166 ) @ ( c_SetInterval_OatLeast @ SV1836 @ SV1166 ) @ ( tc_set @ SV1166 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1166 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8276]) ).

thf(8513,plain,
    ! [SV1937: $i,SV1167: $i,SV1837: $i] :
      ( ( ( ( ( c_SetInterval_OatMost @ SV1837 @ SV1167 )
           != ( c_SetInterval_OatMost @ SV1937 @ SV1167 ) )
          | ( SV1837 = SV1937 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1167 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8277]) ).

thf(8514,plain,
    ! [SV1168: $i,SV1938: $i,SV1838: $i] :
      ( ( ( ~ ( c_in @ SV1838 @ ( c_SetInterval_OatMost @ SV1938 @ SV1168 ) @ SV1168 )
          | ( c_lessequals @ SV1838 @ SV1938 @ SV1168 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1168 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8278]) ).

thf(8515,plain,
    ! [SV1169: $i,SV1939: $i,SV1839: $i] :
      ( ( ( ~ ( c_lessequals @ SV1839 @ SV1939 @ SV1169 )
          | ( c_in @ SV1839 @ ( c_SetInterval_OatMost @ SV1939 @ SV1169 ) @ SV1169 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1169 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8279]) ).

thf(8516,plain,
    ! [SV1940: $i,SV1170: $i,SV1840: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1840 @ SV1170 ) @ ( c_SetInterval_OatMost @ SV1940 @ SV1170 ) @ ( tc_set @ SV1170 ) )
          | ( c_lessequals @ SV1840 @ SV1940 @ SV1170 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1170 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8280]) ).

thf(8517,plain,
    ! [SV1171: $i,SV1941: $i,SV1841: $i] :
      ( ( ( ~ ( c_lessequals @ SV1841 @ SV1941 @ SV1171 )
          | ( c_lessequals @ ( c_SetInterval_OatMost @ SV1841 @ SV1171 ) @ ( c_SetInterval_OatMost @ SV1941 @ SV1171 ) @ ( tc_set @ SV1171 ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1171 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8281]) ).

thf(8518,plain,
    ! [SV1942: $i,SV1172: $i,SV1842: $i] :
      ( ( ( ( ( c_SetInterval_OgreaterThan @ SV1842 @ SV1172 )
           != ( c_SetInterval_OgreaterThan @ SV1942 @ SV1172 ) )
          | ( SV1842 = SV1942 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1172 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8282]) ).

thf(8519,plain,
    ! [SV1173: $i,SV1943: $i,SV1843: $i] :
      ( ( ( ~ ( c_in @ SV1843 @ ( c_SetInterval_OgreaterThan @ SV1943 @ SV1173 ) @ SV1173 )
          | ( c_less @ SV1943 @ SV1843 @ SV1173 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1173 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8283]) ).

thf(8520,plain,
    ! [SV1174: $i,SV1944: $i,SV1844: $i] :
      ( ( ( ~ ( c_less @ SV1844 @ SV1944 @ SV1174 )
          | ( c_in @ SV1944 @ ( c_SetInterval_OgreaterThan @ SV1844 @ SV1174 ) @ SV1174 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1174 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8284]) ).

thf(8521,plain,
    ! [SV1945: $i,SV1175: $i,SV1845: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1845 @ SV1175 ) @ ( c_SetInterval_OgreaterThan @ SV1945 @ SV1175 ) @ ( tc_set @ SV1175 ) )
          | ( c_lessequals @ SV1945 @ SV1845 @ SV1175 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1175 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8285]) ).

thf(8522,plain,
    ! [SV1176: $i,SV1946: $i,SV1846: $i] :
      ( ( ( ~ ( c_lessequals @ SV1846 @ SV1946 @ SV1176 )
          | ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1946 @ SV1176 ) @ ( c_SetInterval_OgreaterThan @ SV1846 @ SV1176 ) @ ( tc_set @ SV1176 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1176 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8286]) ).

thf(8523,plain,
    ! [SV1947: $i,SV1177: $i,SV1847: $i] :
      ( ( ( ( ( c_SetInterval_OlessThan @ SV1847 @ SV1177 )
           != ( c_SetInterval_OlessThan @ SV1947 @ SV1177 ) )
          | ( SV1847 = SV1947 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1177 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8287]) ).

thf(8524,plain,
    ! [SV1178: $i,SV1948: $i,SV1848: $i] :
      ( ( ( ~ ( c_in @ SV1848 @ ( c_SetInterval_OlessThan @ SV1948 @ SV1178 ) @ SV1178 )
          | ( c_less @ SV1848 @ SV1948 @ SV1178 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1178 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8288]) ).

thf(8525,plain,
    ! [SV1179: $i,SV1949: $i,SV1849: $i] :
      ( ( ( ~ ( c_less @ SV1849 @ SV1949 @ SV1179 )
          | ( c_in @ SV1849 @ ( c_SetInterval_OlessThan @ SV1949 @ SV1179 ) @ SV1179 ) )
        = $true )
      | ( ( class_Orderings_Oord @ SV1179 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8289]) ).

thf(8526,plain,
    ! [SV1950: $i,SV1180: $i,SV1850: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1850 @ SV1180 ) @ ( c_SetInterval_OlessThan @ SV1950 @ SV1180 ) @ ( tc_set @ SV1180 ) )
          | ( c_lessequals @ SV1850 @ SV1950 @ SV1180 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1180 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8290]) ).

thf(8527,plain,
    ! [SV1181: $i,SV1951: $i,SV1851: $i] :
      ( ( ( ~ ( c_lessequals @ SV1851 @ SV1951 @ SV1181 )
          | ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1851 @ SV1181 ) @ ( c_SetInterval_OlessThan @ SV1951 @ SV1181 ) @ ( tc_set @ SV1181 ) ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1181 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8291]) ).

thf(8528,plain,
    ! [SV1682: $i,SV1467: $i,SV1182: $i] :
      ( ( ( c_in @ SV1182 @ SV1467 @ SV1682 )
        = $false )
      | ( ( ~ ( c_in @ SV1182 @ ( c_uminus @ SV1467 @ ( tc_set @ SV1682 ) ) @ SV1682 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8292]) ).

thf(8529,plain,
    ! [SV1684: $i,SV1469: $i,SV1184: $i] :
      ( ( ( ( c_uminus @ SV1184 @ ( tc_set @ SV1469 ) )
          = ( c_uminus @ SV1684 @ ( tc_set @ SV1469 ) ) )
        = $false )
      | ( ( SV1184 = SV1684 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8294]) ).

thf(8530,plain,
    ! [SV1685: $i,SV1470: $i,SV1185: $i] :
      ( ( ( c_lessequals @ ( c_uminus @ SV1185 @ ( tc_set @ SV1470 ) ) @ ( c_uminus @ SV1685 @ ( tc_set @ SV1470 ) ) @ ( tc_set @ SV1470 ) )
        = $false )
      | ( ( c_lessequals @ SV1685 @ SV1185 @ ( tc_set @ SV1470 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8295]) ).

thf(8531,plain,
    ! [SV1686: $i,SV1471: $i,SV1186: $i] :
      ( ( ( c_lessequals @ SV1186 @ SV1471 @ ( tc_set @ SV1686 ) )
        = $false )
      | ( ( c_lessequals @ ( c_uminus @ SV1471 @ ( tc_set @ SV1686 ) ) @ ( c_uminus @ SV1186 @ ( tc_set @ SV1686 ) ) @ ( tc_set @ SV1686 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8296]) ).

thf(8532,plain,
    ! [SV1687: $i,SV1472: $i,SV1187: $i] :
      ( ( ( c_in @ SV1187 @ SV1472 @ SV1687 )
        = $false )
      | ( ( ! [SY3306: $i] :
              ~ ( c_in @ SV1187 @ ( c_minus @ SY3306 @ SV1472 @ ( tc_set @ SV1687 ) ) @ SV1687 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8297]) ).

thf(8533,plain,
    ! [SV1852: $i,SV1688: $i,SV1473: $i,SV1188: $i] :
      ( ( ( ~ ( c_in @ SV1188 @ ( c_minus @ SV1473 @ SV1688 @ ( tc_set @ SV1852 ) ) @ SV1852 ) )
        = $true )
      | ( ( c_in @ SV1188 @ SV1473 @ SV1852 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8298]) ).

thf(8534,plain,
    ! [SV1689: $i,SV1474: $i,SV1189: $i] :
      ( ( ( c_in @ SV1189 @ SV1474 @ SV1689 )
        = $false )
      | ( ( ! [SY3308: $i] :
              ( ( c_in @ SV1189 @ SY3308 @ SV1689 )
              | ( c_in @ SV1189 @ ( c_minus @ SV1474 @ SY3308 @ ( tc_set @ SV1689 ) ) @ SV1689 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8299]) ).

thf(8535,plain,
    ! [SV1853: $i,SV1690: $i,SV1475: $i,SV1190: $i] :
      ( ( ( ~ ( c_in @ SV1190 @ ( c_inter @ SV1475 @ SV1690 @ SV1853 ) @ SV1853 ) )
        = $true )
      | ( ( c_in @ SV1190 @ SV1690 @ SV1853 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8300]) ).

thf(8536,plain,
    ! [SV1854: $i,SV1691: $i,SV1476: $i,SV1191: $i] :
      ( ( ( ~ ( c_in @ SV1191 @ ( c_inter @ SV1476 @ SV1691 @ SV1854 ) @ SV1854 ) )
        = $true )
      | ( ( c_in @ SV1191 @ SV1476 @ SV1854 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8301]) ).

thf(8537,plain,
    ! [SV1692: $i,SV1477: $i,SV1192: $i] :
      ( ( ( c_in @ SV1192 @ SV1477 @ SV1692 )
        = $false )
      | ( ( ! [SY3311: $i] :
              ( ~ ( c_in @ SV1192 @ SY3311 @ SV1692 )
              | ( c_in @ SV1192 @ ( c_inter @ SY3311 @ SV1477 @ SV1692 ) @ SV1692 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8302]) ).

thf(8538,plain,
    ! [SV1693: $i,SV1478: $i,SV1193: $i] :
      ( ( ( c_in @ SV1193 @ SV1478 @ ( tc_set @ SV1693 ) )
        = $false )
      | ( ( ! [SY3312: $i] :
              ( ~ ( c_in @ SY3312 @ ( c_Inter @ SV1478 @ SV1693 ) @ SV1693 )
              | ( c_in @ SY3312 @ SV1193 @ SV1693 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8303]) ).

thf(8539,plain,
    ! [SV1694: $i,SV1479: $i,SV1194: $i] :
      ( ( ( c_in @ SV1194 @ ( c_Pow @ SV1479 @ SV1694 ) @ ( tc_set @ SV1694 ) )
        = $false )
      | ( ( c_lessequals @ SV1194 @ SV1479 @ ( tc_set @ SV1694 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8304]) ).

thf(8540,plain,
    ! [SV1695: $i,SV1480: $i,SV1195: $i] :
      ( ( ( c_lessequals @ SV1195 @ SV1480 @ ( tc_set @ SV1695 ) )
        = $false )
      | ( ( c_in @ SV1195 @ ( c_Pow @ SV1480 @ SV1695 ) @ ( tc_set @ SV1695 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8305]) ).

thf(8541,plain,
    ! [SV1696: $i,SV1481: $i,SV1196: $i] :
      ( ( ( c_in @ SV1196 @ SV1481 @ SV1696 )
        = $false )
      | ( ( ! [SY3313: $i] : ( c_in @ SV1196 @ ( c_union @ SY3313 @ SV1481 @ SV1696 ) @ SV1696 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8306]) ).

thf(8542,plain,
    ! [SV1697: $i,SV1482: $i,SV1197: $i] :
      ( ( ( c_in @ SV1197 @ SV1482 @ SV1697 )
        = $false )
      | ( ( ! [SY3314: $i] : ( c_in @ SV1197 @ ( c_union @ SV1482 @ SY3314 @ SV1697 ) @ SV1697 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8307]) ).

thf(8543,plain,
    ! [SV1855: $i,SV1698: $i,SV1483: $i,SV1198: $i] :
      ( ( ( ~ ( c_in @ SV1198 @ ( c_union @ SV1483 @ SV1698 @ SV1855 ) @ SV1855 ) )
        = $true )
      | ( ( ( c_in @ SV1198 @ SV1698 @ SV1855 )
          | ( c_in @ SV1198 @ SV1483 @ SV1855 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8308]) ).

thf(8544,plain,
    ! [SV1856: $i,SV1699: $i,SV1199: $i] :
      ( ( ( ( c_union @ SV1199 @ SV1699 @ SV1856 )
          = c_emptyset )
        = $false )
      | ( ( SV1199 = c_emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8309]) ).

thf(8545,plain,
    ! [SV1857: $i,SV1484: $i,SV1200: $i] :
      ( ( ( ( c_union @ SV1200 @ SV1484 @ SV1857 )
          = c_emptyset )
        = $false )
      | ( ( SV1484 = c_emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8310]) ).

thf(8546,plain,
    ! [SV1700: $i,SV1485: $i,SV1202: $i] :
      ( ( ( c_in @ SV1202 @ SV1485 @ SV1700 )
        = $false )
      | ( ( ! [SY3317: $i] :
              ( ~ ( c_in @ SV1485 @ SY3317 @ ( tc_set @ SV1700 ) )
              | ( c_in @ SV1202 @ ( c_Union @ SY3317 @ SV1700 ) @ SV1700 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8311]) ).

thf(8547,plain,
    ! [SV1701: $i,SV1487: $i,SV1204: $i] :
      ( ( ( c_in @ SV1204 @ SV1487 @ SV1701 )
        = $false )
      | ( ( ! [SY3318: $i] : ( c_in @ SV1204 @ ( c_insert @ SY3318 @ SV1487 @ SV1701 ) @ SV1701 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8312]) ).

thf(8548,plain,
    ! [SV1858: $i,SV1703: $i,SV1489: $i,SV1206: $i] :
      ( ( ( ~ ( c_in @ SV1206 @ ( c_insert @ SV1489 @ SV1703 @ SV1858 ) @ SV1858 ) )
        = $true )
      | ( ( ( SV1206 = SV1489 )
          | ( c_in @ SV1206 @ SV1703 @ SV1858 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8313]) ).

thf(8549,plain,
    ! [SV1859: $i,SV1704: $i,SV1491: $i,SV1208: $i] :
      ( ( ( ( c_insert @ SV1208 @ SV1491 @ SV1704 )
         != ( c_insert @ SV1859 @ c_emptyset @ SV1704 ) )
        = $true )
      | ( ( SV1208 = SV1859 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8314]) ).

thf(8550,plain,
    ! [SV1860: $i,SV1705: $i,SV1492: $i,SV1209: $i] :
      ( ( ( ( c_insert @ SV1209 @ SV1492 @ SV1705 )
         != ( c_insert @ SV1860 @ c_emptyset @ SV1705 ) )
        = $true )
      | ( ( c_lessequals @ SV1492 @ ( c_insert @ SV1860 @ c_emptyset @ SV1705 ) @ ( tc_set @ SV1705 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8315]) ).

thf(8551,plain,
    ! [SV1706: $i,SV1493: $i,SV1210: $i] :
      ( ( ( c_lessequals @ SV1210 @ ( c_insert @ SV1493 @ c_emptyset @ SV1706 ) @ ( tc_set @ SV1706 ) )
        = $false )
      | ( ( ( c_insert @ SV1493 @ SV1210 @ SV1706 )
          = ( c_insert @ SV1493 @ c_emptyset @ SV1706 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8316]) ).

thf(8552,plain,
    ! [SV1952: $i,SV1707: $i,SV1494: $i,SV1211: $i] :
      ( ( ( ( c_insert @ SV1211 @ c_emptyset @ SV1494 )
         != ( c_insert @ SV1707 @ SV1952 @ SV1494 ) )
        = $true )
      | ( ( SV1707 = SV1211 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8317]) ).

thf(8553,plain,
    ! [SV1861: $i,SV1708: $i,SV1495: $i,SV1212: $i] :
      ( ( ( ( c_insert @ SV1212 @ c_emptyset @ SV1495 )
         != ( c_insert @ SV1708 @ SV1861 @ SV1495 ) )
        = $true )
      | ( ( c_lessequals @ SV1861 @ ( c_insert @ SV1212 @ c_emptyset @ SV1495 ) @ ( tc_set @ SV1495 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8318]) ).

thf(8554,plain,
    ! [SV1709: $i,SV1496: $i,SV1213: $i] :
      ( ( ( c_lessequals @ SV1213 @ ( c_insert @ SV1496 @ c_emptyset @ SV1709 ) @ ( tc_set @ SV1709 ) )
        = $false )
      | ( ( ( c_insert @ SV1496 @ c_emptyset @ SV1709 )
          = ( c_insert @ SV1496 @ SV1213 @ SV1709 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8319]) ).

thf(8555,plain,
    ! [SV1862: $i,SV1710: $i,SV1497: $i,SV1214: $i] :
      ( ( ( ( c_Sum__Type_OInl @ SV1214 @ SV1497 @ SV1710 )
         != ( c_Sum__Type_OInl @ SV1862 @ SV1497 @ SV1710 ) )
        = $true )
      | ( ( SV1214 = SV1862 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8320]) ).

thf(8556,plain,
    ! [SV1863: $i,SV1711: $i,SV1498: $i,SV1215: $i] :
      ( ( ( c_Sum__Type_OInl @ SV1215 @ SV1498 @ SV1711 )
        = ( c_Sum__Type_OInr @ SV1863 @ SV1711 @ SV1498 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8321]) ).

thf(8557,plain,
    ! [SV1864: $i,SV1712: $i,SV1499: $i,SV1216: $i] :
      ( ( ( ( c_Sum__Type_OInr @ SV1216 @ SV1499 @ SV1712 )
         != ( c_Sum__Type_OInr @ SV1864 @ SV1499 @ SV1712 ) )
        = $true )
      | ( ( SV1216 = SV1864 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8322]) ).

thf(8558,plain,
    ! [SV1865: $i,SV1713: $i,SV1500: $i,SV1217: $i] :
      ( ( ( c_Sum__Type_OInr @ SV1217 @ SV1500 @ SV1713 )
        = ( c_Sum__Type_OInl @ SV1865 @ SV1713 @ SV1500 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8323]) ).

thf(8559,plain,
    ! [SV1866: $i,SV1714: $i,SV1503: $i,SV1220: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1220 @ SV1503 @ SV1714 @ SV1714 ) @ SV1866 @ ( tc_prod @ SV1714 @ SV1714 ) ) @ SV1714 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ SV1866 @ SV1714 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8326]) ).

thf(8560,plain,
    ! [SV1867: $i,SV1715: $i,SV1504: $i,SV1221: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1221 @ SV1504 @ SV1715 @ SV1715 ) @ SV1867 @ ( tc_prod @ SV1715 @ SV1715 ) ) @ SV1715 ) )
        = $true )
      | ( ( ~ ( c_in @ ( c_Pair @ SV1504 @ SV1221 @ SV1715 @ SV1715 ) @ ( c_Transitive__Closure_Ortrancl @ SV1867 @ SV1715 ) @ ( tc_prod @ SV1715 @ SV1715 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8327]) ).

thf(8561,plain,
    ! [SV1222: $i,SV1505: $i,SV1953: $i] :
      ( ( ( ! [SY3448: $i] :
              ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1953 @ SY3448 @ SV1505 @ SV1505 ) @ SV1222 @ ( tc_prod @ SV1505 @ SV1505 ) ) @ SV1505 )
              | ( c_in @ ( c_Pair @ SY3448 @ SV1953 @ SV1505 @ SV1505 ) @ ( c_Transitive__Closure_Ortrancl @ SV1222 @ SV1505 ) @ ( tc_prod @ SV1505 @ SV1505 ) ) ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ SV1222 @ SV1505 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8328]) ).

thf(8562,plain,
    ! [SV1868: $i,SV1716: $i,SV1506: $i,SV1223: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1223 @ SV1506 @ SV1716 @ SV1716 ) @ SV1868 @ ( tc_prod @ SV1716 @ SV1716 ) ) @ SV1716 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV1868 @ SV1716 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8329]) ).

thf(8563,plain,
    ! [SV1869: $i,SV1717: $i,SV1507: $i,SV1224: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1224 @ SV1507 @ SV1717 @ SV1717 ) @ SV1869 @ ( tc_prod @ SV1717 @ SV1717 ) ) @ SV1717 ) )
        = $true )
      | ( ( ~ ( c_in @ ( c_Pair @ SV1507 @ SV1224 @ SV1717 @ SV1717 ) @ ( c_Transitive__Closure_Ortrancl @ SV1869 @ SV1717 ) @ ( tc_prod @ SV1717 @ SV1717 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8330]) ).

thf(8564,plain,
    ! [SV1225: $i,SV1508: $i,SV1954: $i] :
      ( ( ( ! [SY3449: $i] :
              ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1954 @ SY3449 @ SV1508 @ SV1508 ) @ SV1225 @ ( tc_prod @ SV1508 @ SV1508 ) ) @ SV1508 )
              | ( c_in @ ( c_Pair @ SY3449 @ SV1954 @ SV1508 @ SV1508 ) @ ( c_Transitive__Closure_Ortrancl @ SV1225 @ SV1508 ) @ ( tc_prod @ SV1508 @ SV1508 ) ) ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV1225 @ SV1508 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8331]) ).

thf(8565,plain,
    ! [SV1718: $i,SV1511: $i,SV1228: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ ( c_Message_Osynth @ SV1718 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ SV1718 @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OKey @ SV1228 ) @ SV1718 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8334]) ).

thf(8566,plain,
    ! [SV1719: $i,SV1512: $i,SV1229: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ( c_in @ SV1512 @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ SV1719 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8335]) ).

thf(8567,plain,
    ! [SV1513: $i,SV1230: $i] :
      ( ( ( c_in @ SV1230 @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ SV1513 @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OHash @ SV1230 ) @ ( c_Message_Osynth @ SV1513 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8336]) ).

thf(8568,plain,
    ! [SV1720: $i,SV1515: $i,SV1232: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1232 @ SV1515 ) @ ( c_Message_Oanalz @ SV1720 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1515 @ ( c_Message_Oanalz @ SV1720 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8338]) ).

thf(8569,plain,
    ! [SV1721: $i,SV1516: $i,SV1233: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1233 @ SV1516 ) @ ( c_Message_Oanalz @ SV1721 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1233 @ ( c_Message_Oanalz @ SV1721 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8339]) ).

thf(8570,plain,
    ! [SV1722: $i,SV1517: $i,SV1234: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1234 @ SV1517 ) @ ( c_Message_Oparts @ SV1722 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1517 @ ( c_Message_Oparts @ SV1722 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8340]) ).

thf(8571,plain,
    ! [SV1723: $i,SV1518: $i,SV1235: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1235 @ SV1518 ) @ ( c_Message_Oparts @ SV1723 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1235 @ ( c_Message_Oparts @ SV1723 ) @ tc_Message_Omsg )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8341]) ).

thf(8572,plain,
    ! [SV1724: $i,SV1519: $i,SV1236: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ( c_in @ SV1519 @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ SV1724 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8342]) ).

thf(8573,plain,
    ! [SV1725: $i,SV1520: $i,SV1237: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ( c_in @ SV1237 @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ SV1725 @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8343]) ).

thf(8574,plain,
    ! [SV1726: $i,SV1523: $i,SV1244: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1244 @ SV1523 ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1244 ) ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
          | ( c_in @ SV1523 @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8346]) ).

thf(8575,plain,
    ! [SV1727: $i,SV1526: $i,SV1247: $i] :
      ( ( ( c_in @ SV1247 @ ( c_Message_Oparts @ ( c_union @ SV1526 @ SV1727 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
        = $false )
      | ( ( ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1727 ) @ tc_Message_Omsg )
          | ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1526 ) @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8349]) ).

thf(8576,plain,
    ! [SV1955: $i,SV1728: $i,SV1532: $i,SV1253: $i] :
      ( ( ( ( c_Message_Omsg_OMPair @ SV1253 @ SV1532 )
         != ( c_Message_Omsg_OMPair @ SV1728 @ SV1955 ) )
        = $true )
      | ( ( SV1253 = SV1728 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8355]) ).

thf(8577,plain,
    ! [SV1870: $i,SV1729: $i,SV1533: $i,SV1254: $i] :
      ( ( ( ( c_Message_Omsg_OMPair @ SV1254 @ SV1533 )
         != ( c_Message_Omsg_OMPair @ SV1729 @ SV1870 ) )
        = $true )
      | ( ( SV1533 = SV1870 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8356]) ).

thf(8578,plain,
    ! [SV1956: $i,SV1730: $i,SV1534: $i,SV1255: $i] :
      ( ( ( ( c_Message_Omsg_OCrypt @ SV1255 @ SV1534 )
         != ( c_Message_Omsg_OCrypt @ SV1730 @ SV1956 ) )
        = $true )
      | ( ( SV1255 = SV1730 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8357]) ).

thf(8579,plain,
    ! [SV1871: $i,SV1731: $i,SV1535: $i,SV1256: $i] :
      ( ( ( ( c_Message_Omsg_OCrypt @ SV1256 @ SV1535 )
         != ( c_Message_Omsg_OCrypt @ SV1731 @ SV1871 ) )
        = $true )
      | ( ( SV1535 = SV1871 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8358]) ).

thf(8580,plain,
    ! [SV1261: $i,SV1539: $i,SV1957: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV1957 ) @ SV1539 @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OCrypt @ SV1957 @ SV1261 ) @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1261 @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8361]) ).

thf(8581,plain,
    ! [SV1264: $i,SV1542: $i,SV1958: $i] :
      ( ( ( ~ ( c_in @ SV1958 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_OMPair @ SV1958 @ SV1264 ) @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1264 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8364]) ).

thf(8582,plain,
    ! [SV1544: $i,SV1266: $i,SV1959: $i] :
      ( ( ( ! [SY3450: $i] :
              ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV1959 ) @ ( c_Message_Oanalz @ SY3450 ) @ ( tc_set @ tc_Message_Omsg ) )
              | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SV1959 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SY3450 @ SV1544 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
        = $true )
      | ( ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SV1544 ) @ ( tc_set @ tc_Message_Omsg ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8365]) ).

thf(8583,plain,
    ! [SV1732: $i,SV1546: $i,SV1268: $i,SV1: $i] :
      ( ( ( ( c_Datatype__Universe_OLeaf @ SV1 @ SV1268 @ SV1546 )
          = ( c_Datatype__Universe_OLeaf @ SV1732 @ SV1268 @ SV1546 ) )
        = $false )
      | ( ( SV1 = SV1732 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8367]) ).

thf(8584,plain,
    ! [SV1733: $i,SV1547: $i,SV1269: $i,SV2: $i] :
      ( ( ( ( c_Datatype__Universe_ONumb @ SV2 @ SV1269 @ SV1547 )
          = ( c_Datatype__Universe_ONumb @ SV1733 @ SV1269 @ SV1547 ) )
        = $false )
      | ( ( SV2 = SV1733 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8368]) ).

thf(8585,plain,
    ! [SV1872: $i,SV1734: $i,SV1548: $i,SV1270: $i,SV3: $i] :
      ( ( ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) ) ) )
        = $true )
      | ( ( SV3
          = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( c_Main_OdprodE__2 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ SV1734 @ SV1872 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( c_Main_OdprodE__4 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ SV1734 @ SV1872 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8369]) ).

thf(8586,plain,
    ! [SV1873: $i,SV1735: $i,SV1549: $i,SV1271: $i,SV4: $i] :
      ( ( ( ~ ( c_in @ SV4 @ ( c_Datatype__Universe_Odprod @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( c_Main_OdprodE__4 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) @ SV1549 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8370]) ).

thf(8587,plain,
    ! [SV1874: $i,SV1736: $i,SV1550: $i,SV1272: $i,SV5: $i] :
      ( ( ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odprod @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( c_Main_OdprodE__3 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) @ SV1272 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8371]) ).

thf(8588,plain,
    ! [SV1960: $i,SV1875: $i,SV1737: $i,SV1551: $i,SV1273: $i,SV6: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        | ! [SY3451: $i,SY3452: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1960 @ SY3451 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SY3452 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
            | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1960 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SY3451 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3452 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8372]) ).

thf(8589,plain,
    ! [SV1876: $i,SV1738: $i,SV1552: $i,SV1274: $i,SV7: $i] :
      ( ( ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1274 @ SV1552 @ SV1738 @ SV1876 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) ) )
        = $true )
      | ( ( ( SV7
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
          | ( SV7
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8373]) ).

thf(8590,plain,
    ! [SV1877: $i,SV1739: $i,SV1553: $i,SV1275: $i,SV8: $i] :
      ( ( ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1275 @ SV1553 @ SV1739 @ SV1877 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) ) )
        = $true )
      | ( ( ( SV8
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( c_Main_OdsumE__4 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) @ SV1553 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8374]) ).

thf(8591,plain,
    ! [SV1878: $i,SV1740: $i,SV1554: $i,SV1276: $i,SV9: $i] :
      ( ( ( ~ ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SV1276 @ SV1554 @ SV1740 @ SV1878 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) ) )
        = $true )
      | ( ( ( SV9
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( c_Main_OdsumE__2 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) @ SV1276 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8375]) ).

thf(8592,plain,
    ! [SV1879: $i,SV1741: $i,SV1555: $i,SV1277: $i,SV10: $i] :
      ( ( ( ~ ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SV1277 @ SV1555 @ SV1741 @ SV1879 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) ) )
        = $true )
      | ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__2 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1277 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__4 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1555 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8376]) ).

thf(8593,plain,
    ! [SV1880: $i,SV1742: $i,SV1556: $i,SV1278: $i,SV11: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV11 @ SV1278 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ SV1880 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) ) )
        = $true )
      | ( ( ! [SY3433: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SV1556 @ SV1742 ) @ ( c_Datatype__Universe_OIn0 @ SV1278 @ SV1556 @ SV1742 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1880 @ SY3433 @ SV1556 @ SV1742 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8377]) ).

thf(8594,plain,
    ! [SV1881: $i,SV1743: $i,SV1557: $i,SV1279: $i,SV12: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV12 @ SV1279 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ SV1881 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) ) )
        = $true )
      | ( ( ! [SY3434: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SV1557 @ SV1743 ) @ ( c_Datatype__Universe_OIn1 @ SV1279 @ SV1557 @ SV1743 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3434 @ SV1881 @ SV1557 @ SV1743 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8378]) ).

thf(8595,plain,
    ! [SV1882: $i,SV1744: $i,SV1558: $i,SV1280: $i,SV13: $i] :
      ( ( ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1280 @ SV1558 @ SV1744 @ SV1882 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1744 @ SV1882 ) ) ) )
        = $true )
      | ( ( SV13
          = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SV1882 ) @ ( c_Main_OuprodE__2 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SV1882 ) @ SV1744 @ SV1882 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8379]) ).

thf(8596,plain,
    ! [SV1883: $i,SV1745: $i,SV1559: $i,SV1281: $i,SV14: $i] :
      ( ( ( ~ ( c_in @ SV14 @ ( c_Datatype__Universe_Ouprod @ SV1281 @ SV1559 @ SV1745 @ SV1883 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SV1883 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Main_OuprodE__2 @ SV1281 @ SV1559 @ SV14 @ SV1745 @ SV1883 ) @ SV1559 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SV1883 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8380]) ).

thf(8597,plain,
    ! [SV1884: $i,SV1746: $i,SV1560: $i,SV1282: $i,SV15: $i] :
      ( ( ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ouprod @ SV1282 @ SV1560 @ SV1746 @ SV1884 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SV1884 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Main_OuprodE__1 @ SV1282 @ SV1560 @ SV15 @ SV1746 @ SV1884 ) @ SV1282 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SV1884 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8381]) ).

thf(8598,plain,
    ! [SV1747: $i,SV1561: $i,SV1283: $i,SV16: $i] :
      ( ( ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $false )
      | ( ( ! [SY3354: $i,SY3355: $i] :
              ( ~ ( c_in @ SY3354 @ SY3355 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
              | ( c_in @ ( c_Datatype__Universe_OScons @ SY3354 @ SV16 @ SV1561 @ SV1747 ) @ ( c_Datatype__Universe_Ouprod @ SY3355 @ SV1283 @ SV1561 @ SV1747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8382]) ).

thf(8599,plain,
    ! [SV1885: $i,SV1748: $i,SV1562: $i,SV1284: $i,SV17: $i] :
      ( ( ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1284 @ SV1562 @ SV1748 @ SV1885 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1748 @ SV1885 ) ) ) )
        = $true )
      | ( ( ( SV17
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1284 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) )
          | ( SV17
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1562 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8383]) ).

thf(8600,plain,
    ! [SV1886: $i,SV1749: $i,SV1563: $i,SV1285: $i,SV18: $i] :
      ( ( ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1285 @ SV1563 @ SV1749 @ SV1886 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) ) )
        = $true )
      | ( ( ( SV18
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1285 @ SV18 @ SV1749 @ SV1886 ) @ SV1749 @ SV1886 ) )
          | ( c_in @ ( c_Main_OusumE__2 @ SV1563 @ SV18 @ SV1749 @ SV1886 ) @ SV1563 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8384]) ).

thf(8601,plain,
    ! [SV1887: $i,SV1750: $i,SV1564: $i,SV1286: $i,SV19: $i] :
      ( ( ( ~ ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SV1286 @ SV1564 @ SV1750 @ SV1887 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) ) )
        = $true )
      | ( ( ( SV19
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1564 @ SV19 @ SV1750 @ SV1887 ) @ SV1750 @ SV1887 ) )
          | ( c_in @ ( c_Main_OusumE__1 @ SV1286 @ SV19 @ SV1750 @ SV1887 ) @ SV1286 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8385]) ).

thf(8602,plain,
    ! [SV1888: $i,SV1751: $i,SV1565: $i,SV1287: $i,SV20: $i] :
      ( ( ( ~ ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SV1287 @ SV1565 @ SV1751 @ SV1888 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) ) )
        = $true )
      | ( ( ( c_in @ ( c_Main_OusumE__1 @ SV1287 @ SV20 @ SV1751 @ SV1888 ) @ SV1287 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
          | ( c_in @ ( c_Main_OusumE__2 @ SV1565 @ SV20 @ SV1751 @ SV1888 ) @ SV1565 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8386]) ).

thf(8603,plain,
    ! [SV1752: $i,SV1566: $i,SV1288: $i,SV21: $i] :
      ( ( ( c_in @ SV21 @ SV1288 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) )
        = $false )
      | ( ( ! [SY3360: $i] : ( c_in @ ( c_Datatype__Universe_OIn0 @ SV21 @ SV1566 @ SV1752 ) @ ( c_Datatype__Universe_Ousum @ SV1288 @ SY3360 @ SV1566 @ SV1752 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8387]) ).

thf(8604,plain,
    ! [SV1753: $i,SV1567: $i,SV1289: $i,SV22: $i] :
      ( ( ( c_in @ SV22 @ SV1289 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) )
        = $false )
      | ( ( ! [SY3361: $i] : ( c_in @ ( c_Datatype__Universe_OIn1 @ SV22 @ SV1567 @ SV1753 ) @ ( c_Datatype__Universe_Ousum @ SY3361 @ SV1289 @ SV1567 @ SV1753 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8388]) ).

thf(8605,plain,
    ! [SV1297: $i,SV33: $i] :
      ( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) )
        = $false )
      | ( ( c_in @ ( c_Union @ SV33 @ SV1297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1297 ) )
        = $true )
      | ( ( c_in @ SV33 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1297 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8393]) ).

thf(8606,plain,
    ! [SV1300: $i,SV36: $i,SV1892: $i] :
      ( ( ( ~ ( c_in @ SV1892 @ SV36 @ SV1300 ) )
        = $true )
      | ( ( ! [SY3435: $i] :
              ( ~ ( c_in @ SY3435 @ SV36 @ SV1300 )
              | ( SV1892 = SY3435 ) ) )
        = $true )
      | ( ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8394]) ).

thf(8607,plain,
    ! [SV1308: $i,SV1568: $i,SV46: $i,SV1961: $i] :
      ( ( ( ~ ( c_in @ SV1961 @ ( c_List_Oset @ SV46 @ SV1568 ) @ SV1568 )
          | ( c_in @ SV1961 @ SV1308 @ SV1568 ) )
        = $true )
      | ( ( c_in @ SV46 @ ( c_List_Olists @ SV1308 @ SV1568 ) @ ( tc_List_Olist @ SV1568 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8395]) ).

thf(8608,plain,
    ! [SV1893: $i,SV1754: $i,SV1571: $i,SV1312: $i,SV50: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV50 @ SV1312 @ SV1571 ) @ SV1754 @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) @ ( c_List_Olistrel @ SV1893 @ SV1571 ) @ ( tc_prod @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) ) )
        = $true )
      | ( ( SV1754
          = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SV1893 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ ( c_Main_Olistrel__Cons1__2 @ SV1893 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ SV1571 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8397]) ).

thf(8609,plain,
    ! [SV1894: $i,SV1755: $i,SV1572: $i,SV1313: $i,SV51: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV51 @ SV1313 @ SV1572 ) @ SV1755 @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SV1894 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1313 @ ( c_Main_Olistrel__Cons1__2 @ SV1894 @ SV1755 @ SV51 @ SV1313 @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SV1894 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8398]) ).

thf(8610,plain,
    ! [SV1895: $i,SV1756: $i,SV1573: $i,SV1314: $i,SV52: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV52 @ SV1314 @ SV1573 ) @ SV1756 @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) @ ( c_List_Olistrel @ SV1895 @ SV1573 ) @ ( tc_prod @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV52 @ ( c_Main_Olistrel__Cons1__1 @ SV1895 @ SV1756 @ SV52 @ SV1314 @ SV1573 ) @ SV1573 @ SV1573 ) @ SV1895 @ ( tc_prod @ SV1573 @ SV1573 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8399]) ).

thf(8611,plain,
    ! [SV1896: $i,SV1757: $i,SV1574: $i,SV1315: $i,SV53: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV53 @ ( c_List_Olist_OCons @ SV1315 @ SV1574 @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) @ ( c_List_Olistrel @ SV1896 @ SV1757 ) @ ( tc_prod @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) ) )
        = $true )
      | ( ( SV53
          = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SV1896 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ ( c_Main_Olistrel__Cons2__2 @ SV1896 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ SV1757 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8400]) ).

thf(8612,plain,
    ! [SV1897: $i,SV1758: $i,SV1575: $i,SV1316: $i,SV54: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV54 @ ( c_List_Olist_OCons @ SV1316 @ SV1575 @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SV1897 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SV1897 @ SV54 @ SV1316 @ SV1575 @ SV1758 ) @ SV1575 @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SV1897 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8401]) ).

thf(8613,plain,
    ! [SV1898: $i,SV1759: $i,SV1576: $i,SV1317: $i,SV55: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV55 @ ( c_List_Olist_OCons @ SV1317 @ SV1576 @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) @ ( c_List_Olistrel @ SV1898 @ SV1759 ) @ ( tc_prod @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SV1898 @ SV55 @ SV1317 @ SV1576 @ SV1759 ) @ SV1317 @ SV1759 @ SV1759 ) @ SV1898 @ ( tc_prod @ SV1759 @ SV1759 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8402]) ).

thf(8614,plain,
    ! [SV1762: $i,SV1579: $i,SV1318: $i,SV58: $i] :
      ( ( ( c_in @ ( c_List_Olist_OCons @ SV58 @ SV1318 @ SV1579 ) @ ( c_List_Olists @ SV1762 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) )
        = $false )
      | ( ( c_in @ SV1318 @ ( c_List_Olists @ SV1762 @ SV1579 ) @ ( tc_List_Olist @ SV1579 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8405]) ).

thf(8615,plain,
    ! [SV1763: $i,SV1580: $i,SV1319: $i,SV59: $i] :
      ( ( ( c_in @ ( c_List_Olist_OCons @ SV59 @ SV1319 @ SV1580 ) @ ( c_List_Olists @ SV1763 @ SV1580 ) @ ( tc_List_Olist @ SV1580 ) )
        = $false )
      | ( ( c_in @ SV59 @ SV1763 @ SV1580 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8406]) ).

thf(8616,plain,
    ! [SV60: $i,SV1581: $i,SV1320: $i,SV1962: $i] :
      ( ( ( ~ ( c_in @ SV1962 @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) )
          | ( c_in @ ( c_List_Olist_OCons @ SV60 @ SV1962 @ SV1581 ) @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) ) )
        = $true )
      | ( ( c_in @ SV60 @ SV1320 @ SV1581 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8407]) ).

thf(8617,plain,
    ! [SV1765: $i,SV1582: $i,SV1324: $i,SV69: $i] :
      ( ( ( c_in @ SV69 @ ( c_Relation_ODomain @ SV1324 @ SV1582 @ SV1765 ) @ SV1582 )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV69 @ ( c_Main_ODomainE__1 @ SV69 @ SV1324 @ SV1582 @ SV1765 ) @ SV1582 @ SV1765 ) @ SV1324 @ ( tc_prod @ SV1582 @ SV1765 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8408]) ).

thf(8618,plain,
    ! [SV1899: $i,SV1766: $i,SV1583: $i,SV1325: $i,SV70: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1325 @ SV1583 @ SV1766 ) @ SV1899 @ ( tc_prod @ SV1583 @ SV1766 ) ) )
        = $true )
      | ( ( c_in @ SV70 @ ( c_Relation_ODomain @ SV1899 @ SV1583 @ SV1766 ) @ SV1583 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8409]) ).

thf(8619,plain,
    ! [SV1900: $i,SV1767: $i,SV1584: $i,SV1327: $i,SV72: $i] :
      ( ( ( ~ ( c_in @ SV72 @ ( c_Relation_OImage @ SV1327 @ SV1584 @ SV1767 @ SV1900 ) @ SV1900 ) )
        = $true )
      | ( ( c_in @ ( c_Main_OImageE__1 @ SV1584 @ SV72 @ SV1327 @ SV1767 @ SV1900 ) @ SV1584 @ SV1767 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8410]) ).

thf(8620,plain,
    ! [SV1901: $i,SV1768: $i,SV1585: $i,SV1328: $i,SV73: $i] :
      ( ( ( ~ ( c_in @ SV73 @ ( c_Relation_OImage @ SV1328 @ SV1585 @ SV1768 @ SV1901 ) @ SV1901 ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1585 @ SV73 @ SV1328 @ SV1768 @ SV1901 ) @ SV73 @ SV1768 @ SV1901 ) @ SV1328 @ ( tc_prod @ SV1768 @ SV1901 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8411]) ).

thf(8621,plain,
    ! [SV1769: $i,SV1586: $i,SV1329: $i,SV74: $i] :
      ( ( ( c_in @ SV74 @ SV1329 @ SV1586 )
        = $false )
      | ( ( ! [SY3371: $i,SY3372: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV74 @ SV1769 @ SV1586 @ SY3371 ) @ SY3372 @ ( tc_prod @ SV1586 @ SY3371 ) )
              | ( c_in @ SV1769 @ ( c_Relation_OImage @ SY3372 @ SV1329 @ SV1586 @ SY3371 ) @ SY3371 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8412]) ).

thf(8622,plain,
    ! [SV1770: $i,SV1587: $i,SV1330: $i,SV75: $i] :
      ( ( ( c_in @ SV75 @ ( c_Relation_ORange @ SV1330 @ SV1587 @ SV1770 ) @ SV1770 )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV75 @ SV1330 @ SV1770 @ SV1587 ) @ SV75 @ SV1587 @ SV1770 ) @ SV1330 @ ( tc_prod @ SV1587 @ SV1770 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8413]) ).

thf(8623,plain,
    ! [SV1902: $i,SV1771: $i,SV1588: $i,SV1331: $i,SV76: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV76 @ SV1331 @ SV1588 @ SV1771 ) @ SV1902 @ ( tc_prod @ SV1588 @ SV1771 ) ) )
        = $true )
      | ( ( c_in @ SV1331 @ ( c_Relation_ORange @ SV1902 @ SV1588 @ SV1771 ) @ SV1771 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8414]) ).

thf(8624,plain,
    ! [SV1772: $i,SV1589: $i,SV1332: $i,SV77: $i] :
      ( ( ( c_in @ SV77 @ ( c_Relation_Oconverse @ SV1332 @ SV1589 @ SV1772 ) @ ( tc_prod @ SV1772 @ SV1589 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1332 @ SV77 @ SV1589 @ SV1772 ) @ ( c_Main_OconverseE__2 @ SV1332 @ SV77 @ SV1589 @ SV1772 ) @ SV1589 @ SV1772 ) @ SV1332 @ ( tc_prod @ SV1589 @ SV1772 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8415]) ).

thf(8625,plain,
    ! [SV1773: $i,SV1590: $i,SV1333: $i,SV78: $i] :
      ( ( ( c_in @ SV78 @ ( c_Relation_Oconverse @ SV1333 @ SV1590 @ SV1773 ) @ ( tc_prod @ SV1773 @ SV1590 ) )
        = $false )
      | ( ( SV78
          = ( c_Pair @ ( c_Main_OconverseE__2 @ SV1333 @ SV78 @ SV1590 @ SV1773 ) @ ( c_Main_OconverseE__1 @ SV1333 @ SV78 @ SV1590 @ SV1773 ) @ SV1773 @ SV1590 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8416]) ).

thf(8626,plain,
    ! [SV1963: $i,SV1903: $i,SV1774: $i,SV1594: $i,SV1337: $i,SV82: $i] :
      ( ( ~ ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SV1337 @ SV1594 @ SV1774 @ SV1903 @ SV1963 ) @ ( tc_prod @ SV1963 @ SV1903 ) )
        | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SV1963 ) @ ( c_Main_Orel__compE__3 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SV1963 ) @ SV1774 @ SV1903 ) @ SV1337 @ ( tc_prod @ SV1774 @ SV1903 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8420]) ).

thf(8627,plain,
    ! [SV1964: $i,SV1904: $i,SV1775: $i,SV1595: $i,SV1338: $i,SV83: $i] :
      ( ( ~ ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SV1338 @ SV1595 @ SV1775 @ SV1904 @ SV1964 ) @ ( tc_prod @ SV1964 @ SV1904 ) )
        | ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SV1964 ) @ ( c_Main_Orel__compE__2 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SV1964 ) @ SV1964 @ SV1775 ) @ SV1595 @ ( tc_prod @ SV1964 @ SV1775 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8421]) ).

thf(8628,plain,
    ! [SV1965: $i,SV1905: $i,SV1776: $i,SV1596: $i,SV1339: $i,SV84: $i] :
      ( ( ~ ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SV1339 @ SV1596 @ SV1776 @ SV1905 @ SV1965 ) @ ( tc_prod @ SV1965 @ SV1905 ) )
        | ( SV84
          = ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SV1965 ) @ ( c_Main_Orel__compE__3 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SV1965 ) @ SV1965 @ SV1905 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8422]) ).

thf(8629,plain,
    ! [SV1966: $i,SV1906: $i,SV1777: $i,SV1597: $i,SV1340: $i,SV85: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) )
        | ! [SY3453: $i,SY3454: $i] :
            ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV85 @ SY3453 @ SV1597 ) @ SY3454 @ ( tc_prod @ SY3453 @ SV1597 ) )
            | ( c_in @ ( c_Pair @ SV1966 @ SV1340 @ SY3453 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SY3454 @ SV1597 @ SV1777 @ SY3453 ) @ ( tc_prod @ SY3453 @ SV1777 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8423]) ).

thf(8630,plain,
    ! [SV1602: $i,SV102: $i,SV1355: $i] :
      ( ( ( c_lessequals @ SV1355 @ SV102 @ ( tc_set @ SV1602 ) )
        = $false )
      | ( ( c_less @ SV102 @ SV1355 @ ( tc_set @ SV1602 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8427]) ).

thf(8631,plain,
    ! [SV1604: $i,SV1357: $i,SV104: $i] :
      ( ( ( SV104 = SV1357 )
        = $true )
      | ( ( c_less @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) )
        = $true )
      | ( ( c_lessequals @ SV104 @ SV1357 @ ( tc_set @ SV1604 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8429]) ).

thf(8632,plain,
    ! [SV108: $i,SV1606: $i,SV1967: $i,SV1361: $i] :
      ( ( ( ~ ( c_lessequals @ SV1361 @ SV1967 @ ( tc_set @ SV1606 ) )
          | ( c_in @ SV108 @ SV1967 @ SV1606 ) )
        = $true )
      | ( ( c_in @ SV108 @ SV1361 @ SV1606 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8432]) ).

thf(8633,plain,
    ! [SV1609: $i,SV111: $i,SV1364: $i] :
      ( ( ( ~ ( c_lessequals @ SV1364 @ SV111 @ ( tc_set @ SV1609 ) ) )
        = $true )
      | ( ( SV1364 = SV111 )
        = $true )
      | ( ( c_lessequals @ SV111 @ SV1364 @ ( tc_set @ SV1609 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8434]) ).

thf(8634,plain,
    ! [SV1366: $i,SV1968: $i,SV1610: $i,SV113: $i] :
      ( ( ( ! [SY3455: $i] : ( c_in @ ( c_Sum__Type_OInl @ SV113 @ SV1610 @ SV1968 ) @ ( c_Sum__Type_OPlus @ SV1366 @ SY3455 @ SV1610 @ SV1968 ) @ ( tc_sum @ SV1610 @ SV1968 ) ) )
        = $true )
      | ( ( c_in @ SV113 @ SV1366 @ SV1610 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8435]) ).

thf(8635,plain,
    ! [SV1367: $i,SV1969: $i,SV1611: $i,SV114: $i] :
      ( ( ( ! [SY3456: $i] : ( c_in @ ( c_Sum__Type_OInr @ SV114 @ SV1611 @ SV1969 ) @ ( c_Sum__Type_OPlus @ SY3456 @ SV1367 @ SV1969 @ SV1611 ) @ ( tc_sum @ SV1969 @ SV1611 ) ) )
        = $true )
      | ( ( c_in @ SV114 @ SV1367 @ SV1611 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8436]) ).

thf(8636,plain,
    ! [SV1907: $i,SV1779: $i,SV1612: $i,SV1368: $i,SV115: $i] :
      ( ( ( ~ ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SV1368 @ SV1612 @ SV1779 @ SV1907 ) @ ( tc_sum @ SV1779 @ SV1907 ) ) )
        = $true )
      | ( ( ( SV115
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1368 @ SV115 @ SV1779 @ SV1907 ) @ SV1779 @ SV1907 ) )
          | ( SV115
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1612 @ SV115 @ SV1907 @ SV1779 ) @ SV1907 @ SV1779 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8437]) ).

thf(8637,plain,
    ! [SV1908: $i,SV1780: $i,SV1613: $i,SV1369: $i,SV116: $i] :
      ( ( ( ~ ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SV1369 @ SV1613 @ SV1780 @ SV1908 ) @ ( tc_sum @ SV1780 @ SV1908 ) ) )
        = $true )
      | ( ( ( SV116
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1369 @ SV116 @ SV1780 @ SV1908 ) @ SV1780 @ SV1908 ) )
          | ( c_in @ ( c_Main_OPlusE__2 @ SV1613 @ SV116 @ SV1908 @ SV1780 ) @ SV1613 @ SV1908 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8438]) ).

thf(8638,plain,
    ! [SV1909: $i,SV1781: $i,SV1614: $i,SV1370: $i,SV117: $i] :
      ( ( ( ~ ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SV1370 @ SV1614 @ SV1781 @ SV1909 ) @ ( tc_sum @ SV1781 @ SV1909 ) ) )
        = $true )
      | ( ( ( SV117
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1614 @ SV117 @ SV1909 @ SV1781 ) @ SV1909 @ SV1781 ) )
          | ( c_in @ ( c_Main_OPlusE__1 @ SV1370 @ SV117 @ SV1781 @ SV1909 ) @ SV1370 @ SV1781 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8439]) ).

thf(8639,plain,
    ! [SV1910: $i,SV1782: $i,SV1615: $i,SV1371: $i,SV118: $i] :
      ( ( ( ~ ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SV1371 @ SV1615 @ SV1782 @ SV1910 ) @ ( tc_sum @ SV1782 @ SV1910 ) ) )
        = $true )
      | ( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1371 @ SV118 @ SV1782 @ SV1910 ) @ SV1371 @ SV1782 )
          | ( c_in @ ( c_Main_OPlusE__2 @ SV1615 @ SV118 @ SV1910 @ SV1782 ) @ SV1615 @ SV1910 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8440]) ).

thf(8640,plain,
    ! [SV1783: $i,SV1618: $i,SV1374: $i,SV121: $i] :
      ( ( ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ SV1783 @ ( tc_prod @ SV1618 @ SV1618 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV121 @ SV1374 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SV1783 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8442]) ).

thf(8641,plain,
    ! [SV1784: $i,SV1619: $i,SV1375: $i,SV122: $i] :
      ( ( ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Otrancl @ SV1784 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV122 @ SV1375 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1784 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8443]) ).

thf(8642,plain,
    ! [SV1376: $i,SV124: $i,SV1970: $i,SV1911: $i] :
      ( ( ( ~ ( c_Relation_Otrans @ SV1911 @ SV1970 )
          | ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1911 @ SV124 @ SV1970 @ SV1376 ) @ ( tc_prod @ SV1970 @ SV1376 ) ) )
        = $true )
      | ( ( c_Relation_Otrans @ SV124 @ SV1376 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8444]) ).

thf(8643,plain,
    ! [SV1377: $i,SV125: $i,SV1971: $i,SV1912: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1912 @ SV1971 )
          | ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1912 @ SV125 @ SV1971 @ SV1377 ) @ ( tc_prod @ SV1971 @ SV1377 ) ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV125 @ SV1377 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8445]) ).

thf(8644,plain,
    ! [SV1378: $i,SV127: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV127 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ SV1378 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV127 @ SV1378 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8446]) ).

thf(8645,plain,
    ! [SV1380: $i,SV129: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV129 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ SV1380 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV129 @ SV1380 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8447]) ).

thf(8646,plain,
    ! [SV1381: $i,SV135: $i] :
      ( ( ( class_Finite__Set_Ofinite @ SV135 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ SV1381 )
        = $false )
      | ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV135 @ SV1381 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8448]) ).

thf(8647,plain,
    ! [SV1785: $i,SV1624: $i,SV1387: $i,SV1050: $i] :
      ( ( ( ( c_Datatype__Universe_OAtom @ SV1050 @ SV1387 @ SV1624 )
          = ( c_Datatype__Universe_OAtom @ SV1785 @ SV1387 @ SV1624 ) )
        = $false )
      | ( ( SV1050 = SV1785 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8451]) ).

thf(8648,plain,
    ! [SV1913: $i,SV1786: $i,SV1625: $i,SV1388: $i,SV1051: $i] :
      ( ( ( c_Datatype__Universe_OAtom @ SV1051 @ SV1388 @ SV1625 )
        = ( c_Datatype__Universe_OScons @ SV1786 @ SV1913 @ SV1388 @ SV1625 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8452]) ).

thf(8649,plain,
    ! [SV1787: $i,SV1626: $i,SV1389: $i,SV1052: $i] :
      ( ( ( ( c_Datatype__Universe_OIn0 @ SV1052 @ SV1389 @ SV1626 )
          = ( c_Datatype__Universe_OIn0 @ SV1787 @ SV1389 @ SV1626 ) )
        = $false )
      | ( ( SV1052 = SV1787 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8453]) ).

thf(8650,plain,
    ! [SV1789: $i,SV1628: $i,SV1391: $i,SV1054: $i] :
      ( ( ( ( c_Datatype__Universe_OIn1 @ SV1054 @ SV1391 @ SV1628 )
          = ( c_Datatype__Universe_OIn1 @ SV1789 @ SV1391 @ SV1628 ) )
        = $false )
      | ( ( SV1054 = SV1789 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8455]) ).

thf(8651,plain,
    ! [SV1914: $i,SV1792: $i,SV1631: $i,SV1394: $i,SV1057: $i] :
      ( ( ( c_Datatype__Universe_OLeaf @ SV1057 @ SV1394 @ SV1631 )
        = ( c_Datatype__Universe_OScons @ SV1792 @ SV1914 @ SV1394 @ SV1631 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8458]) ).

thf(8652,plain,
    ! [SV1915: $i,SV1794: $i,SV1633: $i,SV1396: $i,SV1059: $i] :
      ( ( ( c_Datatype__Universe_ONumb @ SV1059 @ SV1396 @ SV1633 )
        = ( c_Datatype__Universe_OScons @ SV1794 @ SV1915 @ SV1396 @ SV1633 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8460]) ).

thf(8653,plain,
    ! [SV1916: $i,SV1795: $i,SV1634: $i,SV1397: $i,SV1060: $i] :
      ( ( ( ! [SY3444: $i] :
              ( ( c_Datatype__Universe_OScons @ SV1060 @ SV1397 @ SV1634 @ SV1795 )
             != ( c_Datatype__Universe_OScons @ SV1916 @ SY3444 @ SV1634 @ SV1795 ) ) )
        = $true )
      | ( ( SV1060 = SV1916 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8461]) ).

thf(8654,plain,
    ! [SV1972: $i,SV1917: $i,SV1796: $i,SV1635: $i,SV1398: $i,SV1061: $i] :
      ( ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SV1398 @ SV1635 @ SV1796 )
         != ( c_Datatype__Universe_OScons @ SV1917 @ SV1972 @ SV1635 @ SV1796 ) )
        | ( SV1398 = SV1972 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8462]) ).

thf(8655,plain,
    ! [SV1918: $i,SV1797: $i,SV1636: $i,SV1399: $i,SV1062: $i] :
      ( ( ( c_Datatype__Universe_OScons @ SV1062 @ SV1399 @ SV1636 @ SV1797 )
        = ( c_Datatype__Universe_OAtom @ SV1918 @ SV1636 @ SV1797 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8463]) ).

thf(8656,plain,
    ! [SV1919: $i,SV1798: $i,SV1637: $i,SV1400: $i,SV1063: $i] :
      ( ( ( c_Datatype__Universe_OScons @ SV1063 @ SV1400 @ SV1637 @ SV1798 )
        = ( c_Datatype__Universe_OLeaf @ SV1919 @ SV1637 @ SV1798 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8464]) ).

thf(8657,plain,
    ! [SV1920: $i,SV1799: $i,SV1638: $i,SV1401: $i,SV1064: $i] :
      ( ( ( c_Datatype__Universe_OScons @ SV1064 @ SV1401 @ SV1638 @ SV1799 )
        = ( c_Datatype__Universe_ONumb @ SV1920 @ SV1638 @ SV1799 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8465]) ).

thf(8658,plain,
    ! [SV1802: $i,SV1641: $i,SV1404: $i,SV1070: $i] :
      ( ( ( c_in @ ( c_minus @ SV1070 @ ( c_insert @ SV1404 @ SV1641 @ SV1802 ) @ ( tc_set @ SV1802 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1802 ) )
        = $false )
      | ( ( c_in @ ( c_minus @ SV1070 @ SV1641 @ ( tc_set @ SV1802 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1802 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8468]) ).

thf(8659,plain,
    ! [SV1642: $i,SV1405: $i,SV1973: $i,SV1071: $i] :
      ( ( ( c_in @ ( c_minus @ SV1071 @ ( c_insert @ SV1973 @ SV1405 @ SV1642 ) @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) )
        = $true )
      | ( ( c_in @ ( c_minus @ SV1071 @ SV1405 @ ( tc_set @ SV1642 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1642 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8469]) ).

thf(8660,plain,
    ! [SV1076: $i,SV1410: $i,SV1921: $i] :
      ( ( ( ~ ( c_in @ SV1921 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) ) )
        = $true )
      | ( ( c_in @ ( c_union @ SV1921 @ SV1076 @ SV1410 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        = $true )
      | ( ( c_in @ SV1076 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8472]) ).

thf(8661,plain,
    ! [SV1415: $i,SV1922: $i,SV1081: $i] :
      ( ( ( ~ ( c_Divides_Oop_Advd @ SV1081 @ SV1922 @ tc_nat ) )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1081 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1922 @ SV1415 @ tc_nat @ tc_nat ) ) @ tc_nat )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1081 @ SV1415 @ tc_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8477]) ).

thf(8662,plain,
    ! [SV1974: $i,SV1806: $i,SV1652: $i,SV1424: $i,SV1095: $i] :
      ( ( ( ( c_append @ SV1095 @ ( c_List_Olist_OCons @ SV1424 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 )
         != ( c_append @ SV1806 @ ( c_List_Olist_OCons @ SV1974 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 ) )
        = $true )
      | ( ( SV1095 = SV1806 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8480]) ).

thf(8663,plain,
    ! [SV1923: $i,SV1807: $i,SV1653: $i,SV1425: $i,SV1096: $i] :
      ( ( ( ( c_append @ SV1096 @ ( c_List_Olist_OCons @ SV1425 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 )
         != ( c_append @ SV1807 @ ( c_List_Olist_OCons @ SV1923 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 ) )
        = $true )
      | ( ( SV1425 = SV1923 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8481]) ).

thf(8664,plain,
    ! [SV1808: $i,SV1654: $i,SV1426: $i,SV1097: $i] :
      ( ( ( c_in @ ( c_append @ SV1097 @ SV1426 @ SV1654 ) @ ( c_List_Olists @ SV1808 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) )
        = $false )
      | ( ( c_in @ SV1097 @ ( c_List_Olists @ SV1808 @ SV1654 ) @ ( tc_List_Olist @ SV1654 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8482]) ).

thf(8665,plain,
    ! [SV1809: $i,SV1655: $i,SV1427: $i,SV1098: $i] :
      ( ( ( c_in @ ( c_append @ SV1098 @ SV1427 @ SV1655 ) @ ( c_List_Olists @ SV1809 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) )
        = $false )
      | ( ( c_in @ SV1427 @ ( c_List_Olists @ SV1809 @ SV1655 ) @ ( tc_List_Olist @ SV1655 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8483]) ).

thf(8666,plain,
    ! [SV1099: $i,SV1656: $i,SV1428: $i,SV1975: $i] :
      ( ( ( ~ ( c_in @ SV1975 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
          | ( c_in @ ( c_append @ SV1975 @ SV1099 @ SV1656 ) @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) ) )
        = $true )
      | ( ( c_in @ SV1099 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8484]) ).

thf(8667,plain,
    ! [SV1812: $i,SV1658: $i,SV1430: $i,SV1103: $i] :
      ( ( ( ( c_append @ SV1103 @ SV1430 @ SV1658 )
          = ( c_append @ SV1812 @ SV1430 @ SV1658 ) )
        = $false )
      | ( ( SV1103 = SV1812 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8487]) ).

thf(8668,plain,
    ! [SV1924: $i,SV1660: $i,SV1434: $i,SV1108: $i] :
      ( ( ( ( c_List_Ochar_OChar @ SV1108 @ SV1434 )
          = ( c_List_Ochar_OChar @ SV1660 @ SV1924 ) )
        = $false )
      | ( ( SV1108 = SV1660 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8490]) ).

thf(8669,plain,
    ! [SV1815: $i,SV1661: $i,SV1435: $i,SV1109: $i] :
      ( ( ( ( c_List_Ochar_OChar @ SV1109 @ SV1435 )
          = ( c_List_Ochar_OChar @ SV1661 @ SV1815 ) )
        = $false )
      | ( ( SV1435 = SV1815 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8491]) ).

thf(8670,plain,
    ! [SV1976: $i,SV1816: $i,SV1666: $i,SV1440: $i,SV1118: $i] :
      ( ( ( ( c_List_Olist_OCons @ SV1118 @ SV1440 @ SV1666 )
         != ( c_List_Olist_OCons @ SV1816 @ SV1976 @ SV1666 ) )
        = $true )
      | ( ( SV1118 = SV1816 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8492]) ).

thf(8671,plain,
    ! [SV1925: $i,SV1817: $i,SV1667: $i,SV1441: $i,SV1119: $i] :
      ( ( ( ( c_List_Olist_OCons @ SV1119 @ SV1441 @ SV1667 )
         != ( c_List_Olist_OCons @ SV1817 @ SV1925 @ SV1667 ) )
        = $true )
      | ( ( SV1441 = SV1925 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8493]) ).

thf(8672,plain,
    ! [SV1818: $i,SV1668: $i,SV1442: $i,SV1120: $i] :
      ( ( ( ( c_List_Orev @ SV1120 @ SV1442 )
          = ( c_List_Olist_OCons @ SV1668 @ SV1818 @ SV1442 ) )
        = $false )
      | ( ( SV1120
          = ( c_append @ ( c_List_Orev @ SV1818 @ SV1442 ) @ ( c_List_Olist_OCons @ SV1668 @ c_List_Olist_ONil @ SV1442 ) @ SV1442 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8494]) ).

thf(8673,plain,
    ! [SV1819: $i,SV1672: $i,SV1445: $i,SV1125: $i] :
      ( ( ( ( c_append @ SV1125 @ SV1445 @ SV1672 )
          = ( c_append @ SV1125 @ SV1819 @ SV1672 ) )
        = $false )
      | ( ( SV1445 = SV1819 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8496]) ).

thf(8674,plain,
    ! [SV1926: $i,SV1825: $i,SV1676: $i,SV1459: $i,SV1154: $i] :
      ( ( ( ! [SY3446: $i] :
              ( ( c_Pair @ SV1154 @ SV1459 @ SV1676 @ SV1825 )
             != ( c_Pair @ SV1926 @ SY3446 @ SV1676 @ SV1825 ) ) )
        = $true )
      | ( ( SV1154 = SV1926 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8501]) ).

thf(8675,plain,
    ! [SV1977: $i,SV1927: $i,SV1826: $i,SV1677: $i,SV1460: $i,SV1155: $i] :
      ( ( ( ( c_Pair @ SV1155 @ SV1460 @ SV1677 @ SV1826 )
         != ( c_Pair @ SV1927 @ SV1977 @ SV1677 @ SV1826 ) )
        | ( SV1460 = SV1977 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8502]) ).

thf(8676,plain,
    ! [SV1928: $i,SV1827: $i,SV1678: $i,SV1462: $i,SV1157: $i] :
      ( ( ( ~ ( c_in @ SV1157 @ ( c_Relation_OImage @ SV1462 @ ( c_insert @ SV1678 @ c_emptyset @ SV1827 ) @ SV1827 @ SV1928 ) @ SV1928 ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1678 @ SV1157 @ SV1827 @ SV1928 ) @ SV1462 @ ( tc_prod @ SV1827 @ SV1928 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8503]) ).

thf(8677,plain,
    ! [SV1929: $i,SV1828: $i,SV1679: $i,SV1463: $i,SV1158: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1158 @ SV1463 @ SV1679 @ SV1828 ) @ SV1929 @ ( tc_prod @ SV1679 @ SV1828 ) ) )
        = $true )
      | ( ( c_in @ SV1463 @ ( c_Relation_OImage @ SV1929 @ ( c_insert @ SV1158 @ c_emptyset @ SV1679 ) @ SV1679 @ SV1828 ) @ SV1828 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8504]) ).

thf(8678,plain,
    ! [SV1930: $i,SV1829: $i,SV1680: $i,SV1464: $i,SV1159: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1159 @ SV1464 @ SV1680 @ SV1829 ) @ ( c_Relation_Oconverse @ SV1930 @ SV1829 @ SV1680 ) @ ( tc_prod @ SV1680 @ SV1829 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1464 @ SV1159 @ SV1829 @ SV1680 ) @ SV1930 @ ( tc_prod @ SV1829 @ SV1680 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8505]) ).

thf(8679,plain,
    ! [SV1931: $i,SV1830: $i,SV1681: $i,SV1465: $i,SV1160: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1160 @ SV1465 @ SV1681 @ SV1830 ) @ SV1931 @ ( tc_prod @ SV1681 @ SV1830 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1465 @ SV1160 @ SV1830 @ SV1681 ) @ ( c_Relation_Oconverse @ SV1931 @ SV1681 @ SV1830 ) @ ( tc_prod @ SV1830 @ SV1681 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8506]) ).

thf(8680,plain,
    ! [SV1932: $i,SV1162: $i,SV1832: $i] :
      ( ( ( ( c_SetInterval_OatLeast @ SV1832 @ SV1162 )
         != ( c_SetInterval_OatLeast @ SV1932 @ SV1162 ) )
        = $true )
      | ( ( SV1832 = SV1932 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1162 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8508]) ).

thf(8681,plain,
    ! [SV1163: $i,SV1933: $i,SV1833: $i] :
      ( ( ( ~ ( c_in @ SV1833 @ ( c_SetInterval_OatLeast @ SV1933 @ SV1163 ) @ SV1163 ) )
        = $true )
      | ( ( c_lessequals @ SV1933 @ SV1833 @ SV1163 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1163 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8509]) ).

thf(8682,plain,
    ! [SV1164: $i,SV1934: $i,SV1834: $i] :
      ( ( ( ~ ( c_lessequals @ SV1834 @ SV1934 @ SV1164 ) )
        = $true )
      | ( ( c_in @ SV1934 @ ( c_SetInterval_OatLeast @ SV1834 @ SV1164 ) @ SV1164 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1164 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8510]) ).

thf(8683,plain,
    ! [SV1935: $i,SV1165: $i,SV1835: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1835 @ SV1165 ) @ ( c_SetInterval_OatLeast @ SV1935 @ SV1165 ) @ ( tc_set @ SV1165 ) ) )
        = $true )
      | ( ( c_lessequals @ SV1935 @ SV1835 @ SV1165 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1165 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8511]) ).

thf(8684,plain,
    ! [SV1166: $i,SV1936: $i,SV1836: $i] :
      ( ( ( ~ ( c_lessequals @ SV1836 @ SV1936 @ SV1166 ) )
        = $true )
      | ( ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1936 @ SV1166 ) @ ( c_SetInterval_OatLeast @ SV1836 @ SV1166 ) @ ( tc_set @ SV1166 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1166 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8512]) ).

thf(8685,plain,
    ! [SV1937: $i,SV1167: $i,SV1837: $i] :
      ( ( ( ( c_SetInterval_OatMost @ SV1837 @ SV1167 )
         != ( c_SetInterval_OatMost @ SV1937 @ SV1167 ) )
        = $true )
      | ( ( SV1837 = SV1937 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1167 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8513]) ).

thf(8686,plain,
    ! [SV1168: $i,SV1938: $i,SV1838: $i] :
      ( ( ( ~ ( c_in @ SV1838 @ ( c_SetInterval_OatMost @ SV1938 @ SV1168 ) @ SV1168 ) )
        = $true )
      | ( ( c_lessequals @ SV1838 @ SV1938 @ SV1168 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1168 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8514]) ).

thf(8687,plain,
    ! [SV1169: $i,SV1939: $i,SV1839: $i] :
      ( ( ( ~ ( c_lessequals @ SV1839 @ SV1939 @ SV1169 ) )
        = $true )
      | ( ( c_in @ SV1839 @ ( c_SetInterval_OatMost @ SV1939 @ SV1169 ) @ SV1169 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1169 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8515]) ).

thf(8688,plain,
    ! [SV1940: $i,SV1170: $i,SV1840: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1840 @ SV1170 ) @ ( c_SetInterval_OatMost @ SV1940 @ SV1170 ) @ ( tc_set @ SV1170 ) ) )
        = $true )
      | ( ( c_lessequals @ SV1840 @ SV1940 @ SV1170 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1170 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8516]) ).

thf(8689,plain,
    ! [SV1171: $i,SV1941: $i,SV1841: $i] :
      ( ( ( ~ ( c_lessequals @ SV1841 @ SV1941 @ SV1171 ) )
        = $true )
      | ( ( c_lessequals @ ( c_SetInterval_OatMost @ SV1841 @ SV1171 ) @ ( c_SetInterval_OatMost @ SV1941 @ SV1171 ) @ ( tc_set @ SV1171 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1171 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8517]) ).

thf(8690,plain,
    ! [SV1942: $i,SV1172: $i,SV1842: $i] :
      ( ( ( ( c_SetInterval_OgreaterThan @ SV1842 @ SV1172 )
         != ( c_SetInterval_OgreaterThan @ SV1942 @ SV1172 ) )
        = $true )
      | ( ( SV1842 = SV1942 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1172 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8518]) ).

thf(8691,plain,
    ! [SV1173: $i,SV1943: $i,SV1843: $i] :
      ( ( ( ~ ( c_in @ SV1843 @ ( c_SetInterval_OgreaterThan @ SV1943 @ SV1173 ) @ SV1173 ) )
        = $true )
      | ( ( c_less @ SV1943 @ SV1843 @ SV1173 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1173 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8519]) ).

thf(8692,plain,
    ! [SV1174: $i,SV1944: $i,SV1844: $i] :
      ( ( ( ~ ( c_less @ SV1844 @ SV1944 @ SV1174 ) )
        = $true )
      | ( ( c_in @ SV1944 @ ( c_SetInterval_OgreaterThan @ SV1844 @ SV1174 ) @ SV1174 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1174 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8520]) ).

thf(8693,plain,
    ! [SV1945: $i,SV1175: $i,SV1845: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1845 @ SV1175 ) @ ( c_SetInterval_OgreaterThan @ SV1945 @ SV1175 ) @ ( tc_set @ SV1175 ) ) )
        = $true )
      | ( ( c_lessequals @ SV1945 @ SV1845 @ SV1175 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1175 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8521]) ).

thf(8694,plain,
    ! [SV1176: $i,SV1946: $i,SV1846: $i] :
      ( ( ( ~ ( c_lessequals @ SV1846 @ SV1946 @ SV1176 ) )
        = $true )
      | ( ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1946 @ SV1176 ) @ ( c_SetInterval_OgreaterThan @ SV1846 @ SV1176 ) @ ( tc_set @ SV1176 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1176 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8522]) ).

thf(8695,plain,
    ! [SV1947: $i,SV1177: $i,SV1847: $i] :
      ( ( ( ( c_SetInterval_OlessThan @ SV1847 @ SV1177 )
         != ( c_SetInterval_OlessThan @ SV1947 @ SV1177 ) )
        = $true )
      | ( ( SV1847 = SV1947 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1177 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8523]) ).

thf(8696,plain,
    ! [SV1178: $i,SV1948: $i,SV1848: $i] :
      ( ( ( ~ ( c_in @ SV1848 @ ( c_SetInterval_OlessThan @ SV1948 @ SV1178 ) @ SV1178 ) )
        = $true )
      | ( ( c_less @ SV1848 @ SV1948 @ SV1178 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1178 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8524]) ).

thf(8697,plain,
    ! [SV1179: $i,SV1949: $i,SV1849: $i] :
      ( ( ( ~ ( c_less @ SV1849 @ SV1949 @ SV1179 ) )
        = $true )
      | ( ( c_in @ SV1849 @ ( c_SetInterval_OlessThan @ SV1949 @ SV1179 ) @ SV1179 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1179 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8525]) ).

thf(8698,plain,
    ! [SV1950: $i,SV1180: $i,SV1850: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1850 @ SV1180 ) @ ( c_SetInterval_OlessThan @ SV1950 @ SV1180 ) @ ( tc_set @ SV1180 ) ) )
        = $true )
      | ( ( c_lessequals @ SV1850 @ SV1950 @ SV1180 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1180 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8526]) ).

thf(8699,plain,
    ! [SV1181: $i,SV1951: $i,SV1851: $i] :
      ( ( ( ~ ( c_lessequals @ SV1851 @ SV1951 @ SV1181 ) )
        = $true )
      | ( ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1851 @ SV1181 ) @ ( c_SetInterval_OlessThan @ SV1951 @ SV1181 ) @ ( tc_set @ SV1181 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1181 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8527]) ).

thf(8700,plain,
    ! [SV1682: $i,SV1467: $i,SV1182: $i] :
      ( ( ( c_in @ SV1182 @ ( c_uminus @ SV1467 @ ( tc_set @ SV1682 ) ) @ SV1682 )
        = $false )
      | ( ( c_in @ SV1182 @ SV1467 @ SV1682 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8528]) ).

thf(8701,plain,
    ! [SV1687: $i,SV1472: $i,SV1978: $i,SV1187: $i] :
      ( ( ( ~ ( c_in @ SV1187 @ ( c_minus @ SV1978 @ SV1472 @ ( tc_set @ SV1687 ) ) @ SV1687 ) )
        = $true )
      | ( ( c_in @ SV1187 @ SV1472 @ SV1687 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8532]) ).

thf(8702,plain,
    ! [SV1852: $i,SV1688: $i,SV1473: $i,SV1188: $i] :
      ( ( ( c_in @ SV1188 @ ( c_minus @ SV1473 @ SV1688 @ ( tc_set @ SV1852 ) ) @ SV1852 )
        = $false )
      | ( ( c_in @ SV1188 @ SV1473 @ SV1852 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8533]) ).

thf(8703,plain,
    ! [SV1474: $i,SV1689: $i,SV1979: $i,SV1189: $i] :
      ( ( ( ( c_in @ SV1189 @ SV1979 @ SV1689 )
          | ( c_in @ SV1189 @ ( c_minus @ SV1474 @ SV1979 @ ( tc_set @ SV1689 ) ) @ SV1689 ) )
        = $true )
      | ( ( c_in @ SV1189 @ SV1474 @ SV1689 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8534]) ).

thf(8704,plain,
    ! [SV1853: $i,SV1690: $i,SV1475: $i,SV1190: $i] :
      ( ( ( c_in @ SV1190 @ ( c_inter @ SV1475 @ SV1690 @ SV1853 ) @ SV1853 )
        = $false )
      | ( ( c_in @ SV1190 @ SV1690 @ SV1853 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8535]) ).

thf(8705,plain,
    ! [SV1854: $i,SV1691: $i,SV1476: $i,SV1191: $i] :
      ( ( ( c_in @ SV1191 @ ( c_inter @ SV1476 @ SV1691 @ SV1854 ) @ SV1854 )
        = $false )
      | ( ( c_in @ SV1191 @ SV1476 @ SV1854 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8536]) ).

thf(8706,plain,
    ! [SV1477: $i,SV1692: $i,SV1980: $i,SV1192: $i] :
      ( ( ( ~ ( c_in @ SV1192 @ SV1980 @ SV1692 )
          | ( c_in @ SV1192 @ ( c_inter @ SV1980 @ SV1477 @ SV1692 ) @ SV1692 ) )
        = $true )
      | ( ( c_in @ SV1192 @ SV1477 @ SV1692 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8537]) ).

thf(8707,plain,
    ! [SV1193: $i,SV1693: $i,SV1478: $i,SV1981: $i] :
      ( ( ( ~ ( c_in @ SV1981 @ ( c_Inter @ SV1478 @ SV1693 ) @ SV1693 )
          | ( c_in @ SV1981 @ SV1193 @ SV1693 ) )
        = $true )
      | ( ( c_in @ SV1193 @ SV1478 @ ( tc_set @ SV1693 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8538]) ).

thf(8708,plain,
    ! [SV1696: $i,SV1481: $i,SV1982: $i,SV1196: $i] :
      ( ( ( c_in @ SV1196 @ ( c_union @ SV1982 @ SV1481 @ SV1696 ) @ SV1696 )
        = $true )
      | ( ( c_in @ SV1196 @ SV1481 @ SV1696 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8541]) ).

thf(8709,plain,
    ! [SV1697: $i,SV1983: $i,SV1482: $i,SV1197: $i] :
      ( ( ( c_in @ SV1197 @ ( c_union @ SV1482 @ SV1983 @ SV1697 ) @ SV1697 )
        = $true )
      | ( ( c_in @ SV1197 @ SV1482 @ SV1697 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8542]) ).

thf(8710,plain,
    ! [SV1855: $i,SV1698: $i,SV1483: $i,SV1198: $i] :
      ( ( ( c_in @ SV1198 @ ( c_union @ SV1483 @ SV1698 @ SV1855 ) @ SV1855 )
        = $false )
      | ( ( ( c_in @ SV1198 @ SV1698 @ SV1855 )
          | ( c_in @ SV1198 @ SV1483 @ SV1855 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8543]) ).

thf(8711,plain,
    ! [SV1202: $i,SV1700: $i,SV1984: $i,SV1485: $i] :
      ( ( ( ~ ( c_in @ SV1485 @ SV1984 @ ( tc_set @ SV1700 ) )
          | ( c_in @ SV1202 @ ( c_Union @ SV1984 @ SV1700 ) @ SV1700 ) )
        = $true )
      | ( ( c_in @ SV1202 @ SV1485 @ SV1700 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8546]) ).

thf(8712,plain,
    ! [SV1701: $i,SV1487: $i,SV1985: $i,SV1204: $i] :
      ( ( ( c_in @ SV1204 @ ( c_insert @ SV1985 @ SV1487 @ SV1701 ) @ SV1701 )
        = $true )
      | ( ( c_in @ SV1204 @ SV1487 @ SV1701 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8547]) ).

thf(8713,plain,
    ! [SV1858: $i,SV1703: $i,SV1489: $i,SV1206: $i] :
      ( ( ( c_in @ SV1206 @ ( c_insert @ SV1489 @ SV1703 @ SV1858 ) @ SV1858 )
        = $false )
      | ( ( ( SV1206 = SV1489 )
          | ( c_in @ SV1206 @ SV1703 @ SV1858 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8548]) ).

thf(8714,plain,
    ! [SV1859: $i,SV1704: $i,SV1491: $i,SV1208: $i] :
      ( ( ( ( c_insert @ SV1208 @ SV1491 @ SV1704 )
          = ( c_insert @ SV1859 @ c_emptyset @ SV1704 ) )
        = $false )
      | ( ( SV1208 = SV1859 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8549]) ).

thf(8715,plain,
    ! [SV1860: $i,SV1705: $i,SV1492: $i,SV1209: $i] :
      ( ( ( ( c_insert @ SV1209 @ SV1492 @ SV1705 )
          = ( c_insert @ SV1860 @ c_emptyset @ SV1705 ) )
        = $false )
      | ( ( c_lessequals @ SV1492 @ ( c_insert @ SV1860 @ c_emptyset @ SV1705 ) @ ( tc_set @ SV1705 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8550]) ).

thf(8716,plain,
    ! [SV1952: $i,SV1707: $i,SV1494: $i,SV1211: $i] :
      ( ( ( ( c_insert @ SV1211 @ c_emptyset @ SV1494 )
          = ( c_insert @ SV1707 @ SV1952 @ SV1494 ) )
        = $false )
      | ( ( SV1707 = SV1211 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8552]) ).

thf(8717,plain,
    ! [SV1861: $i,SV1708: $i,SV1495: $i,SV1212: $i] :
      ( ( ( ( c_insert @ SV1212 @ c_emptyset @ SV1495 )
          = ( c_insert @ SV1708 @ SV1861 @ SV1495 ) )
        = $false )
      | ( ( c_lessequals @ SV1861 @ ( c_insert @ SV1212 @ c_emptyset @ SV1495 ) @ ( tc_set @ SV1495 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8553]) ).

thf(8718,plain,
    ! [SV1862: $i,SV1710: $i,SV1497: $i,SV1214: $i] :
      ( ( ( ( c_Sum__Type_OInl @ SV1214 @ SV1497 @ SV1710 )
          = ( c_Sum__Type_OInl @ SV1862 @ SV1497 @ SV1710 ) )
        = $false )
      | ( ( SV1214 = SV1862 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8555]) ).

thf(8719,plain,
    ! [SV1864: $i,SV1712: $i,SV1499: $i,SV1216: $i] :
      ( ( ( ( c_Sum__Type_OInr @ SV1216 @ SV1499 @ SV1712 )
          = ( c_Sum__Type_OInr @ SV1864 @ SV1499 @ SV1712 ) )
        = $false )
      | ( ( SV1216 = SV1864 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8557]) ).

thf(8720,plain,
    ! [SV1866: $i,SV1714: $i,SV1503: $i,SV1220: $i] :
      ( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1220 @ SV1503 @ SV1714 @ SV1714 ) @ SV1866 @ ( tc_prod @ SV1714 @ SV1714 ) ) @ SV1714 )
        = $false )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ SV1866 @ SV1714 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8559]) ).

thf(8721,plain,
    ! [SV1867: $i,SV1715: $i,SV1504: $i,SV1221: $i] :
      ( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1221 @ SV1504 @ SV1715 @ SV1715 ) @ SV1867 @ ( tc_prod @ SV1715 @ SV1715 ) ) @ SV1715 )
        = $false )
      | ( ( ~ ( c_in @ ( c_Pair @ SV1504 @ SV1221 @ SV1715 @ SV1715 ) @ ( c_Transitive__Closure_Ortrancl @ SV1867 @ SV1715 ) @ ( tc_prod @ SV1715 @ SV1715 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8560]) ).

thf(8722,plain,
    ! [SV1222: $i,SV1505: $i,SV1986: $i,SV1953: $i] :
      ( ( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1953 @ SV1986 @ SV1505 @ SV1505 ) @ SV1222 @ ( tc_prod @ SV1505 @ SV1505 ) ) @ SV1505 )
          | ( c_in @ ( c_Pair @ SV1986 @ SV1953 @ SV1505 @ SV1505 ) @ ( c_Transitive__Closure_Ortrancl @ SV1222 @ SV1505 ) @ ( tc_prod @ SV1505 @ SV1505 ) ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ SV1222 @ SV1505 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8561]) ).

thf(8723,plain,
    ! [SV1868: $i,SV1716: $i,SV1506: $i,SV1223: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1223 @ SV1506 @ SV1716 @ SV1716 ) @ SV1868 @ ( tc_prod @ SV1716 @ SV1716 ) ) @ SV1716 )
        = $false )
      | ( ( c_Wellfounded__Recursion_Owf @ SV1868 @ SV1716 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8562]) ).

thf(8724,plain,
    ! [SV1869: $i,SV1717: $i,SV1507: $i,SV1224: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1224 @ SV1507 @ SV1717 @ SV1717 ) @ SV1869 @ ( tc_prod @ SV1717 @ SV1717 ) ) @ SV1717 )
        = $false )
      | ( ( ~ ( c_in @ ( c_Pair @ SV1507 @ SV1224 @ SV1717 @ SV1717 ) @ ( c_Transitive__Closure_Ortrancl @ SV1869 @ SV1717 ) @ ( tc_prod @ SV1717 @ SV1717 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8563]) ).

thf(8725,plain,
    ! [SV1225: $i,SV1508: $i,SV1987: $i,SV1954: $i] :
      ( ( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1954 @ SV1987 @ SV1508 @ SV1508 ) @ SV1225 @ ( tc_prod @ SV1508 @ SV1508 ) ) @ SV1508 )
          | ( c_in @ ( c_Pair @ SV1987 @ SV1954 @ SV1508 @ SV1508 ) @ ( c_Transitive__Closure_Ortrancl @ SV1225 @ SV1508 ) @ ( tc_prod @ SV1508 @ SV1508 ) ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV1225 @ SV1508 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8564]) ).

thf(8726,plain,
    ! [SV1718: $i,SV1511: $i,SV1228: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ SV1718 @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OKey @ SV1228 ) @ SV1718 @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1228 @ SV1511 ) @ ( c_Message_Osynth @ SV1718 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8565]) ).

thf(8727,plain,
    ! [SV1229: $i,SV1719: $i,SV1512: $i] :
      ( ( ( c_in @ SV1512 @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ SV1719 @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1229 @ SV1512 ) @ ( c_Message_Osynth @ SV1719 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8566]) ).

thf(8728,plain,
    ! [SV1236: $i,SV1724: $i,SV1519: $i] :
      ( ( ( c_in @ SV1519 @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ SV1724 @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1236 @ SV1519 ) @ ( c_Message_Osynth @ SV1724 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8572]) ).

thf(8729,plain,
    ! [SV1520: $i,SV1725: $i,SV1237: $i] :
      ( ( ( c_in @ SV1237 @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ SV1725 @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1237 @ SV1520 ) @ ( c_Message_Osynth @ SV1725 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8573]) ).

thf(8730,plain,
    ! [SV1523: $i,SV1726: $i,SV1244: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1244 ) ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ SV1523 @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1244 @ SV1523 ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8574]) ).

thf(8731,plain,
    ! [SV1526: $i,SV1727: $i,SV1247: $i] :
      ( ( ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1727 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ SV1247 @ ( c_Message_Oparts @ SV1526 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ SV1247 @ ( c_Message_Oparts @ ( c_union @ SV1526 @ SV1727 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8575]) ).

thf(8732,plain,
    ! [SV1955: $i,SV1728: $i,SV1532: $i,SV1253: $i] :
      ( ( ( ( c_Message_Omsg_OMPair @ SV1253 @ SV1532 )
          = ( c_Message_Omsg_OMPair @ SV1728 @ SV1955 ) )
        = $false )
      | ( ( SV1253 = SV1728 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8576]) ).

thf(8733,plain,
    ! [SV1870: $i,SV1729: $i,SV1533: $i,SV1254: $i] :
      ( ( ( ( c_Message_Omsg_OMPair @ SV1254 @ SV1533 )
          = ( c_Message_Omsg_OMPair @ SV1729 @ SV1870 ) )
        = $false )
      | ( ( SV1533 = SV1870 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8577]) ).

thf(8734,plain,
    ! [SV1956: $i,SV1730: $i,SV1534: $i,SV1255: $i] :
      ( ( ( ( c_Message_Omsg_OCrypt @ SV1255 @ SV1534 )
          = ( c_Message_Omsg_OCrypt @ SV1730 @ SV1956 ) )
        = $false )
      | ( ( SV1255 = SV1730 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8578]) ).

thf(8735,plain,
    ! [SV1871: $i,SV1731: $i,SV1535: $i,SV1256: $i] :
      ( ( ( ( c_Message_Omsg_OCrypt @ SV1256 @ SV1535 )
          = ( c_Message_Omsg_OCrypt @ SV1731 @ SV1871 ) )
        = $false )
      | ( ( SV1535 = SV1871 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8579]) ).

thf(8736,plain,
    ! [SV1261: $i,SV1539: $i,SV1957: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV1957 ) @ SV1539 @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1957 @ SV1261 ) @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ SV1261 @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8580]) ).

thf(8737,plain,
    ! [SV1264: $i,SV1542: $i,SV1958: $i] :
      ( ( ( ~ ( c_in @ SV1958 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1958 @ SV1264 ) @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ SV1264 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8581]) ).

thf(8738,plain,
    ! [SV1544: $i,SV1266: $i,SV1988: $i,SV1959: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV1959 ) @ ( c_Message_Oanalz @ SV1988 ) @ ( tc_set @ tc_Message_Omsg ) )
          | ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SV1959 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SV1988 @ SV1544 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
        = $true )
      | ( ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SV1544 ) @ ( tc_set @ tc_Message_Omsg ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8582]) ).

thf(8739,plain,
    ! [SV1872: $i,SV1734: $i,SV1548: $i,SV1270: $i,SV3: $i] :
      ( ( ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) ) )
        = $false )
      | ( ( SV3
          = ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( c_Main_OdprodE__2 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ SV1734 @ SV1872 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ ( c_Main_OdprodE__4 @ SV3 @ SV1270 @ SV1548 @ SV1734 @ SV1872 ) @ SV1734 @ SV1872 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1734 @ SV1872 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8585]) ).

thf(8740,plain,
    ! [SV1873: $i,SV1735: $i,SV1549: $i,SV1271: $i,SV4: $i] :
      ( ( ( c_in @ SV4 @ ( c_Datatype__Universe_Odprod @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( c_Main_OdprodE__4 @ SV4 @ SV1271 @ SV1549 @ SV1735 @ SV1873 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) @ SV1549 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1735 @ SV1873 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8586]) ).

thf(8741,plain,
    ! [SV1874: $i,SV1736: $i,SV1550: $i,SV1272: $i,SV5: $i] :
      ( ( ( c_in @ SV5 @ ( c_Datatype__Universe_Odprod @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( c_Main_OdprodE__3 @ SV5 @ SV1272 @ SV1550 @ SV1736 @ SV1874 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) @ SV1272 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1736 @ SV1874 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8587]) ).

thf(8742,plain,
    ! [SV1960: $i,SV1875: $i,SV1737: $i,SV1551: $i,SV1273: $i,SV6: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) )
        = $true )
      | ( ( ! [SY3451: $i,SY3452: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV1960 @ SY3451 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SY3452 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
              | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1960 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SY3451 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3452 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8588]) ).

thf(8743,plain,
    ! [SV1876: $i,SV1738: $i,SV1552: $i,SV1274: $i,SV7: $i] :
      ( ( ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1274 @ SV1552 @ SV1738 @ SV1876 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
        = $false )
      | ( ( ( SV7
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
          | ( SV7
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8589]) ).

thf(8744,plain,
    ! [SV1877: $i,SV1739: $i,SV1553: $i,SV1275: $i,SV8: $i] :
      ( ( ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1275 @ SV1553 @ SV1739 @ SV1877 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
        = $false )
      | ( ( ( SV8
            = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( c_Main_OdsumE__4 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) @ SV1553 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8590]) ).

thf(8745,plain,
    ! [SV1878: $i,SV1740: $i,SV1554: $i,SV1276: $i,SV9: $i] :
      ( ( ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SV1276 @ SV1554 @ SV1740 @ SV1878 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
        = $false )
      | ( ( ( SV9
            = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( c_Main_OdsumE__2 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) @ SV1276 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8591]) ).

thf(8746,plain,
    ! [SV1879: $i,SV1741: $i,SV1555: $i,SV1277: $i,SV10: $i] :
      ( ( ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SV1277 @ SV1555 @ SV1741 @ SV1879 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
        = $false )
      | ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__2 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1277 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__4 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1555 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8592]) ).

thf(8747,plain,
    ! [SV1880: $i,SV1742: $i,SV1556: $i,SV1278: $i,SV11: $i] :
      ( ( ( c_in @ ( c_Pair @ SV11 @ SV1278 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ SV1880 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) )
        = $false )
      | ( ( ! [SY3433: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SV1556 @ SV1742 ) @ ( c_Datatype__Universe_OIn0 @ SV1278 @ SV1556 @ SV1742 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1880 @ SY3433 @ SV1556 @ SV1742 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8593]) ).

thf(8748,plain,
    ! [SV1881: $i,SV1743: $i,SV1557: $i,SV1279: $i,SV12: $i] :
      ( ( ( c_in @ ( c_Pair @ SV12 @ SV1279 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ SV1881 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) )
        = $false )
      | ( ( ! [SY3434: $i] : ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SV1557 @ SV1743 ) @ ( c_Datatype__Universe_OIn1 @ SV1279 @ SV1557 @ SV1743 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3434 @ SV1881 @ SV1557 @ SV1743 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8594]) ).

thf(8749,plain,
    ! [SV1882: $i,SV1744: $i,SV1558: $i,SV1280: $i,SV13: $i] :
      ( ( ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1280 @ SV1558 @ SV1744 @ SV1882 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1744 @ SV1882 ) ) )
        = $false )
      | ( ( SV13
          = ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SV1882 ) @ ( c_Main_OuprodE__2 @ SV1280 @ SV1558 @ SV13 @ SV1744 @ SV1882 ) @ SV1744 @ SV1882 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8595]) ).

thf(8750,plain,
    ! [SV1883: $i,SV1745: $i,SV1559: $i,SV1281: $i,SV14: $i] :
      ( ( ( c_in @ SV14 @ ( c_Datatype__Universe_Ouprod @ SV1281 @ SV1559 @ SV1745 @ SV1883 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SV1883 ) ) )
        = $false )
      | ( ( c_in @ ( c_Main_OuprodE__2 @ SV1281 @ SV1559 @ SV14 @ SV1745 @ SV1883 ) @ SV1559 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1745 @ SV1883 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8596]) ).

thf(8751,plain,
    ! [SV1884: $i,SV1746: $i,SV1560: $i,SV1282: $i,SV15: $i] :
      ( ( ( c_in @ SV15 @ ( c_Datatype__Universe_Ouprod @ SV1282 @ SV1560 @ SV1746 @ SV1884 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SV1884 ) ) )
        = $false )
      | ( ( c_in @ ( c_Main_OuprodE__1 @ SV1282 @ SV1560 @ SV15 @ SV1746 @ SV1884 ) @ SV1282 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1746 @ SV1884 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8597]) ).

thf(8752,plain,
    ! [SV1283: $i,SV16: $i,SV1747: $i,SV1561: $i,SV1989: $i] :
      ( ( ( ! [SY3457: $i] :
              ( ~ ( c_in @ SV1989 @ SY3457 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
              | ( c_in @ ( c_Datatype__Universe_OScons @ SV1989 @ SV16 @ SV1561 @ SV1747 ) @ ( c_Datatype__Universe_Ouprod @ SY3457 @ SV1283 @ SV1561 @ SV1747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) ) ) )
        = $true )
      | ( ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8598]) ).

thf(8753,plain,
    ! [SV1885: $i,SV1748: $i,SV1562: $i,SV1284: $i,SV17: $i] :
      ( ( ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1284 @ SV1562 @ SV1748 @ SV1885 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1748 @ SV1885 ) ) )
        = $false )
      | ( ( ( SV17
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1284 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) )
          | ( SV17
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1562 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8599]) ).

thf(8754,plain,
    ! [SV1886: $i,SV1749: $i,SV1563: $i,SV1285: $i,SV18: $i] :
      ( ( ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1285 @ SV1563 @ SV1749 @ SV1886 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) )
        = $false )
      | ( ( ( SV18
            = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1285 @ SV18 @ SV1749 @ SV1886 ) @ SV1749 @ SV1886 ) )
          | ( c_in @ ( c_Main_OusumE__2 @ SV1563 @ SV18 @ SV1749 @ SV1886 ) @ SV1563 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8600]) ).

thf(8755,plain,
    ! [SV1887: $i,SV1750: $i,SV1564: $i,SV1286: $i,SV19: $i] :
      ( ( ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SV1286 @ SV1564 @ SV1750 @ SV1887 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) )
        = $false )
      | ( ( ( SV19
            = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1564 @ SV19 @ SV1750 @ SV1887 ) @ SV1750 @ SV1887 ) )
          | ( c_in @ ( c_Main_OusumE__1 @ SV1286 @ SV19 @ SV1750 @ SV1887 ) @ SV1286 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8601]) ).

thf(8756,plain,
    ! [SV1888: $i,SV1751: $i,SV1565: $i,SV1287: $i,SV20: $i] :
      ( ( ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SV1287 @ SV1565 @ SV1751 @ SV1888 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
        = $false )
      | ( ( ( c_in @ ( c_Main_OusumE__1 @ SV1287 @ SV20 @ SV1751 @ SV1888 ) @ SV1287 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
          | ( c_in @ ( c_Main_OusumE__2 @ SV1565 @ SV20 @ SV1751 @ SV1888 ) @ SV1565 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8602]) ).

thf(8757,plain,
    ! [SV1990: $i,SV1288: $i,SV1752: $i,SV1566: $i,SV21: $i] :
      ( ( ( c_in @ ( c_Datatype__Universe_OIn0 @ SV21 @ SV1566 @ SV1752 ) @ ( c_Datatype__Universe_Ousum @ SV1288 @ SV1990 @ SV1566 @ SV1752 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) )
        = $true )
      | ( ( c_in @ SV21 @ SV1288 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1566 @ SV1752 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8603]) ).

thf(8758,plain,
    ! [SV1289: $i,SV1991: $i,SV1753: $i,SV1567: $i,SV22: $i] :
      ( ( ( c_in @ ( c_Datatype__Universe_OIn1 @ SV22 @ SV1567 @ SV1753 ) @ ( c_Datatype__Universe_Ousum @ SV1991 @ SV1289 @ SV1567 @ SV1753 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) )
        = $true )
      | ( ( c_in @ SV22 @ SV1289 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1567 @ SV1753 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8604]) ).

thf(8759,plain,
    ! [SV1300: $i,SV36: $i,SV1892: $i] :
      ( ( ( c_in @ SV1892 @ SV36 @ SV1300 )
        = $false )
      | ( ( ! [SY3435: $i] :
              ( ~ ( c_in @ SY3435 @ SV36 @ SV1300 )
              | ( SV1892 = SY3435 ) ) )
        = $true )
      | ( ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8606]) ).

thf(8760,plain,
    ! [SV1308: $i,SV1568: $i,SV46: $i,SV1961: $i] :
      ( ( ( ~ ( c_in @ SV1961 @ ( c_List_Oset @ SV46 @ SV1568 ) @ SV1568 ) )
        = $true )
      | ( ( c_in @ SV1961 @ SV1308 @ SV1568 )
        = $true )
      | ( ( c_in @ SV46 @ ( c_List_Olists @ SV1308 @ SV1568 ) @ ( tc_List_Olist @ SV1568 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8607]) ).

thf(8761,plain,
    ! [SV1893: $i,SV1754: $i,SV1571: $i,SV1312: $i,SV50: $i] :
      ( ( ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV50 @ SV1312 @ SV1571 ) @ SV1754 @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) @ ( c_List_Olistrel @ SV1893 @ SV1571 ) @ ( tc_prod @ ( tc_List_Olist @ SV1571 ) @ ( tc_List_Olist @ SV1571 ) ) )
        = $false )
      | ( ( SV1754
          = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SV1893 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ ( c_Main_Olistrel__Cons1__2 @ SV1893 @ SV1754 @ SV50 @ SV1312 @ SV1571 ) @ SV1571 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8608]) ).

thf(8762,plain,
    ! [SV1894: $i,SV1755: $i,SV1572: $i,SV1313: $i,SV51: $i] :
      ( ( ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV51 @ SV1313 @ SV1572 ) @ SV1755 @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SV1894 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1313 @ ( c_Main_Olistrel__Cons1__2 @ SV1894 @ SV1755 @ SV51 @ SV1313 @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) @ ( c_List_Olistrel @ SV1894 @ SV1572 ) @ ( tc_prod @ ( tc_List_Olist @ SV1572 ) @ ( tc_List_Olist @ SV1572 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8609]) ).

thf(8763,plain,
    ! [SV1895: $i,SV1756: $i,SV1573: $i,SV1314: $i,SV52: $i] :
      ( ( ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV52 @ SV1314 @ SV1573 ) @ SV1756 @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) @ ( c_List_Olistrel @ SV1895 @ SV1573 ) @ ( tc_prod @ ( tc_List_Olist @ SV1573 ) @ ( tc_List_Olist @ SV1573 ) ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV52 @ ( c_Main_Olistrel__Cons1__1 @ SV1895 @ SV1756 @ SV52 @ SV1314 @ SV1573 ) @ SV1573 @ SV1573 ) @ SV1895 @ ( tc_prod @ SV1573 @ SV1573 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8610]) ).

thf(8764,plain,
    ! [SV1896: $i,SV1757: $i,SV1574: $i,SV1315: $i,SV53: $i] :
      ( ( ( c_in @ ( c_Pair @ SV53 @ ( c_List_Olist_OCons @ SV1315 @ SV1574 @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) @ ( c_List_Olistrel @ SV1896 @ SV1757 ) @ ( tc_prod @ ( tc_List_Olist @ SV1757 ) @ ( tc_List_Olist @ SV1757 ) ) )
        = $false )
      | ( ( SV53
          = ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SV1896 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ ( c_Main_Olistrel__Cons2__2 @ SV1896 @ SV53 @ SV1315 @ SV1574 @ SV1757 ) @ SV1757 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8611]) ).

thf(8765,plain,
    ! [SV1897: $i,SV1758: $i,SV1575: $i,SV1316: $i,SV54: $i] :
      ( ( ( c_in @ ( c_Pair @ SV54 @ ( c_List_Olist_OCons @ SV1316 @ SV1575 @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SV1897 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SV1897 @ SV54 @ SV1316 @ SV1575 @ SV1758 ) @ SV1575 @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) @ ( c_List_Olistrel @ SV1897 @ SV1758 ) @ ( tc_prod @ ( tc_List_Olist @ SV1758 ) @ ( tc_List_Olist @ SV1758 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8612]) ).

thf(8766,plain,
    ! [SV1898: $i,SV1759: $i,SV1576: $i,SV1317: $i,SV55: $i] :
      ( ( ( c_in @ ( c_Pair @ SV55 @ ( c_List_Olist_OCons @ SV1317 @ SV1576 @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) @ ( c_List_Olistrel @ SV1898 @ SV1759 ) @ ( tc_prod @ ( tc_List_Olist @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SV1898 @ SV55 @ SV1317 @ SV1576 @ SV1759 ) @ SV1317 @ SV1759 @ SV1759 ) @ SV1898 @ ( tc_prod @ SV1759 @ SV1759 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8613]) ).

thf(8767,plain,
    ! [SV60: $i,SV1581: $i,SV1320: $i,SV1962: $i] :
      ( ( ( ~ ( c_in @ SV1962 @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) ) )
        = $true )
      | ( ( c_in @ ( c_List_Olist_OCons @ SV60 @ SV1962 @ SV1581 ) @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) )
        = $true )
      | ( ( c_in @ SV60 @ SV1320 @ SV1581 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8616]) ).

thf(8768,plain,
    ! [SV1899: $i,SV1766: $i,SV1583: $i,SV1325: $i,SV70: $i] :
      ( ( ( c_in @ ( c_Pair @ SV70 @ SV1325 @ SV1583 @ SV1766 ) @ SV1899 @ ( tc_prod @ SV1583 @ SV1766 ) )
        = $false )
      | ( ( c_in @ SV70 @ ( c_Relation_ODomain @ SV1899 @ SV1583 @ SV1766 ) @ SV1583 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8618]) ).

thf(8769,plain,
    ! [SV1900: $i,SV1767: $i,SV1584: $i,SV1327: $i,SV72: $i] :
      ( ( ( c_in @ SV72 @ ( c_Relation_OImage @ SV1327 @ SV1584 @ SV1767 @ SV1900 ) @ SV1900 )
        = $false )
      | ( ( c_in @ ( c_Main_OImageE__1 @ SV1584 @ SV72 @ SV1327 @ SV1767 @ SV1900 ) @ SV1584 @ SV1767 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8619]) ).

thf(8770,plain,
    ! [SV1901: $i,SV1768: $i,SV1585: $i,SV1328: $i,SV73: $i] :
      ( ( ( c_in @ SV73 @ ( c_Relation_OImage @ SV1328 @ SV1585 @ SV1768 @ SV1901 ) @ SV1901 )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1585 @ SV73 @ SV1328 @ SV1768 @ SV1901 ) @ SV73 @ SV1768 @ SV1901 ) @ SV1328 @ ( tc_prod @ SV1768 @ SV1901 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8620]) ).

thf(8771,plain,
    ! [SV1329: $i,SV1992: $i,SV1586: $i,SV1769: $i,SV74: $i] :
      ( ( ( ! [SY3458: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV74 @ SV1769 @ SV1586 @ SV1992 ) @ SY3458 @ ( tc_prod @ SV1586 @ SV1992 ) )
              | ( c_in @ SV1769 @ ( c_Relation_OImage @ SY3458 @ SV1329 @ SV1586 @ SV1992 ) @ SV1992 ) ) )
        = $true )
      | ( ( c_in @ SV74 @ SV1329 @ SV1586 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8621]) ).

thf(8772,plain,
    ! [SV1902: $i,SV1771: $i,SV1588: $i,SV1331: $i,SV76: $i] :
      ( ( ( c_in @ ( c_Pair @ SV76 @ SV1331 @ SV1588 @ SV1771 ) @ SV1902 @ ( tc_prod @ SV1588 @ SV1771 ) )
        = $false )
      | ( ( c_in @ SV1331 @ ( c_Relation_ORange @ SV1902 @ SV1588 @ SV1771 ) @ SV1771 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8623]) ).

thf(8773,plain,
    ! [SV1963: $i,SV1903: $i,SV1774: $i,SV1594: $i,SV1337: $i,SV82: $i] :
      ( ( ( ~ ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SV1337 @ SV1594 @ SV1774 @ SV1903 @ SV1963 ) @ ( tc_prod @ SV1963 @ SV1903 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SV1963 ) @ ( c_Main_Orel__compE__3 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SV1963 ) @ SV1774 @ SV1903 ) @ SV1337 @ ( tc_prod @ SV1774 @ SV1903 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8626]) ).

thf(8774,plain,
    ! [SV1964: $i,SV1904: $i,SV1775: $i,SV1595: $i,SV1338: $i,SV83: $i] :
      ( ( ( ~ ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SV1338 @ SV1595 @ SV1775 @ SV1904 @ SV1964 ) @ ( tc_prod @ SV1964 @ SV1904 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SV1964 ) @ ( c_Main_Orel__compE__2 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SV1964 ) @ SV1964 @ SV1775 ) @ SV1595 @ ( tc_prod @ SV1964 @ SV1775 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8627]) ).

thf(8775,plain,
    ! [SV1965: $i,SV1905: $i,SV1776: $i,SV1596: $i,SV1339: $i,SV84: $i] :
      ( ( ( ~ ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SV1339 @ SV1596 @ SV1776 @ SV1905 @ SV1965 ) @ ( tc_prod @ SV1965 @ SV1905 ) ) )
        = $true )
      | ( ( SV84
          = ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SV1965 ) @ ( c_Main_Orel__compE__3 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SV1965 ) @ SV1965 @ SV1905 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8628]) ).

thf(8776,plain,
    ! [SV1966: $i,SV1906: $i,SV1777: $i,SV1597: $i,SV1340: $i,SV85: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) ) )
        = $true )
      | ( ( ! [SY3453: $i,SY3454: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV85 @ SY3453 @ SV1597 ) @ SY3454 @ ( tc_prod @ SY3453 @ SV1597 ) )
              | ( c_in @ ( c_Pair @ SV1966 @ SV1340 @ SY3453 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SY3454 @ SV1597 @ SV1777 @ SY3453 ) @ ( tc_prod @ SY3453 @ SV1777 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8629]) ).

thf(8777,plain,
    ! [SV108: $i,SV1606: $i,SV1967: $i,SV1361: $i] :
      ( ( ( ~ ( c_lessequals @ SV1361 @ SV1967 @ ( tc_set @ SV1606 ) ) )
        = $true )
      | ( ( c_in @ SV108 @ SV1967 @ SV1606 )
        = $true )
      | ( ( c_in @ SV108 @ SV1361 @ SV1606 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8632]) ).

thf(8778,plain,
    ! [SV1609: $i,SV111: $i,SV1364: $i] :
      ( ( ( c_lessequals @ SV1364 @ SV111 @ ( tc_set @ SV1609 ) )
        = $false )
      | ( ( SV1364 = SV111 )
        = $true )
      | ( ( c_lessequals @ SV111 @ SV1364 @ ( tc_set @ SV1609 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8633]) ).

thf(8779,plain,
    ! [SV1993: $i,SV1366: $i,SV1968: $i,SV1610: $i,SV113: $i] :
      ( ( ( c_in @ ( c_Sum__Type_OInl @ SV113 @ SV1610 @ SV1968 ) @ ( c_Sum__Type_OPlus @ SV1366 @ SV1993 @ SV1610 @ SV1968 ) @ ( tc_sum @ SV1610 @ SV1968 ) )
        = $true )
      | ( ( c_in @ SV113 @ SV1366 @ SV1610 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8634]) ).

thf(8780,plain,
    ! [SV1367: $i,SV1994: $i,SV1969: $i,SV1611: $i,SV114: $i] :
      ( ( ( c_in @ ( c_Sum__Type_OInr @ SV114 @ SV1611 @ SV1969 ) @ ( c_Sum__Type_OPlus @ SV1994 @ SV1367 @ SV1969 @ SV1611 ) @ ( tc_sum @ SV1969 @ SV1611 ) )
        = $true )
      | ( ( c_in @ SV114 @ SV1367 @ SV1611 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8635]) ).

thf(8781,plain,
    ! [SV1907: $i,SV1779: $i,SV1612: $i,SV1368: $i,SV115: $i] :
      ( ( ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SV1368 @ SV1612 @ SV1779 @ SV1907 ) @ ( tc_sum @ SV1779 @ SV1907 ) )
        = $false )
      | ( ( ( SV115
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1368 @ SV115 @ SV1779 @ SV1907 ) @ SV1779 @ SV1907 ) )
          | ( SV115
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1612 @ SV115 @ SV1907 @ SV1779 ) @ SV1907 @ SV1779 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8636]) ).

thf(8782,plain,
    ! [SV1908: $i,SV1780: $i,SV1613: $i,SV1369: $i,SV116: $i] :
      ( ( ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SV1369 @ SV1613 @ SV1780 @ SV1908 ) @ ( tc_sum @ SV1780 @ SV1908 ) )
        = $false )
      | ( ( ( SV116
            = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1369 @ SV116 @ SV1780 @ SV1908 ) @ SV1780 @ SV1908 ) )
          | ( c_in @ ( c_Main_OPlusE__2 @ SV1613 @ SV116 @ SV1908 @ SV1780 ) @ SV1613 @ SV1908 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8637]) ).

thf(8783,plain,
    ! [SV1909: $i,SV1781: $i,SV1614: $i,SV1370: $i,SV117: $i] :
      ( ( ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SV1370 @ SV1614 @ SV1781 @ SV1909 ) @ ( tc_sum @ SV1781 @ SV1909 ) )
        = $false )
      | ( ( ( SV117
            = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1614 @ SV117 @ SV1909 @ SV1781 ) @ SV1909 @ SV1781 ) )
          | ( c_in @ ( c_Main_OPlusE__1 @ SV1370 @ SV117 @ SV1781 @ SV1909 ) @ SV1370 @ SV1781 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8638]) ).

thf(8784,plain,
    ! [SV1910: $i,SV1782: $i,SV1615: $i,SV1371: $i,SV118: $i] :
      ( ( ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SV1371 @ SV1615 @ SV1782 @ SV1910 ) @ ( tc_sum @ SV1782 @ SV1910 ) )
        = $false )
      | ( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1371 @ SV118 @ SV1782 @ SV1910 ) @ SV1371 @ SV1782 )
          | ( c_in @ ( c_Main_OPlusE__2 @ SV1615 @ SV118 @ SV1910 @ SV1782 ) @ SV1615 @ SV1910 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8639]) ).

thf(8785,plain,
    ! [SV1376: $i,SV124: $i,SV1970: $i,SV1911: $i] :
      ( ( ( ~ ( c_Relation_Otrans @ SV1911 @ SV1970 ) )
        = $true )
      | ( ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1911 @ SV124 @ SV1970 @ SV1376 ) @ ( tc_prod @ SV1970 @ SV1376 ) )
        = $true )
      | ( ( c_Relation_Otrans @ SV124 @ SV1376 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8642]) ).

thf(8786,plain,
    ! [SV1377: $i,SV125: $i,SV1971: $i,SV1912: $i] :
      ( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1912 @ SV1971 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1912 @ SV125 @ SV1971 @ SV1377 ) @ ( tc_prod @ SV1971 @ SV1377 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV125 @ SV1377 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8643]) ).

thf(8787,plain,
    ! [SV1995: $i,SV1916: $i,SV1795: $i,SV1634: $i,SV1397: $i,SV1060: $i] :
      ( ( ( ( c_Datatype__Universe_OScons @ SV1060 @ SV1397 @ SV1634 @ SV1795 )
         != ( c_Datatype__Universe_OScons @ SV1916 @ SV1995 @ SV1634 @ SV1795 ) )
        = $true )
      | ( ( SV1060 = SV1916 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8653]) ).

thf(8788,plain,
    ! [SV1972: $i,SV1917: $i,SV1796: $i,SV1635: $i,SV1398: $i,SV1061: $i] :
      ( ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SV1398 @ SV1635 @ SV1796 )
         != ( c_Datatype__Universe_OScons @ SV1917 @ SV1972 @ SV1635 @ SV1796 ) )
        = $true )
      | ( ( SV1398 = SV1972 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8654]) ).

thf(8789,plain,
    ! [SV1076: $i,SV1410: $i,SV1921: $i] :
      ( ( ( c_in @ SV1921 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        = $false )
      | ( ( c_in @ ( c_union @ SV1921 @ SV1076 @ SV1410 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        = $true )
      | ( ( c_in @ SV1076 @ c_Finite__Set_OFinites @ ( tc_set @ SV1410 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8660]) ).

thf(8790,plain,
    ! [SV1415: $i,SV1922: $i,SV1081: $i] :
      ( ( ( c_Divides_Oop_Advd @ SV1081 @ SV1922 @ tc_nat )
        = $false )
      | ( ( c_Divides_Oop_Advd @ SV1081 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1922 @ SV1415 @ tc_nat @ tc_nat ) ) @ tc_nat )
        = $true )
      | ( ( c_Divides_Oop_Advd @ SV1081 @ SV1415 @ tc_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8661]) ).

thf(8791,plain,
    ! [SV1974: $i,SV1806: $i,SV1652: $i,SV1424: $i,SV1095: $i] :
      ( ( ( ( c_append @ SV1095 @ ( c_List_Olist_OCons @ SV1424 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 )
          = ( c_append @ SV1806 @ ( c_List_Olist_OCons @ SV1974 @ c_List_Olist_ONil @ SV1652 ) @ SV1652 ) )
        = $false )
      | ( ( SV1095 = SV1806 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8662]) ).

thf(8792,plain,
    ! [SV1923: $i,SV1807: $i,SV1653: $i,SV1425: $i,SV1096: $i] :
      ( ( ( ( c_append @ SV1096 @ ( c_List_Olist_OCons @ SV1425 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 )
          = ( c_append @ SV1807 @ ( c_List_Olist_OCons @ SV1923 @ c_List_Olist_ONil @ SV1653 ) @ SV1653 ) )
        = $false )
      | ( ( SV1425 = SV1923 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8663]) ).

thf(8793,plain,
    ! [SV1099: $i,SV1656: $i,SV1428: $i,SV1975: $i] :
      ( ( ( ~ ( c_in @ SV1975 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) ) )
        = $true )
      | ( ( c_in @ ( c_append @ SV1975 @ SV1099 @ SV1656 ) @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        = $true )
      | ( ( c_in @ SV1099 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8666]) ).

thf(8794,plain,
    ! [SV1976: $i,SV1816: $i,SV1666: $i,SV1440: $i,SV1118: $i] :
      ( ( ( ( c_List_Olist_OCons @ SV1118 @ SV1440 @ SV1666 )
          = ( c_List_Olist_OCons @ SV1816 @ SV1976 @ SV1666 ) )
        = $false )
      | ( ( SV1118 = SV1816 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8670]) ).

thf(8795,plain,
    ! [SV1925: $i,SV1817: $i,SV1667: $i,SV1441: $i,SV1119: $i] :
      ( ( ( ( c_List_Olist_OCons @ SV1119 @ SV1441 @ SV1667 )
          = ( c_List_Olist_OCons @ SV1817 @ SV1925 @ SV1667 ) )
        = $false )
      | ( ( SV1441 = SV1925 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8671]) ).

thf(8796,plain,
    ! [SV1996: $i,SV1926: $i,SV1825: $i,SV1676: $i,SV1459: $i,SV1154: $i] :
      ( ( ( ( c_Pair @ SV1154 @ SV1459 @ SV1676 @ SV1825 )
         != ( c_Pair @ SV1926 @ SV1996 @ SV1676 @ SV1825 ) )
        = $true )
      | ( ( SV1154 = SV1926 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8674]) ).

thf(8797,plain,
    ! [SV1977: $i,SV1927: $i,SV1826: $i,SV1677: $i,SV1460: $i,SV1155: $i] :
      ( ( ( ( c_Pair @ SV1155 @ SV1460 @ SV1677 @ SV1826 )
         != ( c_Pair @ SV1927 @ SV1977 @ SV1677 @ SV1826 ) )
        = $true )
      | ( ( SV1460 = SV1977 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8675]) ).

thf(8798,plain,
    ! [SV1928: $i,SV1827: $i,SV1678: $i,SV1462: $i,SV1157: $i] :
      ( ( ( c_in @ SV1157 @ ( c_Relation_OImage @ SV1462 @ ( c_insert @ SV1678 @ c_emptyset @ SV1827 ) @ SV1827 @ SV1928 ) @ SV1928 )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1678 @ SV1157 @ SV1827 @ SV1928 ) @ SV1462 @ ( tc_prod @ SV1827 @ SV1928 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8676]) ).

thf(8799,plain,
    ! [SV1929: $i,SV1828: $i,SV1679: $i,SV1463: $i,SV1158: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1158 @ SV1463 @ SV1679 @ SV1828 ) @ SV1929 @ ( tc_prod @ SV1679 @ SV1828 ) )
        = $false )
      | ( ( c_in @ SV1463 @ ( c_Relation_OImage @ SV1929 @ ( c_insert @ SV1158 @ c_emptyset @ SV1679 ) @ SV1679 @ SV1828 ) @ SV1828 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8677]) ).

thf(8800,plain,
    ! [SV1930: $i,SV1829: $i,SV1680: $i,SV1464: $i,SV1159: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1159 @ SV1464 @ SV1680 @ SV1829 ) @ ( c_Relation_Oconverse @ SV1930 @ SV1829 @ SV1680 ) @ ( tc_prod @ SV1680 @ SV1829 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1464 @ SV1159 @ SV1829 @ SV1680 ) @ SV1930 @ ( tc_prod @ SV1829 @ SV1680 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8678]) ).

thf(8801,plain,
    ! [SV1931: $i,SV1830: $i,SV1681: $i,SV1465: $i,SV1160: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1160 @ SV1465 @ SV1681 @ SV1830 ) @ SV1931 @ ( tc_prod @ SV1681 @ SV1830 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1465 @ SV1160 @ SV1830 @ SV1681 ) @ ( c_Relation_Oconverse @ SV1931 @ SV1681 @ SV1830 ) @ ( tc_prod @ SV1830 @ SV1681 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8679]) ).

thf(8802,plain,
    ! [SV1932: $i,SV1162: $i,SV1832: $i] :
      ( ( ( ( c_SetInterval_OatLeast @ SV1832 @ SV1162 )
          = ( c_SetInterval_OatLeast @ SV1932 @ SV1162 ) )
        = $false )
      | ( ( SV1832 = SV1932 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1162 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8680]) ).

thf(8803,plain,
    ! [SV1163: $i,SV1933: $i,SV1833: $i] :
      ( ( ( c_in @ SV1833 @ ( c_SetInterval_OatLeast @ SV1933 @ SV1163 ) @ SV1163 )
        = $false )
      | ( ( c_lessequals @ SV1933 @ SV1833 @ SV1163 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1163 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8681]) ).

thf(8804,plain,
    ! [SV1164: $i,SV1934: $i,SV1834: $i] :
      ( ( ( c_lessequals @ SV1834 @ SV1934 @ SV1164 )
        = $false )
      | ( ( c_in @ SV1934 @ ( c_SetInterval_OatLeast @ SV1834 @ SV1164 ) @ SV1164 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1164 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8682]) ).

thf(8805,plain,
    ! [SV1935: $i,SV1165: $i,SV1835: $i] :
      ( ( ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1835 @ SV1165 ) @ ( c_SetInterval_OatLeast @ SV1935 @ SV1165 ) @ ( tc_set @ SV1165 ) )
        = $false )
      | ( ( c_lessequals @ SV1935 @ SV1835 @ SV1165 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1165 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8683]) ).

thf(8806,plain,
    ! [SV1166: $i,SV1936: $i,SV1836: $i] :
      ( ( ( c_lessequals @ SV1836 @ SV1936 @ SV1166 )
        = $false )
      | ( ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1936 @ SV1166 ) @ ( c_SetInterval_OatLeast @ SV1836 @ SV1166 ) @ ( tc_set @ SV1166 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1166 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8684]) ).

thf(8807,plain,
    ! [SV1937: $i,SV1167: $i,SV1837: $i] :
      ( ( ( ( c_SetInterval_OatMost @ SV1837 @ SV1167 )
          = ( c_SetInterval_OatMost @ SV1937 @ SV1167 ) )
        = $false )
      | ( ( SV1837 = SV1937 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1167 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8685]) ).

thf(8808,plain,
    ! [SV1168: $i,SV1938: $i,SV1838: $i] :
      ( ( ( c_in @ SV1838 @ ( c_SetInterval_OatMost @ SV1938 @ SV1168 ) @ SV1168 )
        = $false )
      | ( ( c_lessequals @ SV1838 @ SV1938 @ SV1168 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1168 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8686]) ).

thf(8809,plain,
    ! [SV1169: $i,SV1939: $i,SV1839: $i] :
      ( ( ( c_lessequals @ SV1839 @ SV1939 @ SV1169 )
        = $false )
      | ( ( c_in @ SV1839 @ ( c_SetInterval_OatMost @ SV1939 @ SV1169 ) @ SV1169 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1169 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8687]) ).

thf(8810,plain,
    ! [SV1940: $i,SV1170: $i,SV1840: $i] :
      ( ( ( c_lessequals @ ( c_SetInterval_OatMost @ SV1840 @ SV1170 ) @ ( c_SetInterval_OatMost @ SV1940 @ SV1170 ) @ ( tc_set @ SV1170 ) )
        = $false )
      | ( ( c_lessequals @ SV1840 @ SV1940 @ SV1170 )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1170 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8688]) ).

thf(8811,plain,
    ! [SV1171: $i,SV1941: $i,SV1841: $i] :
      ( ( ( c_lessequals @ SV1841 @ SV1941 @ SV1171 )
        = $false )
      | ( ( c_lessequals @ ( c_SetInterval_OatMost @ SV1841 @ SV1171 ) @ ( c_SetInterval_OatMost @ SV1941 @ SV1171 ) @ ( tc_set @ SV1171 ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV1171 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8689]) ).

thf(8812,plain,
    ! [SV1942: $i,SV1172: $i,SV1842: $i] :
      ( ( ( ( c_SetInterval_OgreaterThan @ SV1842 @ SV1172 )
          = ( c_SetInterval_OgreaterThan @ SV1942 @ SV1172 ) )
        = $false )
      | ( ( SV1842 = SV1942 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1172 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8690]) ).

thf(8813,plain,
    ! [SV1173: $i,SV1943: $i,SV1843: $i] :
      ( ( ( c_in @ SV1843 @ ( c_SetInterval_OgreaterThan @ SV1943 @ SV1173 ) @ SV1173 )
        = $false )
      | ( ( c_less @ SV1943 @ SV1843 @ SV1173 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1173 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8691]) ).

thf(8814,plain,
    ! [SV1174: $i,SV1944: $i,SV1844: $i] :
      ( ( ( c_less @ SV1844 @ SV1944 @ SV1174 )
        = $false )
      | ( ( c_in @ SV1944 @ ( c_SetInterval_OgreaterThan @ SV1844 @ SV1174 ) @ SV1174 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1174 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8692]) ).

thf(8815,plain,
    ! [SV1945: $i,SV1175: $i,SV1845: $i] :
      ( ( ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1845 @ SV1175 ) @ ( c_SetInterval_OgreaterThan @ SV1945 @ SV1175 ) @ ( tc_set @ SV1175 ) )
        = $false )
      | ( ( c_lessequals @ SV1945 @ SV1845 @ SV1175 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1175 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8693]) ).

thf(8816,plain,
    ! [SV1176: $i,SV1946: $i,SV1846: $i] :
      ( ( ( c_lessequals @ SV1846 @ SV1946 @ SV1176 )
        = $false )
      | ( ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1946 @ SV1176 ) @ ( c_SetInterval_OgreaterThan @ SV1846 @ SV1176 ) @ ( tc_set @ SV1176 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1176 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8694]) ).

thf(8817,plain,
    ! [SV1947: $i,SV1177: $i,SV1847: $i] :
      ( ( ( ( c_SetInterval_OlessThan @ SV1847 @ SV1177 )
          = ( c_SetInterval_OlessThan @ SV1947 @ SV1177 ) )
        = $false )
      | ( ( SV1847 = SV1947 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1177 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8695]) ).

thf(8818,plain,
    ! [SV1178: $i,SV1948: $i,SV1848: $i] :
      ( ( ( c_in @ SV1848 @ ( c_SetInterval_OlessThan @ SV1948 @ SV1178 ) @ SV1178 )
        = $false )
      | ( ( c_less @ SV1848 @ SV1948 @ SV1178 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1178 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8696]) ).

thf(8819,plain,
    ! [SV1179: $i,SV1949: $i,SV1849: $i] :
      ( ( ( c_less @ SV1849 @ SV1949 @ SV1179 )
        = $false )
      | ( ( c_in @ SV1849 @ ( c_SetInterval_OlessThan @ SV1949 @ SV1179 ) @ SV1179 )
        = $true )
      | ( ( class_Orderings_Oord @ SV1179 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8697]) ).

thf(8820,plain,
    ! [SV1950: $i,SV1180: $i,SV1850: $i] :
      ( ( ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1850 @ SV1180 ) @ ( c_SetInterval_OlessThan @ SV1950 @ SV1180 ) @ ( tc_set @ SV1180 ) )
        = $false )
      | ( ( c_lessequals @ SV1850 @ SV1950 @ SV1180 )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1180 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8698]) ).

thf(8821,plain,
    ! [SV1181: $i,SV1951: $i,SV1851: $i] :
      ( ( ( c_lessequals @ SV1851 @ SV1951 @ SV1181 )
        = $false )
      | ( ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1851 @ SV1181 ) @ ( c_SetInterval_OlessThan @ SV1951 @ SV1181 ) @ ( tc_set @ SV1181 ) )
        = $true )
      | ( ( class_Orderings_Olinorder @ SV1181 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8699]) ).

thf(8822,plain,
    ! [SV1687: $i,SV1472: $i,SV1978: $i,SV1187: $i] :
      ( ( ( c_in @ SV1187 @ ( c_minus @ SV1978 @ SV1472 @ ( tc_set @ SV1687 ) ) @ SV1687 )
        = $false )
      | ( ( c_in @ SV1187 @ SV1472 @ SV1687 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8701]) ).

thf(8823,plain,
    ! [SV1474: $i,SV1689: $i,SV1979: $i,SV1189: $i] :
      ( ( ( c_in @ SV1189 @ SV1979 @ SV1689 )
        = $true )
      | ( ( c_in @ SV1189 @ ( c_minus @ SV1474 @ SV1979 @ ( tc_set @ SV1689 ) ) @ SV1689 )
        = $true )
      | ( ( c_in @ SV1189 @ SV1474 @ SV1689 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8703]) ).

thf(8824,plain,
    ! [SV1477: $i,SV1692: $i,SV1980: $i,SV1192: $i] :
      ( ( ( ~ ( c_in @ SV1192 @ SV1980 @ SV1692 ) )
        = $true )
      | ( ( c_in @ SV1192 @ ( c_inter @ SV1980 @ SV1477 @ SV1692 ) @ SV1692 )
        = $true )
      | ( ( c_in @ SV1192 @ SV1477 @ SV1692 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8706]) ).

thf(8825,plain,
    ! [SV1193: $i,SV1693: $i,SV1478: $i,SV1981: $i] :
      ( ( ( ~ ( c_in @ SV1981 @ ( c_Inter @ SV1478 @ SV1693 ) @ SV1693 ) )
        = $true )
      | ( ( c_in @ SV1981 @ SV1193 @ SV1693 )
        = $true )
      | ( ( c_in @ SV1193 @ SV1478 @ ( tc_set @ SV1693 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8707]) ).

thf(8826,plain,
    ! [SV1483: $i,SV1855: $i,SV1698: $i,SV1198: $i] :
      ( ( ( c_in @ SV1198 @ SV1698 @ SV1855 )
        = $true )
      | ( ( c_in @ SV1198 @ SV1483 @ SV1855 )
        = $true )
      | ( ( c_in @ SV1198 @ ( c_union @ SV1483 @ SV1698 @ SV1855 ) @ SV1855 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8710]) ).

thf(8827,plain,
    ! [SV1202: $i,SV1700: $i,SV1984: $i,SV1485: $i] :
      ( ( ( ~ ( c_in @ SV1485 @ SV1984 @ ( tc_set @ SV1700 ) ) )
        = $true )
      | ( ( c_in @ SV1202 @ ( c_Union @ SV1984 @ SV1700 ) @ SV1700 )
        = $true )
      | ( ( c_in @ SV1202 @ SV1485 @ SV1700 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8711]) ).

thf(8828,plain,
    ! [SV1858: $i,SV1703: $i,SV1489: $i,SV1206: $i] :
      ( ( ( SV1206 = SV1489 )
        = $true )
      | ( ( c_in @ SV1206 @ SV1703 @ SV1858 )
        = $true )
      | ( ( c_in @ SV1206 @ ( c_insert @ SV1489 @ SV1703 @ SV1858 ) @ SV1858 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8713]) ).

thf(8829,plain,
    ! [SV1867: $i,SV1715: $i,SV1221: $i,SV1504: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1504 @ SV1221 @ SV1715 @ SV1715 ) @ ( c_Transitive__Closure_Ortrancl @ SV1867 @ SV1715 ) @ ( tc_prod @ SV1715 @ SV1715 ) )
        = $false )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1221 @ SV1504 @ SV1715 @ SV1715 ) @ SV1867 @ ( tc_prod @ SV1715 @ SV1715 ) ) @ SV1715 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8721]) ).

thf(8830,plain,
    ! [SV1222: $i,SV1505: $i,SV1986: $i,SV1953: $i] :
      ( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1953 @ SV1986 @ SV1505 @ SV1505 ) @ SV1222 @ ( tc_prod @ SV1505 @ SV1505 ) ) @ SV1505 )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1986 @ SV1953 @ SV1505 @ SV1505 ) @ ( c_Transitive__Closure_Ortrancl @ SV1222 @ SV1505 ) @ ( tc_prod @ SV1505 @ SV1505 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Oacyclic @ SV1222 @ SV1505 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8722]) ).

thf(8831,plain,
    ! [SV1869: $i,SV1717: $i,SV1224: $i,SV1507: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1507 @ SV1224 @ SV1717 @ SV1717 ) @ ( c_Transitive__Closure_Ortrancl @ SV1869 @ SV1717 ) @ ( tc_prod @ SV1717 @ SV1717 ) )
        = $false )
      | ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1224 @ SV1507 @ SV1717 @ SV1717 ) @ SV1869 @ ( tc_prod @ SV1717 @ SV1717 ) ) @ SV1717 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8724]) ).

thf(8832,plain,
    ! [SV1225: $i,SV1508: $i,SV1987: $i,SV1954: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1954 @ SV1987 @ SV1508 @ SV1508 ) @ SV1225 @ ( tc_prod @ SV1508 @ SV1508 ) ) @ SV1508 )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1987 @ SV1954 @ SV1508 @ SV1508 ) @ ( c_Transitive__Closure_Ortrancl @ SV1225 @ SV1508 ) @ ( tc_prod @ SV1508 @ SV1508 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV1225 @ SV1508 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8725]) ).

thf(8833,plain,
    ! [SV1523: $i,SV1726: $i,SV1244: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1244 ) ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ SV1523 @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1244 @ SV1523 ) @ ( c_Message_Oanalz @ SV1726 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8730]) ).

thf(8834,plain,
    ! [SV1261: $i,SV1539: $i,SV1957: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_OKey @ SV1957 ) @ SV1539 @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1957 @ SV1261 ) @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ SV1261 @ ( c_Message_Osynth @ SV1539 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8736]) ).

thf(8835,plain,
    ! [SV1264: $i,SV1542: $i,SV1958: $i] :
      ( ( ( c_in @ SV1958 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        = $false )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1958 @ SV1264 ) @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ SV1264 @ ( c_Message_Osynth @ SV1542 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8737]) ).

thf(8836,plain,
    ! [SV1544: $i,SV1266: $i,SV1988: $i,SV1959: $i] :
      ( ( ( ~ ( c_lessequals @ ( c_Message_Oanalz @ SV1959 ) @ ( c_Message_Oanalz @ SV1988 ) @ ( tc_set @ tc_Message_Omsg ) ) )
        = $true )
      | ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SV1959 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SV1988 @ SV1544 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SV1544 ) @ ( tc_set @ tc_Message_Omsg ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8738]) ).

thf(8837,plain,
    ! [SV1960: $i,SV1875: $i,SV1737: $i,SV1551: $i,SV1273: $i,SV6: $i] :
      ( ( ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $false )
      | ( ( ! [SY3451: $i,SY3452: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV1960 @ SY3451 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SY3452 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
              | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1960 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SY3451 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3452 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8742]) ).

thf(8838,plain,
    ! [SV1552: $i,SV1876: $i,SV1738: $i,SV1274: $i,SV7: $i] :
      ( ( ( SV7
          = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1274 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
        = $true )
      | ( ( SV7
          = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1552 @ SV7 @ SV1738 @ SV1876 ) @ SV1738 @ SV1876 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
        = $true )
      | ( ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1274 @ SV1552 @ SV1738 @ SV1876 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1738 @ SV1876 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8743]) ).

thf(8839,plain,
    ! [SV1553: $i,SV1877: $i,SV1739: $i,SV1275: $i,SV8: $i] :
      ( ( ( SV8
          = ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1275 @ SV8 @ SV1739 @ SV1877 ) @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( c_Main_OdsumE__4 @ SV1553 @ SV8 @ SV1739 @ SV1877 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) @ SV1553 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
        = $true )
      | ( ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1275 @ SV1553 @ SV1739 @ SV1877 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1739 @ SV1877 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8744]) ).

thf(8840,plain,
    ! [SV1276: $i,SV1878: $i,SV1740: $i,SV1554: $i,SV9: $i] :
      ( ( ( SV9
          = ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1554 @ SV9 @ SV1740 @ SV1878 ) @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( c_Main_OdsumE__2 @ SV1276 @ SV9 @ SV1740 @ SV1878 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) @ SV1276 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
        = $true )
      | ( ( c_in @ SV9 @ ( c_Datatype__Universe_Odsum @ SV1276 @ SV1554 @ SV1740 @ SV1878 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1740 @ SV1878 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8745]) ).

thf(8841,plain,
    ! [SV1555: $i,SV1879: $i,SV1741: $i,SV10: $i,SV1277: $i] :
      ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__2 @ SV1277 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1277 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( c_Main_OdsumE__4 @ SV1555 @ SV10 @ SV1741 @ SV1879 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) @ SV1555 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
        = $true )
      | ( ( c_in @ SV10 @ ( c_Datatype__Universe_Odsum @ SV1277 @ SV1555 @ SV1741 @ SV1879 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1741 @ SV1879 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8746]) ).

thf(8842,plain,
    ! [SV1997: $i,SV1880: $i,SV1278: $i,SV1742: $i,SV1556: $i,SV11: $i] :
      ( ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV11 @ SV1556 @ SV1742 ) @ ( c_Datatype__Universe_OIn0 @ SV1278 @ SV1556 @ SV1742 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1880 @ SV1997 @ SV1556 @ SV1742 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV11 @ SV1278 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) @ SV1880 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1556 @ SV1742 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8747]) ).

thf(8843,plain,
    ! [SV1881: $i,SV1998: $i,SV1279: $i,SV1743: $i,SV1557: $i,SV12: $i] :
      ( ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV12 @ SV1557 @ SV1743 ) @ ( c_Datatype__Universe_OIn1 @ SV1279 @ SV1557 @ SV1743 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1998 @ SV1881 @ SV1557 @ SV1743 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV12 @ SV1279 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) @ SV1881 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1557 @ SV1743 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8748]) ).

thf(8844,plain,
    ! [SV1283: $i,SV16: $i,SV1747: $i,SV1561: $i,SV1999: $i,SV1989: $i] :
      ( ( ( ~ ( c_in @ SV1989 @ SV1999 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
          | ( c_in @ ( c_Datatype__Universe_OScons @ SV1989 @ SV16 @ SV1561 @ SV1747 ) @ ( c_Datatype__Universe_Ouprod @ SV1999 @ SV1283 @ SV1561 @ SV1747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) ) )
        = $true )
      | ( ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8752]) ).

thf(8845,plain,
    ! [SV1562: $i,SV1885: $i,SV1748: $i,SV1284: $i,SV17: $i] :
      ( ( ( SV17
          = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1284 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) )
        = $true )
      | ( ( SV17
          = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1562 @ SV17 @ SV1748 @ SV1885 ) @ SV1748 @ SV1885 ) )
        = $true )
      | ( ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1284 @ SV1562 @ SV1748 @ SV1885 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1748 @ SV1885 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8753]) ).

thf(8846,plain,
    ! [SV1563: $i,SV1886: $i,SV1749: $i,SV1285: $i,SV18: $i] :
      ( ( ( SV18
          = ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1285 @ SV18 @ SV1749 @ SV1886 ) @ SV1749 @ SV1886 ) )
        = $true )
      | ( ( c_in @ ( c_Main_OusumE__2 @ SV1563 @ SV18 @ SV1749 @ SV1886 ) @ SV1563 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) )
        = $true )
      | ( ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1285 @ SV1563 @ SV1749 @ SV1886 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1749 @ SV1886 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8754]) ).

thf(8847,plain,
    ! [SV1286: $i,SV1887: $i,SV1750: $i,SV1564: $i,SV19: $i] :
      ( ( ( SV19
          = ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1564 @ SV19 @ SV1750 @ SV1887 ) @ SV1750 @ SV1887 ) )
        = $true )
      | ( ( c_in @ ( c_Main_OusumE__1 @ SV1286 @ SV19 @ SV1750 @ SV1887 ) @ SV1286 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) )
        = $true )
      | ( ( c_in @ SV19 @ ( c_Datatype__Universe_Ousum @ SV1286 @ SV1564 @ SV1750 @ SV1887 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1750 @ SV1887 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8755]) ).

thf(8848,plain,
    ! [SV1565: $i,SV1888: $i,SV1751: $i,SV20: $i,SV1287: $i] :
      ( ( ( c_in @ ( c_Main_OusumE__1 @ SV1287 @ SV20 @ SV1751 @ SV1888 ) @ SV1287 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
        = $true )
      | ( ( c_in @ ( c_Main_OusumE__2 @ SV1565 @ SV20 @ SV1751 @ SV1888 ) @ SV1565 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
        = $true )
      | ( ( c_in @ SV20 @ ( c_Datatype__Universe_Ousum @ SV1287 @ SV1565 @ SV1751 @ SV1888 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1751 @ SV1888 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8756]) ).

thf(8849,plain,
    ! [SV1892: $i,SV1300: $i,SV36: $i,SV2000: $i] :
      ( ( ( ~ ( c_in @ SV2000 @ SV36 @ SV1300 )
          | ( SV1892 = SV2000 ) )
        = $true )
      | ( ( c_in @ SV1892 @ SV36 @ SV1300 )
        = $false )
      | ( ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8759]) ).

thf(8850,plain,
    ! [SV1308: $i,SV1568: $i,SV46: $i,SV1961: $i] :
      ( ( ( c_in @ SV1961 @ ( c_List_Oset @ SV46 @ SV1568 ) @ SV1568 )
        = $false )
      | ( ( c_in @ SV1961 @ SV1308 @ SV1568 )
        = $true )
      | ( ( c_in @ SV46 @ ( c_List_Olists @ SV1308 @ SV1568 ) @ ( tc_List_Olist @ SV1568 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8760]) ).

thf(8851,plain,
    ! [SV60: $i,SV1581: $i,SV1320: $i,SV1962: $i] :
      ( ( ( c_in @ SV1962 @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) )
        = $false )
      | ( ( c_in @ ( c_List_Olist_OCons @ SV60 @ SV1962 @ SV1581 ) @ ( c_List_Olists @ SV1320 @ SV1581 ) @ ( tc_List_Olist @ SV1581 ) )
        = $true )
      | ( ( c_in @ SV60 @ SV1320 @ SV1581 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8767]) ).

thf(8852,plain,
    ! [SV1329: $i,SV2001: $i,SV1992: $i,SV1586: $i,SV1769: $i,SV74: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV74 @ SV1769 @ SV1586 @ SV1992 ) @ SV2001 @ ( tc_prod @ SV1586 @ SV1992 ) )
          | ( c_in @ SV1769 @ ( c_Relation_OImage @ SV2001 @ SV1329 @ SV1586 @ SV1992 ) @ SV1992 ) )
        = $true )
      | ( ( c_in @ SV74 @ SV1329 @ SV1586 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8771]) ).

thf(8853,plain,
    ! [SV1963: $i,SV1903: $i,SV1774: $i,SV1594: $i,SV1337: $i,SV82: $i] :
      ( ( ( c_in @ SV82 @ ( c_Relation_Orel__comp @ SV1337 @ SV1594 @ SV1774 @ SV1903 @ SV1963 ) @ ( tc_prod @ SV1963 @ SV1903 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SV1963 ) @ ( c_Main_Orel__compE__3 @ SV1337 @ SV1594 @ SV82 @ SV1774 @ SV1903 @ SV1963 ) @ SV1774 @ SV1903 ) @ SV1337 @ ( tc_prod @ SV1774 @ SV1903 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8773]) ).

thf(8854,plain,
    ! [SV1964: $i,SV1904: $i,SV1775: $i,SV1595: $i,SV1338: $i,SV83: $i] :
      ( ( ( c_in @ SV83 @ ( c_Relation_Orel__comp @ SV1338 @ SV1595 @ SV1775 @ SV1904 @ SV1964 ) @ ( tc_prod @ SV1964 @ SV1904 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SV1964 ) @ ( c_Main_Orel__compE__2 @ SV1338 @ SV1595 @ SV83 @ SV1775 @ SV1904 @ SV1964 ) @ SV1964 @ SV1775 ) @ SV1595 @ ( tc_prod @ SV1964 @ SV1775 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8774]) ).

thf(8855,plain,
    ! [SV1965: $i,SV1905: $i,SV1776: $i,SV1596: $i,SV1339: $i,SV84: $i] :
      ( ( ( c_in @ SV84 @ ( c_Relation_Orel__comp @ SV1339 @ SV1596 @ SV1776 @ SV1905 @ SV1965 ) @ ( tc_prod @ SV1965 @ SV1905 ) )
        = $false )
      | ( ( SV84
          = ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SV1965 ) @ ( c_Main_Orel__compE__3 @ SV1339 @ SV1596 @ SV84 @ SV1776 @ SV1905 @ SV1965 ) @ SV1965 @ SV1905 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8775]) ).

thf(8856,plain,
    ! [SV1966: $i,SV1906: $i,SV1777: $i,SV1597: $i,SV1340: $i,SV85: $i] :
      ( ( ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) )
        = $false )
      | ( ( ! [SY3453: $i,SY3454: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV85 @ SY3453 @ SV1597 ) @ SY3454 @ ( tc_prod @ SY3453 @ SV1597 ) )
              | ( c_in @ ( c_Pair @ SV1966 @ SV1340 @ SY3453 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SY3454 @ SV1597 @ SV1777 @ SY3453 ) @ ( tc_prod @ SY3453 @ SV1777 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8776]) ).

thf(8857,plain,
    ! [SV108: $i,SV1606: $i,SV1967: $i,SV1361: $i] :
      ( ( ( c_lessequals @ SV1361 @ SV1967 @ ( tc_set @ SV1606 ) )
        = $false )
      | ( ( c_in @ SV108 @ SV1967 @ SV1606 )
        = $true )
      | ( ( c_in @ SV108 @ SV1361 @ SV1606 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8777]) ).

thf(8858,plain,
    ! [SV1612: $i,SV1907: $i,SV1779: $i,SV1368: $i,SV115: $i] :
      ( ( ( SV115
          = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1368 @ SV115 @ SV1779 @ SV1907 ) @ SV1779 @ SV1907 ) )
        = $true )
      | ( ( SV115
          = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1612 @ SV115 @ SV1907 @ SV1779 ) @ SV1907 @ SV1779 ) )
        = $true )
      | ( ( c_in @ SV115 @ ( c_Sum__Type_OPlus @ SV1368 @ SV1612 @ SV1779 @ SV1907 ) @ ( tc_sum @ SV1779 @ SV1907 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8781]) ).

thf(8859,plain,
    ! [SV1613: $i,SV1908: $i,SV1780: $i,SV1369: $i,SV116: $i] :
      ( ( ( SV116
          = ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1369 @ SV116 @ SV1780 @ SV1908 ) @ SV1780 @ SV1908 ) )
        = $true )
      | ( ( c_in @ ( c_Main_OPlusE__2 @ SV1613 @ SV116 @ SV1908 @ SV1780 ) @ SV1613 @ SV1908 )
        = $true )
      | ( ( c_in @ SV116 @ ( c_Sum__Type_OPlus @ SV1369 @ SV1613 @ SV1780 @ SV1908 ) @ ( tc_sum @ SV1780 @ SV1908 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8782]) ).

thf(8860,plain,
    ! [SV1370: $i,SV1781: $i,SV1909: $i,SV1614: $i,SV117: $i] :
      ( ( ( SV117
          = ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1614 @ SV117 @ SV1909 @ SV1781 ) @ SV1909 @ SV1781 ) )
        = $true )
      | ( ( c_in @ ( c_Main_OPlusE__1 @ SV1370 @ SV117 @ SV1781 @ SV1909 ) @ SV1370 @ SV1781 )
        = $true )
      | ( ( c_in @ SV117 @ ( c_Sum__Type_OPlus @ SV1370 @ SV1614 @ SV1781 @ SV1909 ) @ ( tc_sum @ SV1781 @ SV1909 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8783]) ).

thf(8861,plain,
    ! [SV1615: $i,SV1910: $i,SV1782: $i,SV118: $i,SV1371: $i] :
      ( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1371 @ SV118 @ SV1782 @ SV1910 ) @ SV1371 @ SV1782 )
        = $true )
      | ( ( c_in @ ( c_Main_OPlusE__2 @ SV1615 @ SV118 @ SV1910 @ SV1782 ) @ SV1615 @ SV1910 )
        = $true )
      | ( ( c_in @ SV118 @ ( c_Sum__Type_OPlus @ SV1371 @ SV1615 @ SV1782 @ SV1910 ) @ ( tc_sum @ SV1782 @ SV1910 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8784]) ).

thf(8862,plain,
    ! [SV1376: $i,SV124: $i,SV1970: $i,SV1911: $i] :
      ( ( ( c_Relation_Otrans @ SV1911 @ SV1970 )
        = $false )
      | ( ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1911 @ SV124 @ SV1970 @ SV1376 ) @ ( tc_prod @ SV1970 @ SV1376 ) )
        = $true )
      | ( ( c_Relation_Otrans @ SV124 @ SV1376 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8785]) ).

thf(8863,plain,
    ! [SV1377: $i,SV125: $i,SV1971: $i,SV1912: $i] :
      ( ( ( c_Wellfounded__Recursion_Owf @ SV1912 @ SV1971 )
        = $false )
      | ( ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1912 @ SV125 @ SV1971 @ SV1377 ) @ ( tc_prod @ SV1971 @ SV1377 ) )
        = $true )
      | ( ( c_Wellfounded__Recursion_Owf @ SV125 @ SV1377 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8786]) ).

thf(8864,plain,
    ! [SV1995: $i,SV1916: $i,SV1795: $i,SV1634: $i,SV1397: $i,SV1060: $i] :
      ( ( ( ( c_Datatype__Universe_OScons @ SV1060 @ SV1397 @ SV1634 @ SV1795 )
          = ( c_Datatype__Universe_OScons @ SV1916 @ SV1995 @ SV1634 @ SV1795 ) )
        = $false )
      | ( ( SV1060 = SV1916 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8787]) ).

thf(8865,plain,
    ! [SV1972: $i,SV1917: $i,SV1796: $i,SV1635: $i,SV1398: $i,SV1061: $i] :
      ( ( ( ( c_Datatype__Universe_OScons @ SV1061 @ SV1398 @ SV1635 @ SV1796 )
          = ( c_Datatype__Universe_OScons @ SV1917 @ SV1972 @ SV1635 @ SV1796 ) )
        = $false )
      | ( ( SV1398 = SV1972 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8788]) ).

thf(8866,plain,
    ! [SV1099: $i,SV1656: $i,SV1428: $i,SV1975: $i] :
      ( ( ( c_in @ SV1975 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        = $false )
      | ( ( c_in @ ( c_append @ SV1975 @ SV1099 @ SV1656 ) @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        = $true )
      | ( ( c_in @ SV1099 @ ( c_List_Olists @ SV1428 @ SV1656 ) @ ( tc_List_Olist @ SV1656 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8793]) ).

thf(8867,plain,
    ! [SV1996: $i,SV1926: $i,SV1825: $i,SV1676: $i,SV1459: $i,SV1154: $i] :
      ( ( ( ( c_Pair @ SV1154 @ SV1459 @ SV1676 @ SV1825 )
          = ( c_Pair @ SV1926 @ SV1996 @ SV1676 @ SV1825 ) )
        = $false )
      | ( ( SV1154 = SV1926 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8796]) ).

thf(8868,plain,
    ! [SV1977: $i,SV1927: $i,SV1826: $i,SV1677: $i,SV1460: $i,SV1155: $i] :
      ( ( ( ( c_Pair @ SV1155 @ SV1460 @ SV1677 @ SV1826 )
          = ( c_Pair @ SV1927 @ SV1977 @ SV1677 @ SV1826 ) )
        = $false )
      | ( ( SV1460 = SV1977 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8797]) ).

thf(8869,plain,
    ! [SV1477: $i,SV1692: $i,SV1980: $i,SV1192: $i] :
      ( ( ( c_in @ SV1192 @ SV1980 @ SV1692 )
        = $false )
      | ( ( c_in @ SV1192 @ ( c_inter @ SV1980 @ SV1477 @ SV1692 ) @ SV1692 )
        = $true )
      | ( ( c_in @ SV1192 @ SV1477 @ SV1692 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8824]) ).

thf(8870,plain,
    ! [SV1193: $i,SV1693: $i,SV1478: $i,SV1981: $i] :
      ( ( ( c_in @ SV1981 @ ( c_Inter @ SV1478 @ SV1693 ) @ SV1693 )
        = $false )
      | ( ( c_in @ SV1981 @ SV1193 @ SV1693 )
        = $true )
      | ( ( c_in @ SV1193 @ SV1478 @ ( tc_set @ SV1693 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8825]) ).

thf(8871,plain,
    ! [SV1202: $i,SV1700: $i,SV1984: $i,SV1485: $i] :
      ( ( ( c_in @ SV1485 @ SV1984 @ ( tc_set @ SV1700 ) )
        = $false )
      | ( ( c_in @ SV1202 @ ( c_Union @ SV1984 @ SV1700 ) @ SV1700 )
        = $true )
      | ( ( c_in @ SV1202 @ SV1485 @ SV1700 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8827]) ).

thf(8872,plain,
    ! [SV1544: $i,SV1266: $i,SV1988: $i,SV1959: $i] :
      ( ( ( c_lessequals @ ( c_Message_Oanalz @ SV1959 ) @ ( c_Message_Oanalz @ SV1988 ) @ ( tc_set @ tc_Message_Omsg ) )
        = $false )
      | ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_union @ SV1959 @ SV1266 @ tc_Message_Omsg ) ) @ ( c_Message_Oanalz @ ( c_union @ SV1988 @ SV1544 @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
        = $true )
      | ( ( c_lessequals @ ( c_Message_Oanalz @ SV1266 ) @ ( c_Message_Oanalz @ SV1544 ) @ ( tc_set @ tc_Message_Omsg ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8836]) ).

thf(8873,plain,
    ! [SV1875: $i,SV1273: $i,SV6: $i,SV1737: $i,SV1551: $i,SV2002: $i,SV1960: $i] :
      ( ( ( ! [SY3459: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV1960 @ SV2002 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SY3459 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
              | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1960 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SV2002 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3459 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8837]) ).

thf(8874,plain,
    ! [SV1283: $i,SV16: $i,SV1747: $i,SV1561: $i,SV1999: $i,SV1989: $i] :
      ( ( ( ~ ( c_in @ SV1989 @ SV1999 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Datatype__Universe_OScons @ SV1989 @ SV16 @ SV1561 @ SV1747 ) @ ( c_Datatype__Universe_Ouprod @ SV1999 @ SV1283 @ SV1561 @ SV1747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $true )
      | ( ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8844]) ).

thf(8875,plain,
    ! [SV1892: $i,SV1300: $i,SV36: $i,SV2000: $i] :
      ( ( ( ~ ( c_in @ SV2000 @ SV36 @ SV1300 ) )
        = $true )
      | ( ( SV1892 = SV2000 )
        = $true )
      | ( ( c_in @ SV1892 @ SV36 @ SV1300 )
        = $false )
      | ( ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8849]) ).

thf(8876,plain,
    ! [SV1329: $i,SV2001: $i,SV1992: $i,SV1586: $i,SV1769: $i,SV74: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV74 @ SV1769 @ SV1586 @ SV1992 ) @ SV2001 @ ( tc_prod @ SV1586 @ SV1992 ) ) )
        = $true )
      | ( ( c_in @ SV1769 @ ( c_Relation_OImage @ SV2001 @ SV1329 @ SV1586 @ SV1992 ) @ SV1992 )
        = $true )
      | ( ( c_in @ SV74 @ SV1329 @ SV1586 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8852]) ).

thf(8877,plain,
    ! [SV1906: $i,SV1777: $i,SV1340: $i,SV1597: $i,SV2003: $i,SV85: $i,SV1966: $i] :
      ( ( ( ! [SY3460: $i] :
              ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV85 @ SV2003 @ SV1597 ) @ SY3460 @ ( tc_prod @ SV2003 @ SV1597 ) )
              | ( c_in @ ( c_Pair @ SV1966 @ SV1340 @ SV2003 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SY3460 @ SV1597 @ SV1777 @ SV2003 ) @ ( tc_prod @ SV2003 @ SV1777 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8856]) ).

thf(8878,plain,
    ! [SV1875: $i,SV1273: $i,SV6: $i,SV2004: $i,SV1737: $i,SV1551: $i,SV2002: $i,SV1960: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1960 @ SV2002 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV2004 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
          | ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1960 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SV2002 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV2004 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8873]) ).

thf(8879,plain,
    ! [SV1283: $i,SV16: $i,SV1747: $i,SV1561: $i,SV1999: $i,SV1989: $i] :
      ( ( ( c_in @ SV1989 @ SV1999 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $false )
      | ( ( c_in @ ( c_Datatype__Universe_OScons @ SV1989 @ SV16 @ SV1561 @ SV1747 ) @ ( c_Datatype__Universe_Ouprod @ SV1999 @ SV1283 @ SV1561 @ SV1747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $true )
      | ( ( c_in @ SV16 @ SV1283 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1561 @ SV1747 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8874]) ).

thf(8880,plain,
    ! [SV1892: $i,SV1300: $i,SV36: $i,SV2000: $i] :
      ( ( ( c_in @ SV2000 @ SV36 @ SV1300 )
        = $false )
      | ( ( SV1892 = SV2000 )
        = $true )
      | ( ( c_in @ SV1892 @ SV36 @ SV1300 )
        = $false )
      | ( ( c_Infinite__Set_Oatmost__one @ SV36 @ SV1300 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8875]) ).

thf(8881,plain,
    ! [SV1329: $i,SV2001: $i,SV1992: $i,SV1586: $i,SV1769: $i,SV74: $i] :
      ( ( ( c_in @ ( c_Pair @ SV74 @ SV1769 @ SV1586 @ SV1992 ) @ SV2001 @ ( tc_prod @ SV1586 @ SV1992 ) )
        = $false )
      | ( ( c_in @ SV1769 @ ( c_Relation_OImage @ SV2001 @ SV1329 @ SV1586 @ SV1992 ) @ SV1992 )
        = $true )
      | ( ( c_in @ SV74 @ SV1329 @ SV1586 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8876]) ).

thf(8882,plain,
    ! [SV1906: $i,SV1777: $i,SV1340: $i,SV2005: $i,SV1597: $i,SV2003: $i,SV85: $i,SV1966: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV85 @ SV2003 @ SV1597 ) @ SV2005 @ ( tc_prod @ SV2003 @ SV1597 ) )
          | ( c_in @ ( c_Pair @ SV1966 @ SV1340 @ SV2003 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SV2005 @ SV1597 @ SV1777 @ SV2003 ) @ ( tc_prod @ SV2003 @ SV1777 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8877]) ).

thf(8883,plain,
    ! [SV1875: $i,SV1273: $i,SV6: $i,SV2004: $i,SV1737: $i,SV1551: $i,SV2002: $i,SV1960: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1960 @ SV2002 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV2004 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1960 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SV2002 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV2004 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8878]) ).

thf(8884,plain,
    ! [SV1906: $i,SV1777: $i,SV1340: $i,SV2005: $i,SV1597: $i,SV2003: $i,SV85: $i,SV1966: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV85 @ SV2003 @ SV1597 ) @ SV2005 @ ( tc_prod @ SV2003 @ SV1597 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1966 @ SV1340 @ SV2003 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SV2005 @ SV1597 @ SV1777 @ SV2003 ) @ ( tc_prod @ SV2003 @ SV1777 ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8882]) ).

thf(8885,plain,
    ! [SV1875: $i,SV1273: $i,SV6: $i,SV2004: $i,SV1737: $i,SV1551: $i,SV2002: $i,SV1960: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1960 @ SV2002 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV2004 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1960 @ SV6 @ SV1551 @ SV1737 ) @ ( c_Datatype__Universe_OScons @ SV2002 @ SV1273 @ SV1551 @ SV1737 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV2004 @ SV1875 @ SV1551 @ SV1737 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV6 @ SV1273 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) @ SV1875 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1551 @ SV1737 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8883]) ).

thf(8886,plain,
    ! [SV1906: $i,SV1777: $i,SV1340: $i,SV2005: $i,SV1597: $i,SV2003: $i,SV85: $i,SV1966: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1966 @ SV85 @ SV2003 @ SV1597 ) @ SV2005 @ ( tc_prod @ SV2003 @ SV1597 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1966 @ SV1340 @ SV2003 @ SV1777 ) @ ( c_Relation_Orel__comp @ SV1906 @ SV2005 @ SV1597 @ SV1777 @ SV2003 ) @ ( tc_prod @ SV2003 @ SV1777 ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV85 @ SV1340 @ SV1597 @ SV1777 ) @ SV1906 @ ( tc_prod @ SV1597 @ SV1777 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8884]) ).

thf(8887,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[3098,8886,8885,8881,8880,8879,8872,8871,8870,8869,8868,8867,8866,8865,8864,8863,8862,8861,8860,8859,8858,8857,8855,8854,8853,8851,8850,8848,8847,8846,8845,8843,8842,8841,8840,8839,8838,8835,8834,8833,8832,8831,8830,8829,8828,8826,8823,8822,8821,8820,8819,8818,8817,8816,8815,8814,8813,8812,8811,8810,8809,8808,8807,8806,8805,8804,8803,8802,8801,8800,8799,8798,8795,8794,8792,8791,8790,8789,8780,8779,8778,8772,8770,8769,8768,8766,8765,8764,8763,8762,8761,8758,8757,8751,8750,8749,8741,8740,8739,8735,8734,8733,8732,8731,8729,8728,8727,8726,8723,8720,8719,8718,8717,8716,8715,8714,8712,8709,8708,8705,8704,8702,8700,8673,8672,8669,8668,8667,8665,8664,8659,8658,8657,8656,8655,8652,8651,8650,8649,8648,8647,8646,8645,8644,8641,8640,8631,8630,8625,8624,8622,8617,8615,8614,8605,8584,8583,8571,8570,8569,8568,8567,8558,8556,8554,8551,8545,8544,8540,8539,8531,8530,8529,8507,8500,8499,8498,8497,8495,8489,8488,8486,8485,8479,8478,8476,8475,8474,8473,8471,8470,8467,8466,8459,8457,8456,8454,8450,8449,8441,8433,8431,8430,8428,8426,8425,8424,8419,8418,8417,8404,8403,8396,8392,8391,8390,8389,8366,8363,8362,8360,8359,8354,8353,8352,8351,8350,8348,8347,8345,8344,8337,8333,8332,8325,8324,8293,8263,8262,8261,8260,8258,8257,8256,8255,8254,8253,8252,8247,8243,8242,8241,8240,8239,8226,8225,8222,8221,8220,8219,8218,8217,8208,8207,8169,8159,8144,8141,8140,8139,8126,8124,8117,8041,8039,8037,7988,7987,7986,7985,7984,7966,7958,7937,7919,7902,7901,7900,7899,7897,7896,7895,7894,7893,7892,7891,7890,7889,7888,7887,7886,7885,7884,7883,7882,7881,7880,7879,7878,7877,7876,7875,7874,7873,7872,7871,7870,7869,7868,7867,7866,7865,7864,7863,7862,7861,7860,7859,7858,7857,7856,7855,7854,7853,7852,7851,7850,7849,7848,7847,7846,7845,7844,7843,7842,7841,7840,7839,7838,7837,7836,7835,7834,7833,7832,7831,7830,7829,7828,7827,7826,7825,7824,7823,7822,7821,7820,7819,7818,7817,7816,7815,7814,7813,7812,7811,7810,7809,7808,7807,7806,7805,7804,7803,7802,7801,7800,7799,7798,7797,7796,7795,7794,7793,7792,7791,7790,7789,7788,7787,7786,7785,7784,7783,7782,7781,7780,7779,7778,7777,7776,7775,7774,7773,7772,7771,7770,7769,7768,7767,7766,7765,7764,7763,7762,7761,7760,7759,7758,7757,7756,7755,7754,7753,7752,7751,7750,7749,7748,7747,7746,7745,7744,7743,7742,7741,7740,7739,7738,7737,7736,7735,7734,7733,7732,7731,7730,7729,7728,7727,7726,7725,7724,7723,7722,7721,7720,7719,7718,7717,7716,7715,7714,7713,7712,7711,7710,7709,7708,7707,7706,7705,7704,7703,7702,7701,7700,7699,7698,7697,7696,7695,7694,7693,7692,7691,7690,7689,7688,7687,7686,7685,7684,7683,7682,7681,7680,7679,7678,7677,7676,7675,7674,7673,7672,7671,7670,7669,7668,7667,7666,7665,7664,7663,7662,7661,7660,7659,7658,7657,7656,7655,7654,7653,7652,7651,7650,7649,7648,7647,7646,7645,7644,7643,7642,7641,7640,7639,7638,7637,7636,7635,7634,7633,7632,7631,7630,7629,7628,7627,7626,7625,7624,7623,7622,7621,7620,7619,7618,7617,7616,7615,7614,7613,7612,7611,7610,7609,7608,7607,7606,7605,7604,7603,7602,7601,7600,7599,7598,7597,7596,7595,7594,7593,7592,7591,7590,7589,7588,7587,7586,7585,7584,7583,7582,7581,7580,7579,7578,7577,7576,7575,7574,7573,7572,7571,7570,7569,7568,7567,7566,7565,7564,7563,7562,7561,7560,7559,7558,7557,7556,7555,7554,7553,7552,7551,7550,7549,7548,7547,7546,7545,7544,7543,7542,7541,7540,7539,7538,7537,7536,7535,7534,7533,7532,7531,7530,7529,7528,7527,7526,7525,7524,7523,7522,7521,7520,7519,7518,7517,7516,7515,7514,7513,7512,7511,7510,7509,7508,7507,7506,7505,7504,7503,7502,7501,7500,7499,7498,7497,7496,7495,7494,7493,7492,7491,7490,7489,7488,7487,7486,7485,7484,7483,7482,7481,7480,7479,7478,7477,7476,7475,7474,7473,7472,7471,7470,7469,7468,7467,7466,7465,7464,7463,7462,7461,7460,7459,7458,7457,7456,7455,7454,7453,7452,7451,7450,7449,7448,7447,7446,7445,7444,7443,7442,7441,7440,7439,7438,7437,7436,7435,7434,7433,7432,7431,7430,7429,7428,7427,7426,7425,7424,7423,7422,7421,7420,7419,7418,7417,7416,7415,7414,7413,7412,7411,7410,7409,7408,7407,7406,7405,7404,7403,7402,7401,7400,7399,7398,7397,7396,7395,7394,7393,7392,7391,7390,7389,7388,7387,7386,7385,7384,7383,7382,7381,7380,7379,7378,7377,7376,7375,7374,7373,7372,7371,7370,7369,7368,7367,7366,7365,7364,7363,7362,7361,7360,7359,7358,7357,7356,7355,7354,7353,7352,7351,7350,7349,7348,7347,7346,7345,7344,7343,7342,7341,7340,7339,7338,7337,7336,7335,7334,7333,7332,7331,7330,7329,7328,7327,7326,7325,7324,7323,7322,7321,7320,7319,7318,7317,7316,7315,7314,7313,7312,7311,7310,7309,7308,7307,7306,7305,7304,7303,7302,7301,7300,7299,7298,7297,7296,7295,7294,7293,7292,7291,7290,7289,7288,7287,7286,7285,7284,7283,7282,7281,7280,7279,7278,7277,7276,7275,7274,7273,7272,7271,7270,7269,7268,7267,7266,7265,7264,7263,7262,7261,7260,7259,7258,7257,7256,7255,7254,7253,7252,7251,7250,7249,7248,7247,7246,7245,7244,7243,7242,7241,7240,7239,7238,7237,7236,7235,7234,7233,7232,7231,7230,7229,7228,7227,7226,7225,7224,7223,7222,7221,7220,7219,7218,7217,7216,7215,7214,7213,7212,7211,7210,7209,7208,7207,7206,7205,7204,7203,7202,7201,7200,7199,7198,7197,7196,7195,7194,7193,7192,7191,7190,7189,7188,7187,7186,7185,7184,7183,7182,7181,7180,7179,7178,7177,7176,7175,7174,7173,7172,7171,7170,7169,7168,7167,7166,7165,7164,7163,7162,7161,7160,7159,7158,7157,7156,7155,7154,7153,7152,7151,7150,7149,7148,7147,7146,7145,7144,7143,7142,7141,7140,7139,7138,7137,7136,7135,7134,7133,7132,7131,7130,7129,7128,7127,7126,7125,7124,7123,7122,7121,7120,7119,7118,7117,7116,7115,7114,7113,7112,7111,7110,7109,7108,7107,7106,7105,7104,7103,7102,7101,7100,7099,7098,7097,7096,7095,7094,7093,7092,7091,7090,7089,7088,7087,7086,7085,7084,7083,7082,7081,7080,7079,7078,7077,7076,7075,7074,7073,7072,7071,7070,7069,7068,7067,7066,7065,7064,7063,7062,7061,7060,7059,7058,7057,7056,7055,7054,7053,7052,7051,7050,7049,7048,7047,7046,7045,7044,7043,7042,7041,7040,7039,7038,7037,7036,7035,7034,7033,7032,7031,7030,7029,7028,7027,7026,7025,7024,7023,7022,7021,7020,7019,7018,7017,7016,7015,7014,7013,7012,7011,7010,7009,7008,7007,7006,7005,7004,7003,7002,7001,7000,6999,6998,6997,6996,6995,6994,6993,6992,6991,6989,6986,6981,6894,6889,6887,6871,6870,6869,6868,6786,6782,6779,6770,6769,6761,6759,6745,6741,6739,6706,6704,6681,5769,5754,5748,5743,5740,5737,5736,5735,5734,5733,5732,5731,5730,5711,5708,5696,5692,5691,5689,5688,5687,5686,5684,5683,5676,5675,5652,5624,5623,5583,5577,5533,5532,5528,5511,5509,5501,5489,5480,5471,5469,5459,5446,5445,4509,4507,4506,4505,4498,4470,4465,4442,4440,4439,4415,4414,4403,4399,4398,4375,4248,4246,4244,4242,4181,4157,3219,3218,3217,3216,3215,3214,3213,3212,3211,3210,3209,3208,3207,3206,3205,3204,3203,3202,3201,3200,3199,3198,3197,3196,3195,3194,3193,3192,3191,3190,3189,3188,3187,3186,3185,3184,3183,3182,3181,3180,3179,3178,3177,3176,3175,3174,3173,3172,3169,3168,3167,3166,3165,3164,3163,3162,3161,3160,3159,3158,3157,3156,3155,3154,3153,3152,3151,3150,3149,3148,3147,3146,3145,3144,3143,3142,3141,3140,3139,3138,3137,3136,3135,3134,3133,3132,3131,3130,3129,3128,3127,3126,3125,3124,3123,3122,3121,3120,3119,3118,3117,3116,3115,3114,3113,3112,3111,3110,3109,3108,3107,3106,3105,3104,3103,3100]) ).

thf(8888,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[8887]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV239-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17  % Computer : n007.cluster.edu
% 0.08/0.17  % Model    : x86_64 x86_64
% 0.08/0.17  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17  % Memory   : 8046.5625MB
% 0.08/0.17  % OS       : Linux 6.8.0-71-generic
% 0.08/0.17  % CPULimit : 300
% 0.08/0.17  % WCLimit  : 300
% 0.08/0.17  % DateTime : Tue Oct  6 16:19:00 UTC 2026
% 0.08/0.17  % CPUTime  : 
% 0.08/0.17  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 181.38/36.50  ..........
% 181.38/36.50  
% 181.38/36.50   No.of.Axioms: 1400
% 181.38/36.50  
% 181.38/36.50   Length.of.Defs: 0
% 181.38/36.50  
% 181.38/36.50   Contains.Choice.Funs: false
% 181.38/36.50  ............................................................................................................................................................................................................................................
% 181.38/36.50  
% 181.38/36.50  ********************************
% 181.38/36.50  *   All subproblems solved!    *
% 181.38/36.50  ********************************
% 181.38/36.50  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1400,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8887,loop_count:0,foatp_calls:1,translation:fof_full)
% 181.38/36.50  
% 181.38/36.50  %**** Beginning of derivation protocol ****
% 181.38/36.50  % SZS output start CNFRefutation
% See solution above
% 181.38/36.55  
% 181.38/36.55  %**** End of derivation protocol ****
% 181.38/36.55  %**** no. of clauses in derivation: 8888 ****
% 181.38/36.55  %**** clause counter: 8887 ****
% 181.38/36.55  
% 181.38/36.55  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1400,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8887,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------