%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV242-1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 10:56:32 AM UTC 2026
% Result : Unsatisfiable 214.71s 43.14s
% Output : CNFRefutation 214.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1393
% Syntax : Number of formulae : 8741 (5138 unt; 0 typ; 0 def)
% Number of atoms : 37017 (11799 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 63051 (7192 ~;8478 |; 0 &;47381 @)
% ( 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 : 222 ( 219 usr; 26 con; 0-6 aty)
% Number of variables : 15171 ( 0 ^;15171 !; 0 ?;15171 :)
% 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_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_G_H,type,
v_G_H: $i ).
thf(tp_v_H,type,
v_H: $i ).
thf(tp_v_H_H,type,
v_H_H: $i ).
thf(1,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
thf(2,axiom,
! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__upper2_0) ).
thf(3,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__upper1_0) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(5,axiom,
! [V_X: $i] :
~ ( c_in @ V_X @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(7,axiom,
! [V_K: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(18,axiom,
! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject__iff1_0) ).
thf(23,axiom,
! [V_nat: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6__iff1_0) ).
thf(24,axiom,
! [V_nat: $i] :
( ( c_Message_Oagent_OFriend @ V_nat )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5__iff1_0) ).
thf(25,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).
thf(26,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).
thf(27,axiom,
! [V_nat_H: $i] :
( ( c_Message_Oagent_OFriend @ V_nat_H )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2__iff1_0) ).
thf(28,axiom,
! [V_nat_H: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1__iff1_0) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(53,axiom,
! [V_A: $i,T_a: $i] :
~ ( c_less @ V_A @ c_emptyset @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(57,axiom,
! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ c_emptyset @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(59,axiom,
! [T_a: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ T_a )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(65,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_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_minus @ V_A @ V_B @ ( tc_set @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__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_OatMost @ V_k @ T_a ) @ T_a )
| ( c_lessequals @ V_i @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__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_OatLeast @ V_k @ T_a ) @ T_a )
| ( c_lessequals @ V_k @ V_i @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(108,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_less @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(109,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2__iff1_0) ).
thf(110,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1__iff1_0) ).
thf(111,axiom,
! [V_n: $i] :
~ ( c_less @ V_n @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(112,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
thf(113,axiom,
! [V_i: $i,V_j: $i] :
~ ( c_less @ ( c_plus @ V_i @ V_j @ tc_nat ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
thf(114,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(115,axiom,
! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(116,axiom,
c_less @ c_0 @ c_1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).
thf(117,axiom,
! [V_n: $i] :
( ~ ( c_less @ V_n @ c_1 @ tc_nat )
| ( V_n = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).
thf(118,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).
thf(119,axiom,
! [V_n: $i] :
( ~ ( c_less @ V_n @ ( c_Suc @ c_0 ) @ tc_nat )
| ( V_n = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
thf(120,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(121,axiom,
! [V_i: $i] :
( ~ ( c_lessequals @ V_i @ c_0 @ tc_nat )
| ( V_i = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(122,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
thf(123,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_plus @ V_m @ V_n @ tc_nat )
!= c_0 )
| ( V_n = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
thf(124,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_plus @ V_m @ V_n @ tc_nat )
!= c_0 )
| ( V_m = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
thf(128,axiom,
! [V_m: $i] :
( c_0
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
thf(129,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
thf(134,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ V_m )
!= ( c_Suc @ V_n ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
thf(135,axiom,
! [T_a: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ T_a )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(137,axiom,
! [T_a: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(139,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_append @ V_xs @ c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(141,axiom,
! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_append @ c_List_Olist_ONil @ V_ys @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).
thf(145,axiom,
! [T_a: $i] :
( ( c_List_Orev @ c_List_Olist_ONil @ T_a )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff2_0) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff1_0) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff1_0) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff2_0) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(157,axiom,
! [T_a: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_1) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_0) ).
thf(161,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_append @ V_xs @ c_List_Olist_ONil @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(163,axiom,
! [V_ys: $i,T_a: $i] :
( ( c_append @ c_List_Olist_ONil @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(166,axiom,
! [T_a: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(175,axiom,
! [T_a: $i] :
( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff2_0) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff1_0) ).
thf(177,axiom,
! [T_a: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
thf(183,axiom,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
thf(184,axiom,
! [V_m: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_IntDef_Oint )
| ( V_m = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
thf(187,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_IntDef_Oint @ V_m )
!= ( c_IntDef_Oint @ V_n ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
thf(188,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(201,axiom,
c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2__iff1_0) ).
thf(202,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).
thf(203,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff2_0) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff1_0) ).
thf(205,axiom,
! [V_r: $i,T_a: $i] :
( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff2_0) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff1_0) ).
thf(207,axiom,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).
thf(208,axiom,
! [V_m: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_nat )
| ( V_m = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb__iff1_0) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf__iff1_0) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons__iff1_0) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf__iff1_0) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons__iff1_0) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons__iff1_0) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq__iff1_0) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(225,axiom,
! [V_a_H: $i,T_a: $i] :
( ( c_Datatype_Ooption_OSome @ V_a_H @ T_a )
!= c_Datatype_Ooption_ONone ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2__iff1_0) ).
thf(226,axiom,
! [V_a_H: $i,T_a: $i] :
( c_Datatype_Ooption_ONone
!= ( c_Datatype_Ooption_OSome @ V_a_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1__iff1_0) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq__iff1_0) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq__iff1_0) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(231,axiom,
! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
thf(232,axiom,
! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
thf(233,axiom,
! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
thf(234,axiom,
! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
thf(235,axiom,
! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
thf(236,axiom,
! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
thf(237,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
thf(238,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
thf(239,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
thf(240,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
thf(241,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
thf(242,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
thf(243,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
thf(244,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
thf(245,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
thf(246,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
thf(247,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
thf(248,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
thf(249,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
thf(250,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
thf(251,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
thf(252,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
thf(253,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).
thf(254,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).
thf(255,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
thf(256,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).
thf(257,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).
thf(258,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
thf(259,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
thf(260,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
thf(261,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
thf(262,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).
thf(263,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).
thf(264,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
thf(265,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
thf(266,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
thf(267,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
thf(268,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
thf(269,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
thf(270,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
thf(271,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
thf(272,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
thf(273,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
thf(274,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
thf(275,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
thf(276,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).
thf(277,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
thf(278,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).
thf(279,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).
thf(280,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).
thf(281,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).
thf(282,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).
thf(283,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
thf(284,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).
thf(285,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
thf(286,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).
thf(287,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).
thf(288,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).
thf(289,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).
thf(290,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).
thf(291,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
thf(292,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
thf(293,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
thf(294,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
thf(295,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
thf(296,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).
thf(297,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
thf(298,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
thf(299,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
thf(300,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
thf(301,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
thf(302,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).
thf(303,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).
thf(304,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).
thf(305,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).
thf(306,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
thf(307,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
thf(308,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
thf(309,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).
thf(310,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
thf(311,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).
thf(312,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
thf(313,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).
thf(314,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).
thf(315,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).
thf(316,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).
thf(317,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
thf(318,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
thf(319,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
thf(320,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
thf(321,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).
thf(322,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
thf(323,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
thf(324,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).
thf(325,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).
thf(326,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).
thf(327,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).
thf(328,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
thf(329,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
thf(330,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).
thf(331,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
thf(332,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
thf(333,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
thf(334,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
thf(335,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).
thf(336,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).
thf(337,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
thf(338,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
thf(339,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
thf(340,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
thf(341,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
thf(342,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
thf(343,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
thf(344,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
thf(345,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).
thf(346,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
thf(347,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
thf(348,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
thf(349,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
thf(350,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
thf(351,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).
thf(352,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).
thf(353,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).
thf(354,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).
thf(355,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
thf(356,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
thf(357,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
thf(358,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
thf(359,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
thf(360,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
thf(361,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
thf(362,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
thf(363,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
thf(364,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
thf(365,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(366,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(367,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
thf(368,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
thf(369,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
thf(370,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
thf(371,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
thf(372,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
thf(373,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
thf(374,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_9) ).
thf(375,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_8) ).
thf(376,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_7) ).
thf(377,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_6) ).
thf(378,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_5) ).
thf(379,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_4) ).
thf(380,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_3) ).
thf(381,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_24) ).
thf(382,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_23) ).
thf(383,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_22) ).
thf(384,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_21) ).
thf(385,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_20) ).
thf(386,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_2) ).
thf(387,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_19) ).
thf(388,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_18) ).
thf(389,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_17) ).
thf(390,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_16) ).
thf(391,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_15) ).
thf(392,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_14) ).
thf(393,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_13) ).
thf(394,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_12) ).
thf(395,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_11) ).
thf(396,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_10) ).
thf(397,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_1) ).
thf(398,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__ring_0) ).
thf(399,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
thf(400,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
thf(401,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
thf(402,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
thf(403,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
thf(404,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
thf(405,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
thf(406,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
thf(407,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
thf(408,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
thf(409,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
thf(410,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
thf(411,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
thf(412,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
thf(413,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
thf(414,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
thf(415,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
thf(416,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
thf(417,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
thf(418,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
thf(419,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
thf(420,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
thf(421,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
thf(422,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
thf(423,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
thf(424,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
thf(425,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
thf(426,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
thf(427,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
thf(428,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
thf(429,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
thf(430,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
thf(431,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
thf(432,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
thf(433,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
thf(434,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
thf(435,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
thf(436,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
thf(437,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
thf(438,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
thf(439,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
thf(440,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
thf(441,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
thf(442,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
thf(443,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
thf(444,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
thf(445,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
thf(446,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
thf(447,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
thf(448,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
thf(449,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
thf(450,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
thf(451,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
thf(452,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
thf(453,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
thf(454,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
thf(455,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
thf(456,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
thf(457,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
thf(458,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
thf(459,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
thf(460,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
thf(461,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
thf(462,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
thf(463,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(464,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(465,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
thf(466,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
thf(467,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
thf(468,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
thf(469,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(470,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(471,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
thf(472,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
thf(473,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(474,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
thf(475,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(476,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
thf(477,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(478,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(479,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
thf(480,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(481,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
thf(482,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
thf(483,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).
thf(484,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).
thf(485,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
thf(486,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).
thf(487,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(488,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
thf(489,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).
thf(490,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
thf(491,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
thf(492,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).
thf(493,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
thf(494,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
thf(495,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(496,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(497,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
thf(498,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
thf(499,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
thf(500,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
thf(501,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
thf(502,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
thf(503,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
thf(504,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
thf(505,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
thf(506,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
thf(507,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
thf(508,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
thf(509,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
thf(510,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
thf(511,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
thf(512,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
thf(513,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
thf(514,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
thf(515,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
thf(516,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
thf(517,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
thf(518,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
thf(519,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
thf(520,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
thf(521,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
thf(522,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
thf(523,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
thf(524,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
thf(525,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
thf(526,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
thf(527,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
thf(528,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
thf(529,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
thf(530,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
thf(531,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
thf(532,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
thf(533,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
thf(534,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
thf(535,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
thf(536,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
thf(537,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
thf(538,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(539,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
thf(540,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
thf(541,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oidom @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
thf(542,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(543,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__semidom @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
thf(544,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(545,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(546,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(547,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(548,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(549,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(550,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
thf(551,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
thf(552,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__ring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
thf(553,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(554,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
thf(555,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
thf(556,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
thf(557,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(558,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(559,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(560,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(561,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
thf(562,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(563,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(564,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(565,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(566,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(567,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(568,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(569,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
thf(570,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
thf(571,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
thf(572,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).
thf(573,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).
thf(574,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
thf(575,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).
thf(576,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
thf(577,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).
thf(578,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(579,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
thf(580,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
thf(581,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
thf(582,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
thf(583,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
thf(584,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
thf(585,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(586,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
thf(587,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
thf(588,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
thf(589,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
thf(590,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(591,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(592,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
thf(593,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
thf(594,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
thf(595,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_9) ).
thf(596,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_8) ).
thf(597,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_7) ).
thf(598,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__semidom @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_60) ).
thf(599,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_6) ).
thf(600,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_59) ).
thf(601,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
thf(602,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_57) ).
thf(603,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_56) ).
thf(604,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_55) ).
thf(605,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_54) ).
thf(606,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_53) ).
thf(607,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_52) ).
thf(608,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_51) ).
thf(609,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_50) ).
thf(610,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_5) ).
thf(611,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_49) ).
thf(612,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_48) ).
thf(613,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
thf(614,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
thf(615,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_45) ).
thf(616,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_44) ).
thf(617,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_43) ).
thf(618,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_42) ).
thf(619,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_41) ).
thf(620,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_40) ).
thf(621,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_4) ).
thf(622,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_39) ).
thf(623,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__ring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_38) ).
thf(624,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_37) ).
thf(625,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_36) ).
thf(626,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_35) ).
thf(627,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__idom @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
thf(628,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_33) ).
thf(629,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_32) ).
thf(630,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_31) ).
thf(631,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_30) ).
thf(632,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_3) ).
thf(633,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_29) ).
thf(634,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_28) ).
thf(635,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_27) ).
thf(636,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_26) ).
thf(637,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_25) ).
thf(638,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_24) ).
thf(639,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_23) ).
thf(640,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_22) ).
thf(641,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_21) ).
thf(642,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_20) ).
thf(643,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oidom @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_2) ).
thf(644,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_19) ).
thf(645,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_18) ).
thf(646,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_17) ).
thf(647,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_16) ).
thf(648,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_15) ).
thf(649,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_14) ).
thf(650,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_13) ).
thf(651,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_12) ).
thf(652,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_11) ).
thf(653,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_10) ).
thf(654,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oinverse @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_1) ).
thf(655,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ofield @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
thf(656,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
thf(657,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
thf(658,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
thf(659,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
thf(660,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
thf(661,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
thf(662,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
thf(663,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
thf(664,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
thf(665,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
thf(666,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
thf(667,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
thf(668,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
thf(669,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
thf(670,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
thf(671,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
thf(672,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
thf(673,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
thf(674,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
thf(675,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
thf(676,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
thf(677,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
thf(678,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
thf(679,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
thf(680,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
thf(681,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
thf(682,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
thf(683,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
thf(684,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
thf(685,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
thf(686,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
thf(687,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
thf(688,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
thf(689,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
thf(690,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
thf(691,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).
thf(692,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
thf(693,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
thf(694,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
thf(695,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
thf(696,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
thf(697,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
thf(698,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
thf(699,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
thf(700,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).
thf(701,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).
thf(702,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
thf(703,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).
thf(704,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
thf(705,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
thf(706,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).
thf(707,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
thf(708,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).
thf(709,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).
thf(710,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
thf(711,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
thf(712,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
thf(713,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
thf(714,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
thf(715,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
thf(716,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
thf(717,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
thf(718,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
thf(719,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
thf(720,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
thf(721,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).
thf(722,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
thf(723,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).
thf(724,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
thf(725,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).
thf(726,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).
thf(727,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
thf(728,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).
thf(729,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
thf(730,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).
thf(731,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
thf(732,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).
thf(733,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).
thf(734,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
thf(735,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
thf(736,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
thf(737,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
thf(738,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).
thf(739,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
thf(740,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
thf(741,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
thf(742,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
thf(743,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
thf(744,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
thf(745,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
thf(746,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
thf(747,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
thf(748,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_9) ).
thf(749,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_8) ).
thf(750,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_7) ).
thf(751,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_6) ).
thf(752,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_5) ).
thf(753,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_4) ).
thf(754,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_32) ).
thf(755,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oidom @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_31) ).
thf(756,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oinverse @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_30) ).
thf(757,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_3) ).
thf(758,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_29) ).
thf(759,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_28) ).
thf(760,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_27) ).
thf(761,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_26) ).
thf(762,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_25) ).
thf(763,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_24) ).
thf(764,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_23) ).
thf(765,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_22) ).
thf(766,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
thf(767,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_20) ).
thf(768,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_2) ).
thf(769,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_19) ).
thf(770,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_18) ).
thf(771,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_17) ).
thf(772,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_16) ).
thf(773,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_15) ).
thf(774,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_14) ).
thf(775,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_13) ).
thf(776,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
thf(777,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_11) ).
thf(778,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_10) ).
thf(779,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_1) ).
thf(780,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_0) ).
thf(781,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
| ( class_HOL_Oinverse @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Odivision__by__zero_1) ).
thf(782,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Odivision__by__zero_0) ).
thf(783,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
thf(784,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
thf(785,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
thf(786,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
thf(787,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
thf(788,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
thf(789,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
thf(790,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
thf(791,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
thf(792,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
thf(793,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
thf(794,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
thf(795,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
thf(796,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
thf(797,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
thf(798,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
thf(799,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
thf(800,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
thf(801,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
thf(802,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
thf(803,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
thf(804,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
thf(805,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
thf(806,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
thf(807,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
thf(808,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
thf(809,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
thf(810,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
thf(811,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
thf(812,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
thf(813,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
thf(814,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
thf(815,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
thf(816,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
thf(817,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
thf(818,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
thf(819,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
thf(820,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
thf(821,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
thf(822,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
thf(823,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
thf(824,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
thf(825,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
thf(826,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
thf(827,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
thf(828,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
thf(829,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
thf(830,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
thf(831,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
thf(832,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
thf(833,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
thf(834,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
thf(835,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
thf(836,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
thf(837,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
thf(838,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
thf(839,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
thf(840,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
thf(841,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
thf(842,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
thf(843,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
thf(844,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
thf(845,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
thf(846,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
thf(847,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
thf(848,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
thf(849,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
thf(850,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
thf(851,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
thf(852,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
thf(853,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
thf(854,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
thf(855,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
thf(856,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
thf(857,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
thf(858,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
thf(859,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
thf(860,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
thf(861,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
thf(862,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
thf(863,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
thf(864,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
thf(865,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
thf(866,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
thf(867,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
thf(868,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
thf(869,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
thf(870,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
thf(871,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
thf(872,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
thf(873,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
thf(874,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
thf(875,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
thf(876,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
thf(877,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
thf(878,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
thf(879,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
thf(880,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
thf(881,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
thf(882,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
thf(883,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
thf(884,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
thf(885,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).
thf(886,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).
thf(887,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
thf(888,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).
thf(889,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).
thf(890,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
thf(891,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
thf(892,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).
thf(893,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
thf(894,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
thf(895,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
thf(896,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
thf(897,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
thf(898,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).
thf(899,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
thf(900,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).
thf(901,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).
thf(902,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
thf(903,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
thf(904,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
thf(905,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
thf(906,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
thf(907,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
thf(908,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(909,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
thf(910,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
thf(911,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(912,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).
thf(913,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
thf(914,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).
thf(915,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).
thf(916,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).
thf(917,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(918,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
thf(919,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
thf(920,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
thf(921,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
thf(922,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
thf(923,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
thf(924,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
thf(925,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
thf(926,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
thf(927,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(928,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(929,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
thf(930,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
thf(931,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
thf(932,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
thf(933,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
thf(934,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).
thf(935,axiom,
! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Nat_Opower @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).
thf(936,axiom,
! [T: $i] :
( ~ ( class_Orderings_Oorder @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(937,axiom,
! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(938,axiom,
! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(939,axiom,
! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
thf(940,axiom,
! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
thf(941,axiom,
! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
thf(942,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Osemigroup__mult @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).
thf(943,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).
thf(944,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
thf(945,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
thf(946,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
thf(947,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
thf(948,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
thf(949,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
thf(950,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
thf(951,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
thf(952,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
thf(953,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
thf(954,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
thf(955,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
thf(956,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
thf(957,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
thf(958,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
thf(959,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
thf(960,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
thf(961,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
thf(962,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
thf(963,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
thf(964,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
thf(965,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
thf(966,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
thf(967,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
thf(968,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
thf(969,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
thf(970,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
thf(971,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
thf(972,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
thf(973,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
thf(974,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
thf(975,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
thf(976,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
thf(977,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
thf(978,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
thf(979,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
thf(980,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Olinorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
thf(981,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
thf(982,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
thf(983,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
thf(984,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
thf(985,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
thf(986,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
thf(987,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
thf(988,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
thf(989,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(990,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(991,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(992,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
thf(993,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(994,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
thf(995,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).
thf(996,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
thf(997,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
thf(998,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
thf(999,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
thf(1000,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(1001,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
thf(1002,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
thf(1003,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
thf(1004,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(1005,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(1006,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(1007,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(1008,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(1009,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
thf(1010,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
thf(1011,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
thf(1012,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
thf(1013,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
thf(1014,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
thf(1015,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
thf(1016,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
thf(1017,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
thf(1018,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
thf(1019,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(1020,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
thf(1021,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
thf(1022,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
thf(1023,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(1024,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(1025,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(1026,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(1027,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(1028,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
thf(1029,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
thf(1030,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
thf(1031,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
thf(1032,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
thf(1033,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
thf(1034,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
thf(1035,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
thf(1036,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
thf(1037,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(1038,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
thf(1039,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
thf(1040,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
thf(1041,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(1042,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
thf(1043,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
thf(1044,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(1045,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(1046,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(1047,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(1048,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
thf(1049,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
thf(1050,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
thf(1051,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
thf(1052,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(1053,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(1054,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
thf(1055,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
thf(1056,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
thf(1057,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(1058,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
thf(1059,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).
thf(1060,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
thf(1061,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(1062,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(1063,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(1064,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Olorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(1065,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).
thf(1066,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).
thf(1067,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
thf(1068,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).
thf(1069,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
thf(1070,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
thf(1071,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
thf(1072,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(1073,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
thf(1074,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
thf(1075,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(1076,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
thf(1077,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
thf(1078,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
thf(1079,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
thf(1080,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
thf(1081,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
thf(1082,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
thf(1083,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
thf(1084,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
thf(1085,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
thf(1086,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
thf(1087,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
thf(1088,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
thf(1089,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
thf(1090,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
thf(1091,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
thf(1092,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
thf(1093,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).
thf(1094,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).
thf(1095,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).
thf(1096,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).
thf(1097,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
thf(1098,axiom,
! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
thf(1099,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
thf(1100,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Ozero @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).
thf(1101,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
thf(1102,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
thf(1103,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).
thf(1104,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).
thf(1105,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Numeral_Onumber @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
thf(1106,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Otimes @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).
thf(1107,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
thf(1108,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
thf(1109,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
thf(1110,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
thf(1111,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
thf(1112,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
thf(1113,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
thf(1114,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
thf(1115,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
thf(1116,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Oone @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
thf(1117,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).
thf(1118,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
thf(1119,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
thf(1120,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
thf(1121,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
thf(1122,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
thf(1123,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
thf(1124,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
thf(1125,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Ominus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).
thf(1126,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
thf(1127,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
thf(1128,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).
thf(1129,axiom,
! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Oplus @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).
thf(1130,axiom,
! [T: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
thf(1131,axiom,
! [T: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
thf(1132,axiom,
! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(1133,axiom,
! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
thf(1134,axiom,
! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
thf(1135,axiom,
! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1136,axiom,
! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(1137,axiom,
! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oord @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
thf(1138,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/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
thf(1139,axiom,
! [T_1: $i] : ( class_Nat_Opower @ ( tc_set @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(1140,axiom,
! [T_1: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(1141,axiom,
! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(1142,axiom,
! [T_1: $i] : ( class_Orderings_Oord @ ( tc_set @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(1143,axiom,
! [T_1: $i] : ( class_HOL_Ominus @ ( tc_set @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(1144,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/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
thf(1145,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(1146,axiom,
class_Wellfounded__Recursion_Owellorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
thf(1147,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(1148,axiom,
class_LOrder_Olorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(1149,axiom,
class_LOrder_Ojoin__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(1150,axiom,
class_Parity_Oeven__odd @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_47) ).
thf(1151,axiom,
class_Numeral_Onumber @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).
thf(1152,axiom,
class_Power_Orecpower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(1153,axiom,
class_Divides_Odiv @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_44) ).
thf(1154,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(1155,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
thf(1156,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
thf(1157,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(1158,axiom,
class_LOrder_Omeet__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(1159,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
thf(1160,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
thf(1161,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(1162,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(1163,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
thf(1164,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(1165,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
thf(1166,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
thf(1167,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).
thf(1168,axiom,
class_Ring__and__Field_Osemiring__1__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).
thf(1169,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(1170,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(1171,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).
thf(1172,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).
thf(1173,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).
thf(1174,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).
thf(1175,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(1176,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(1177,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).
thf(1178,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).
thf(1179,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
thf(1180,axiom,
class_Orderings_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(1181,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).
thf(1182,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).
thf(1183,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(1184,axiom,
class_OrderedGroup_Osemigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_16) ).
thf(1185,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_15) ).
thf(1186,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_14) ).
thf(1187,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(1188,axiom,
class_Nat_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(1189,axiom,
class_HOL_Otimes @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).
thf(1190,axiom,
class_HOL_Oplus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_10) ).
thf(1191,axiom,
class_HOL_Ozero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_1) ).
thf(1192,axiom,
class_HOL_Oone @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
thf(1193,axiom,
! [T_2: $i,T_1: $i] : ( class_Nat_Opower @ ( tc_fun @ T_2 @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).
thf(1194,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/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
thf(1195,axiom,
class_Finite__Set_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
thf(1196,axiom,
class_Finite__Set_Ofinite @ tc_Product__Type_Ounit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(1197,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(1198,axiom,
class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).
thf(1199,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).
thf(1200,axiom,
class_Parity_Oeven__odd @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).
thf(1201,axiom,
class_Power_Orecpower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(1202,axiom,
class_Nat_Opower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(1203,axiom,
class_Divides_Odiv @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).
thf(1204,axiom,
class_Numeral_Onumber__ring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
thf(1205,axiom,
class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).
thf(1206,axiom,
class_Numeral_Onumber @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
thf(1207,axiom,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(1208,axiom,
class_Ring__and__Field_Oidom @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
thf(1209,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(1210,axiom,
class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(1211,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(1212,axiom,
class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
thf(1213,axiom,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(1214,axiom,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(1215,axiom,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(1216,axiom,
class_Orderings_Oord @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(1217,axiom,
class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
thf(1218,axiom,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(1219,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
thf(1220,axiom,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(1221,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
thf(1222,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
thf(1223,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(1224,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
thf(1225,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
thf(1226,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(1227,axiom,
class_HOL_Ozero @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).
thf(1228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(1229,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
thf(1230,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(1231,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
thf(1232,axiom,
class_Orderings_Olinorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(1233,axiom,
class_LOrder_Olorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(1234,axiom,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(1235,axiom,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(1236,axiom,
class_Orderings_Oorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(1237,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
thf(1238,axiom,
class_HOL_Otimes @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
thf(1239,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
thf(1240,axiom,
class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
thf(1241,axiom,
class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
thf(1242,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
thf(1243,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
thf(1244,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(1245,axiom,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(1246,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(1247,axiom,
class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
thf(1248,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
thf(1249,axiom,
class_HOL_Oplus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).
thf(1250,axiom,
class_Ring__and__Field_Oring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
thf(1251,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(1252,axiom,
class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
thf(1253,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
thf(1254,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
thf(1255,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
thf(1256,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
thf(1257,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
thf(1258,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
thf(1259,axiom,
class_Ring__and__Field_Osemiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
thf(1260,axiom,
class_HOL_Oone @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
thf(1261,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(1262,axiom,
! [T_1: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
thf(1263,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(1264,axiom,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(1265,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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
thf(1266,axiom,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(1267,axiom,
! [T_a: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(1268,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(1269,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(1270,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(1271,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/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(1272,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(1273,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(1274,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(1275,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(1276,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(1277,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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(1278,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(1279,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(1280,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(1281,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(1282,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(1283,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(1284,axiom,
! [V_a: $i,T_a: $i] : ( c_in @ V_a @ ( c_insert @ V_a @ c_emptyset @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(1285,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(1286,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/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(1287,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/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(1288,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/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(1289,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(1290,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(1291,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(1292,axiom,
! [V_x: $i,T_a: $i] : ( c_in @ V_x @ c_UNIV @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1293,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(1294,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(1295,axiom,
! [V_k: $i] : ( c_in @ ( c_SetInterval_OlessThan @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(1296,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(1297,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(1298,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(1299,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(1300,axiom,
! [V_k: $i] : ( c_in @ ( c_SetInterval_OatMost @ V_k @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(1301,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(1302,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(1303,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(1304,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(1305,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(1306,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(1307,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(1308,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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(1309,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(1310,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(1311,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(1312,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(1313,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(1314,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(1315,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(1316,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(1317,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(1318,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(1319,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/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(1320,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(1321,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/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(1322,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(1323,axiom,
! [V_n: $i] : ( c_less @ c_0 @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(1324,axiom,
! [V_n: $i] :
~ ( c_less @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(1325,axiom,
! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(1326,axiom,
! [V_n: $i] : ( c_lessequals @ c_0 @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(1327,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/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(1328,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/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(1329,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/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(1330,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/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(1331,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/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(1332,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/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(1333,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(1334,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(1335,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(1336,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(1337,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(1338,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(1339,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(1340,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(1341,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
thf(1342,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/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(1343,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/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(1344,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/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(1345,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/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(1346,axiom,
! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
thf(1347,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(1348,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
thf(1349,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/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
thf(1350,axiom,
! [V_m: $i] : ( c_Divides_Oop_Advd @ c_1 @ V_m @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
thf(1351,axiom,
! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(1352,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(1353,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/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(1354,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/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(1355,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/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
thf(1356,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/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
thf(1357,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(1358,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(1359,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(1360,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(1361,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(1362,axiom,
! [T_a: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(1363,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(1364,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
thf(1365,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/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
thf(1366,axiom,
! [V_k: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ V_k @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(1367,axiom,
! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(1368,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
thf(1369,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
thf(1370,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
thf(1371,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
thf(1372,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
thf(1373,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
thf(1374,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(1375,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(1376,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(1377,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(1378,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(1379,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(1380,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).
thf(1381,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
thf(1382,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
thf(1383,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
thf(1384,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(1385,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(1386,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(1387,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(1388,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
thf(1389,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
thf(1390,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(1391,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[1390]) ).
thf(1392,negated_conjecture,
( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(1393,negated_conjecture,
c_lessequals @ v_H @ ( c_Message_Oanalz @ v_H_H ) @ ( tc_set @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(1394,negated_conjecture,
c_lessequals @ v_G @ ( c_Message_Oanalz @ v_G_H ) @ ( tc_set @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1395,plain,
$false = $false,
inference(unfold_def,[status(thm)],[1391]) ).
thf(1396,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(1397,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(1398,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(1399,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)],[4]) ).
thf(1400,plain,
( ( ! [V_X: $i] :
~ ( c_in @ V_X @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(1401,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)],[6]) ).
thf(1402,plain,
( ( ! [V_K: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( 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)],[7]) ).
thf(1403,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)],[8]) ).
thf(1404,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)],[9]) ).
thf(1405,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)],[10]) ).
thf(1406,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)],[11]) ).
thf(1407,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)],[12]) ).
thf(1408,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)],[13]) ).
thf(1409,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)],[14]) ).
thf(1410,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)],[15]) ).
thf(1411,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)],[16]) ).
thf(1412,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)],[17]) ).
thf(1413,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(1414,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)],[19]) ).
thf(1415,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)],[20]) ).
thf(1416,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)],[21]) ).
thf(1417,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)],[22]) ).
thf(1418,plain,
( ( ! [V_nat: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(1419,plain,
( ( ! [V_nat: $i] :
( ( c_Message_Oagent_OFriend @ V_nat )
!= c_Message_Oagent_OSpy ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(1420,plain,
( ( c_Message_Oagent_OSpy != c_Message_Oagent_OServer )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(1421,plain,
( ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(1422,plain,
( ( ! [V_nat_H: $i] :
( ( c_Message_Oagent_OFriend @ V_nat_H )
!= c_Message_Oagent_OServer ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(1423,plain,
( ( ! [V_nat_H: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(1424,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)],[29]) ).
thf(1425,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)],[30]) ).
thf(1426,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)],[31]) ).
thf(1427,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)],[32]) ).
thf(1428,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)],[33]) ).
thf(1429,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)],[34]) ).
thf(1430,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)],[35]) ).
thf(1431,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)],[36]) ).
thf(1432,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)],[37]) ).
thf(1433,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)],[38]) ).
thf(1434,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)],[39]) ).
thf(1435,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)],[40]) ).
thf(1436,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)],[41]) ).
thf(1437,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)],[42]) ).
thf(1438,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)],[43]) ).
thf(1439,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)],[44]) ).
thf(1440,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)],[45]) ).
thf(1441,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)],[46]) ).
thf(1442,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)],[47]) ).
thf(1443,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)],[48]) ).
thf(1444,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)],[49]) ).
thf(1445,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)],[50]) ).
thf(1446,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)],[51]) ).
thf(1447,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)],[52]) ).
thf(1448,plain,
( ( ! [V_A: $i,T_a: $i] :
~ ( c_less @ V_A @ c_emptyset @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(1449,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)],[54]) ).
thf(1450,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)],[55]) ).
thf(1451,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)],[56]) ).
thf(1452,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ c_emptyset @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(1453,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)],[58]) ).
thf(1454,plain,
( ( ! [T_a: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ T_a )
= c_emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(1455,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)],[60]) ).
thf(1456,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)],[61]) ).
thf(1457,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)],[62]) ).
thf(1458,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)],[63]) ).
thf(1459,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)],[64]) ).
thf(1460,plain,
( ( c_UNIV != c_emptyset )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(1461,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)],[66]) ).
thf(1462,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)],[67]) ).
thf(1463,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)],[68]) ).
thf(1464,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)],[69]) ).
thf(1465,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)],[70]) ).
thf(1466,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)],[71]) ).
thf(1467,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)],[72]) ).
thf(1468,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)],[73]) ).
thf(1469,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)],[74]) ).
thf(1470,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)],[75]) ).
thf(1471,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)],[76]) ).
thf(1472,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)],[77]) ).
thf(1473,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)],[78]) ).
thf(1474,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)],[79]) ).
thf(1475,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)],[80]) ).
thf(1476,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)],[81]) ).
thf(1477,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)],[82]) ).
thf(1478,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)],[83]) ).
thf(1479,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)],[84]) ).
thf(1480,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)],[85]) ).
thf(1481,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)],[86]) ).
thf(1482,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)],[87]) ).
thf(1483,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)],[88]) ).
thf(1484,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)],[89]) ).
thf(1485,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)],[90]) ).
thf(1486,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)],[91]) ).
thf(1487,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)],[92]) ).
thf(1488,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)],[93]) ).
thf(1489,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)],[94]) ).
thf(1490,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)],[95]) ).
thf(1491,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)],[96]) ).
thf(1492,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)],[97]) ).
thf(1493,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)],[98]) ).
thf(1494,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)],[99]) ).
thf(1495,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)],[100]) ).
thf(1496,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)],[101]) ).
thf(1497,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)],[102]) ).
thf(1498,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)],[103]) ).
thf(1499,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)],[104]) ).
thf(1500,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)],[105]) ).
thf(1501,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)],[106]) ).
thf(1502,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)],[107]) ).
thf(1503,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)],[108]) ).
thf(1504,plain,
( ( c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0 )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(1505,plain,
( ( c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(1506,plain,
( ( ! [V_n: $i] :
~ ( c_less @ V_n @ c_0 @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(1507,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)],[112]) ).
thf(1508,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)],[113]) ).
thf(1509,plain,
( ( ~ ( c_less @ c_0 @ c_0 @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(1510,plain,
( ( ! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(1511,plain,
( ( c_less @ c_0 @ c_1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(1512,plain,
( ( ! [V_n: $i] :
( ~ ( c_less @ V_n @ c_1 @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(1513,plain,
( ( c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(1514,plain,
( ( ! [V_n: $i] :
( ~ ( c_less @ V_n @ ( c_Suc @ c_0 ) @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(1515,plain,
( ( c_lessequals @ c_0 @ c_0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(1516,plain,
( ( ! [V_i: $i] :
( ~ ( c_lessequals @ V_i @ c_0 @ tc_nat )
| ( V_i = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(1517,plain,
( ( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(1518,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)],[123]) ).
thf(1519,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)],[124]) ).
thf(1520,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)],[125]) ).
thf(1521,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)],[126]) ).
thf(1522,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)],[127]) ).
thf(1523,plain,
( ( ! [V_m: $i] :
( c_0
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(1524,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= c_0 ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(1525,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)],[130]) ).
thf(1526,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)],[131]) ).
thf(1527,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)],[132]) ).
thf(1528,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)],[133]) ).
thf(1529,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)],[134]) ).
thf(1530,plain,
( ( ! [T_a: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ T_a )
= c_emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(1531,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)],[136]) ).
thf(1532,plain,
( ( ! [T_a: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(1533,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)],[138]) ).
thf(1534,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)],[139]) ).
thf(1535,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)],[140]) ).
thf(1536,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)],[141]) ).
thf(1537,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)],[142]) ).
thf(1538,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)],[143]) ).
thf(1539,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)],[144]) ).
thf(1540,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ c_List_Olist_ONil @ T_a )
= c_List_Olist_ONil ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(1541,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)],[146]) ).
thf(1542,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)],[147]) ).
thf(1543,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)],[148]) ).
thf(1544,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)],[149]) ).
thf(1545,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)],[150]) ).
thf(1546,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)],[151]) ).
thf(1547,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)],[152]) ).
thf(1548,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)],[153]) ).
thf(1549,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)],[154]) ).
thf(1550,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)],[155]) ).
thf(1551,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)],[156]) ).
thf(1552,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) )
= c_0 ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(1553,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)],[158]) ).
thf(1554,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)],[159]) ).
thf(1555,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)],[160]) ).
thf(1556,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)],[161]) ).
thf(1557,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)],[162]) ).
thf(1558,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)],[163]) ).
thf(1559,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)],[164]) ).
thf(1560,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)],[165]) ).
thf(1561,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)],[166]) ).
thf(1562,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)],[167]) ).
thf(1563,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)],[168]) ).
thf(1564,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)],[169]) ).
thf(1565,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)],[170]) ).
thf(1566,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)],[171]) ).
thf(1567,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)],[172]) ).
thf(1568,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)],[173]) ).
thf(1569,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)],[174]) ).
thf(1570,plain,
( ( ! [T_a: $i] :
( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(1571,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)],[176]) ).
thf(1572,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)],[177]) ).
thf(1573,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)],[178]) ).
thf(1574,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)],[179]) ).
thf(1575,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)],[180]) ).
thf(1576,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)],[181]) ).
thf(1577,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)],[182]) ).
thf(1578,plain,
( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(1579,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)],[184]) ).
thf(1580,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)],[185]) ).
thf(1581,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)],[186]) ).
thf(1582,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)],[187]) ).
thf(1583,plain,
( ( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(1584,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)],[189]) ).
thf(1585,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)],[190]) ).
thf(1586,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)],[191]) ).
thf(1587,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)],[192]) ).
thf(1588,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)],[193]) ).
thf(1589,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)],[194]) ).
thf(1590,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)],[195]) ).
thf(1591,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)],[196]) ).
thf(1592,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)],[197]) ).
thf(1593,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)],[198]) ).
thf(1594,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)],[199]) ).
thf(1595,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)],[200]) ).
thf(1596,plain,
( ( c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(1597,plain,
( ( c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(1598,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)],[203]) ).
thf(1599,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)],[204]) ).
thf(1600,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)],[205]) ).
thf(1601,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)],[206]) ).
thf(1602,plain,
( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(1603,plain,
( ( ! [V_m: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_nat )
| ( V_m = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(1604,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)],[209]) ).
thf(1605,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)],[210]) ).
thf(1606,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)],[211]) ).
thf(1607,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)],[212]) ).
thf(1608,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)],[213]) ).
thf(1609,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)],[214]) ).
thf(1610,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)],[215]) ).
thf(1611,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)],[216]) ).
thf(1612,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)],[217]) ).
thf(1613,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)],[218]) ).
thf(1614,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)],[219]) ).
thf(1615,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)],[220]) ).
thf(1616,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)],[221]) ).
thf(1617,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)],[222]) ).
thf(1618,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)],[223]) ).
thf(1619,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)],[224]) ).
thf(1620,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)],[225]) ).
thf(1621,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)],[226]) ).
thf(1622,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)],[227]) ).
thf(1623,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)],[228]) ).
thf(1624,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)],[229]) ).
thf(1625,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)],[230]) ).
thf(1626,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(1627,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(1628,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(1629,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(1630,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(1631,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(1632,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(1633,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(1634,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(1635,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(1636,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(1637,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(1638,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(1639,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(1640,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)],[245]) ).
thf(1641,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(1642,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(1643,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(1644,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(1645,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(1646,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)],[251]) ).
thf(1647,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(1648,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(1649,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(1650,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(1651,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(1652,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(1653,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(1654,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(1655,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(1656,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(1657,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(1658,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(1659,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)],[264]) ).
thf(1660,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(1661,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(1662,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(1663,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(1664,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(1665,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(1666,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(1667,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(1668,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(1669,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(1670,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(1671,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(1672,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(1673,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(1674,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(1675,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(1676,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(1677,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(1678,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(1679,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(1680,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(1681,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(1682,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(1683,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(1684,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(1685,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(1686,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(1687,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(1688,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(1689,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(1690,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(1691,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(1692,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(1693,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(1694,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(1695,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)],[300]) ).
thf(1696,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(1697,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(1698,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(1699,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(1700,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(1701,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(1702,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(1703,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(1704,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(1705,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(1706,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(1707,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1708,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(1709,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(1710,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(1711,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(1712,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(1713,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(1714,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(1715,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(1716,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(1717,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(1718,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(1719,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(1720,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(1721,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(1722,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(1723,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(1724,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(1725,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1726,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(1727,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(1728,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(1729,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(1730,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(1731,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(1732,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(1733,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(1734,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(1735,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(1736,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(1737,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(1738,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(1739,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)],[344]) ).
thf(1740,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1741,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(1742,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(1743,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(1744,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1745,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1746,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(1747,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1748,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(1749,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(1750,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1751,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(1752,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(1753,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1754,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(1755,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(1756,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1757,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(1758,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(1759,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(1760,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(1761,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(1762,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1763,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(1764,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(1765,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(1766,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(1767,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(1768,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)],[373]) ).
thf(1769,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(1770,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)],[375]) ).
thf(1771,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(1772,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(1773,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)],[378]) ).
thf(1774,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)],[379]) ).
thf(1775,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(1776,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(1777,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(1778,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(1779,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(1780,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)],[385]) ).
thf(1781,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(1782,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(1783,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(1784,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1785,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1786,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1787,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(1788,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(1789,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(1790,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(1791,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1792,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1793,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1794,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1795,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1796,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1797,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1798,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1799,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1800,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1801,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(1802,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)],[407]) ).
thf(1803,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(1804,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1805,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1806,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1807,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1808,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1809,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1810,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1811,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1812,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(1813,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1814,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1815,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)],[420]) ).
thf(1816,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1817,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)],[422]) ).
thf(1818,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)],[423]) ).
thf(1819,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)],[424]) ).
thf(1820,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)],[425]) ).
thf(1821,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1822,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)],[427]) ).
thf(1823,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1824,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1825,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(1826,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1827,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(1828,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)],[433]) ).
thf(1829,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)],[434]) ).
thf(1830,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)],[435]) ).
thf(1831,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)],[436]) ).
thf(1832,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1833,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1834,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1835,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1836,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1837,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1838,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1839,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)],[444]) ).
thf(1840,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)],[445]) ).
thf(1841,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1842,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1843,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1844,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1845,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1846,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1847,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)],[452]) ).
thf(1848,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)],[453]) ).
thf(1849,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1850,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1851,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1852,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1853,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1854,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1855,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1856,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)],[461]) ).
thf(1857,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1858,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1859,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)],[464]) ).
thf(1860,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1861,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1862,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1863,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1864,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1865,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1866,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1867,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)],[472]) ).
thf(1868,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1869,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)],[474]) ).
thf(1870,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1871,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1872,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1873,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1874,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1875,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1876,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1877,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)],[482]) ).
thf(1878,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1879,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1880,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1881,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1882,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1883,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1884,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1885,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1886,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1887,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1888,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1889,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1890,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1891,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1892,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1893,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1894,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)],[499]) ).
thf(1895,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1896,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1897,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1898,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1899,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(1900,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1901,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)],[506]) ).
thf(1902,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1903,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1904,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1905,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1906,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1907,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1908,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)],[513]) ).
thf(1909,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1910,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)],[515]) ).
thf(1911,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1912,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1913,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1914,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1915,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)],[520]) ).
thf(1916,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)],[521]) ).
thf(1917,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)],[522]) ).
thf(1918,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1919,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1920,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1921,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1922,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1923,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)],[528]) ).
thf(1924,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)],[529]) ).
thf(1925,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1926,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1927,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1928,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1929,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1930,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1931,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1932,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1933,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1934,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1935,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)],[540]) ).
thf(1936,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1937,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)],[542]) ).
thf(1938,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1939,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1940,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1941,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1942,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1943,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1944,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1945,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1946,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1947,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1948,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1949,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1950,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1951,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1952,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1953,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1954,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1955,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1956,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)],[561]) ).
thf(1957,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1958,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)],[563]) ).
thf(1959,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(1960,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1961,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1962,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1963,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1964,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1965,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)],[570]) ).
thf(1966,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1967,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1968,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1969,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1970,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1971,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1972,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1973,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1974,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1975,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1976,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1977,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1978,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(1979,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(1980,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1981,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1982,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1983,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)],[588]) ).
thf(1984,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(1985,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(1986,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)],[591]) ).
thf(1987,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1988,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1989,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1990,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)],[595]) ).
thf(1991,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1992,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1993,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1994,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1995,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1996,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1997,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1998,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(1999,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)],[604]) ).
thf(2000,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(2001,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(2002,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(2003,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(2004,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(2005,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(2006,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(2007,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(2008,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(2009,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(2010,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(2011,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(2012,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(2013,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(2014,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(2015,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(2016,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(2017,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(2018,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(2019,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(2020,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)],[625]) ).
thf(2021,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)],[626]) ).
thf(2022,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__idom @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(2023,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(2024,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(2025,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)],[630]) ).
thf(2026,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(2027,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(2028,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(2029,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(2030,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(2031,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(2032,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(2033,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(2034,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(2035,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(2036,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(2037,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(2038,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(2039,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(2040,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(2041,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)],[646]) ).
thf(2042,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(2043,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(2044,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)],[649]) ).
thf(2045,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(2046,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(2047,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(2048,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(2049,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oinverse @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(2050,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ofield @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(2051,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(2052,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(2053,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(2054,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(2055,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(2056,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(2057,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)],[662]) ).
thf(2058,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)],[663]) ).
thf(2059,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)],[664]) ).
thf(2060,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)],[665]) ).
thf(2061,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)],[666]) ).
thf(2062,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)],[667]) ).
thf(2063,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)],[668]) ).
thf(2064,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(2065,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)],[670]) ).
thf(2066,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(2067,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(2068,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(2069,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)],[674]) ).
thf(2070,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)],[675]) ).
thf(2071,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)],[676]) ).
thf(2072,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(2073,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(2074,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(2075,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(2076,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)],[681]) ).
thf(2077,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(2078,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(2079,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)],[684]) ).
thf(2080,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)],[685]) ).
thf(2081,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(2082,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(2083,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(2084,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(2085,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)],[690]) ).
thf(2086,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(2087,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(2088,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(2089,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(2090,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(2091,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(2092,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(2093,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(2094,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(2095,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(2096,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(2097,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(2098,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(2099,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(2100,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[705]) ).
thf(2101,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(2102,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(2103,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(2104,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(2105,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[710]) ).
thf(2106,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[711]) ).
thf(2107,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[712]) ).
thf(2108,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[713]) ).
thf(2109,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[714]) ).
thf(2110,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[715]) ).
thf(2111,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[716]) ).
thf(2112,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[717]) ).
thf(2113,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[718]) ).
thf(2114,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(2115,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(2116,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(2117,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(2118,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[723]) ).
thf(2119,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[724]) ).
thf(2120,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(2121,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[726]) ).
thf(2122,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(2123,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[728]) ).
thf(2124,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[729]) ).
thf(2125,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[730]) ).
thf(2126,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(2127,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(2128,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[733]) ).
thf(2129,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[734]) ).
thf(2130,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[735]) ).
thf(2131,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(2132,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[737]) ).
thf(2133,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[738]) ).
thf(2134,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(2135,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[740]) ).
thf(2136,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[741]) ).
thf(2137,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[742]) ).
thf(2138,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[743]) ).
thf(2139,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[744]) ).
thf(2140,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[745]) ).
thf(2141,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[746]) ).
thf(2142,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[747]) ).
thf(2143,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(2144,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(2145,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[750]) ).
thf(2146,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(2147,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[752]) ).
thf(2148,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[753]) ).
thf(2149,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[754]) ).
thf(2150,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(2151,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oinverse @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[756]) ).
thf(2152,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[757]) ).
thf(2153,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[758]) ).
thf(2154,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[759]) ).
thf(2155,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[760]) ).
thf(2156,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[761]) ).
thf(2157,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[762]) ).
thf(2158,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[763]) ).
thf(2159,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(2160,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(2161,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[766]) ).
thf(2162,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(2163,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(2164,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(2165,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[770]) ).
thf(2166,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[771]) ).
thf(2167,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[772]) ).
thf(2168,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[773]) ).
thf(2169,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[774]) ).
thf(2170,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[775]) ).
thf(2171,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[776]) ).
thf(2172,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[777]) ).
thf(2173,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[778]) ).
thf(2174,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(2175,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(2176,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
| ( class_HOL_Oinverse @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(2177,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(2178,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(2179,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[784]) ).
thf(2180,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)],[785]) ).
thf(2181,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)],[786]) ).
thf(2182,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)],[787]) ).
thf(2183,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(2184,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[789]) ).
thf(2185,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)],[790]) ).
thf(2186,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)],[791]) ).
thf(2187,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)],[792]) ).
thf(2188,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)],[793]) ).
thf(2189,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[794]) ).
thf(2190,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)],[795]) ).
thf(2191,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[796]) ).
thf(2192,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[797]) ).
thf(2193,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[798]) ).
thf(2194,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[799]) ).
thf(2195,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[800]) ).
thf(2196,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[801]) ).
thf(2197,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[802]) ).
thf(2198,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[803]) ).
thf(2199,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)],[804]) ).
thf(2200,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)],[805]) ).
thf(2201,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[806]) ).
thf(2202,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[807]) ).
thf(2203,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[808]) ).
thf(2204,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[809]) ).
thf(2205,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(2206,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(2207,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)],[812]) ).
thf(2208,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[813]) ).
thf(2209,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[814]) ).
thf(2210,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[815]) ).
thf(2211,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[816]) ).
thf(2212,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[817]) ).
thf(2213,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[818]) ).
thf(2214,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[819]) ).
thf(2215,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[820]) ).
thf(2216,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[821]) ).
thf(2217,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)],[822]) ).
thf(2218,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[823]) ).
thf(2219,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[824]) ).
thf(2220,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[825]) ).
thf(2221,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[826]) ).
thf(2222,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[827]) ).
thf(2223,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[828]) ).
thf(2224,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)],[829]) ).
thf(2225,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[830]) ).
thf(2226,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)],[831]) ).
thf(2227,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[832]) ).
thf(2228,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)],[833]) ).
thf(2229,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[834]) ).
thf(2230,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[835]) ).
thf(2231,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)],[836]) ).
thf(2232,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)],[837]) ).
thf(2233,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[838]) ).
thf(2234,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[839]) ).
thf(2235,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[840]) ).
thf(2236,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[841]) ).
thf(2237,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[842]) ).
thf(2238,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[843]) ).
thf(2239,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[844]) ).
thf(2240,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(2241,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[846]) ).
thf(2242,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[847]) ).
thf(2243,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[848]) ).
thf(2244,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[849]) ).
thf(2245,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[850]) ).
thf(2246,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(2247,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[852]) ).
thf(2248,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[853]) ).
thf(2249,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[854]) ).
thf(2250,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[855]) ).
thf(2251,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[856]) ).
thf(2252,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)],[857]) ).
thf(2253,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[858]) ).
thf(2254,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[859]) ).
thf(2255,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)],[860]) ).
thf(2256,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)],[861]) ).
thf(2257,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[862]) ).
thf(2258,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)],[863]) ).
thf(2259,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)],[864]) ).
thf(2260,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[865]) ).
thf(2261,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[866]) ).
thf(2262,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[867]) ).
thf(2263,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)],[868]) ).
thf(2264,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[869]) ).
thf(2265,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[870]) ).
thf(2266,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)],[871]) ).
thf(2267,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(2268,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[873]) ).
thf(2269,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[874]) ).
thf(2270,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[875]) ).
thf(2271,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[876]) ).
thf(2272,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[877]) ).
thf(2273,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[878]) ).
thf(2274,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[879]) ).
thf(2275,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[880]) ).
thf(2276,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[881]) ).
thf(2277,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[882]) ).
thf(2278,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[883]) ).
thf(2279,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[884]) ).
thf(2280,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[885]) ).
thf(2281,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[886]) ).
thf(2282,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[887]) ).
thf(2283,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(2284,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[889]) ).
thf(2285,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(2286,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[891]) ).
thf(2287,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(2288,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)],[893]) ).
thf(2289,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[894]) ).
thf(2290,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(2291,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[896]) ).
thf(2292,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(2293,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(2294,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(2295,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[900]) ).
thf(2296,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(2297,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(2298,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[903]) ).
thf(2299,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(2300,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(2301,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(2302,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(2303,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(2304,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(2305,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[910]) ).
thf(2306,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(2307,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[912]) ).
thf(2308,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(2309,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(2310,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[915]) ).
thf(2311,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[916]) ).
thf(2312,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(2313,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[918]) ).
thf(2314,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[919]) ).
thf(2315,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[920]) ).
thf(2316,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[921]) ).
thf(2317,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(2318,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[923]) ).
thf(2319,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[924]) ).
thf(2320,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[925]) ).
thf(2321,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[926]) ).
thf(2322,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(2323,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(2324,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(2325,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[930]) ).
thf(2326,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[931]) ).
thf(2327,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(2328,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[933]) ).
thf(2329,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[934]) ).
thf(2330,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Nat_Opower @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[935]) ).
thf(2331,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Oorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[936]) ).
thf(2332,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[937]) ).
thf(2333,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[938]) ).
thf(2334,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(2335,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(2336,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(2337,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Osemigroup__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(2338,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(2339,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[944]) ).
thf(2340,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(2341,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[946]) ).
thf(2342,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[947]) ).
thf(2343,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(2344,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[949]) ).
thf(2345,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(2346,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(2347,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[952]) ).
thf(2348,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(2349,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[954]) ).
thf(2350,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[955]) ).
thf(2351,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)],[956]) ).
thf(2352,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[957]) ).
thf(2353,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[958]) ).
thf(2354,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)],[959]) ).
thf(2355,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)],[960]) ).
thf(2356,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[961]) ).
thf(2357,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[962]) ).
thf(2358,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(2359,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[964]) ).
thf(2360,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(2361,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(2362,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[967]) ).
thf(2363,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[968]) ).
thf(2364,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[969]) ).
thf(2365,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[970]) ).
thf(2366,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[971]) ).
thf(2367,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[972]) ).
thf(2368,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[973]) ).
thf(2369,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[974]) ).
thf(2370,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)],[975]) ).
thf(2371,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[976]) ).
thf(2372,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[977]) ).
thf(2373,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[978]) ).
thf(2374,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[979]) ).
thf(2375,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[980]) ).
thf(2376,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[981]) ).
thf(2377,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[982]) ).
thf(2378,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[983]) ).
thf(2379,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[984]) ).
thf(2380,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[985]) ).
thf(2381,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[986]) ).
thf(2382,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[987]) ).
thf(2383,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)],[988]) ).
thf(2384,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[989]) ).
thf(2385,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[990]) ).
thf(2386,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[991]) ).
thf(2387,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[992]) ).
thf(2388,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)],[993]) ).
thf(2389,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[994]) ).
thf(2390,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[995]) ).
thf(2391,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[996]) ).
thf(2392,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[997]) ).
thf(2393,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[998]) ).
thf(2394,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(2395,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(2396,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)],[1001]) ).
thf(2397,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1002]) ).
thf(2398,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1003]) ).
thf(2399,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1004]) ).
thf(2400,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1005]) ).
thf(2401,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1006]) ).
thf(2402,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(2403,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1008]) ).
thf(2404,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1009]) ).
thf(2405,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1010]) ).
thf(2406,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1011]) ).
thf(2407,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1012]) ).
thf(2408,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1013]) ).
thf(2409,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1014]) ).
thf(2410,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1015]) ).
thf(2411,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1016]) ).
thf(2412,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1017]) ).
thf(2413,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1018]) ).
thf(2414,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1019]) ).
thf(2415,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)],[1020]) ).
thf(2416,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1021]) ).
thf(2417,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1022]) ).
thf(2418,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1023]) ).
thf(2419,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1024]) ).
thf(2420,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1025]) ).
thf(2421,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1026]) ).
thf(2422,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1027]) ).
thf(2423,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1028]) ).
thf(2424,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1029]) ).
thf(2425,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1030]) ).
thf(2426,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1031]) ).
thf(2427,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1032]) ).
thf(2428,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1033]) ).
thf(2429,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1034]) ).
thf(2430,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1035]) ).
thf(2431,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1036]) ).
thf(2432,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1037]) ).
thf(2433,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)],[1038]) ).
thf(2434,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1039]) ).
thf(2435,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1040]) ).
thf(2436,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1041]) ).
thf(2437,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1042]) ).
thf(2438,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1043]) ).
thf(2439,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1044]) ).
thf(2440,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1045]) ).
thf(2441,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1046]) ).
thf(2442,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1047]) ).
thf(2443,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1048]) ).
thf(2444,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1049]) ).
thf(2445,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1050]) ).
thf(2446,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1051]) ).
thf(2447,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1052]) ).
thf(2448,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1053]) ).
thf(2449,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1054]) ).
thf(2450,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1055]) ).
thf(2451,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1056]) ).
thf(2452,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1057]) ).
thf(2453,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1058]) ).
thf(2454,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1059]) ).
thf(2455,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1060]) ).
thf(2456,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1061]) ).
thf(2457,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1062]) ).
thf(2458,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1063]) ).
thf(2459,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1064]) ).
thf(2460,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1065]) ).
thf(2461,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1066]) ).
thf(2462,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1067]) ).
thf(2463,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1068]) ).
thf(2464,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1069]) ).
thf(2465,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1070]) ).
thf(2466,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1071]) ).
thf(2467,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1072]) ).
thf(2468,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1073]) ).
thf(2469,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1074]) ).
thf(2470,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1075]) ).
thf(2471,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1076]) ).
thf(2472,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1077]) ).
thf(2473,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1078]) ).
thf(2474,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1079]) ).
thf(2475,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1080]) ).
thf(2476,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1081]) ).
thf(2477,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1082]) ).
thf(2478,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1083]) ).
thf(2479,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1084]) ).
thf(2480,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1085]) ).
thf(2481,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1086]) ).
thf(2482,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1087]) ).
thf(2483,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1088]) ).
thf(2484,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1089]) ).
thf(2485,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1090]) ).
thf(2486,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1091]) ).
thf(2487,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1092]) ).
thf(2488,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1093]) ).
thf(2489,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1094]) ).
thf(2490,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1095]) ).
thf(2491,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1096]) ).
thf(2492,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1097]) ).
thf(2493,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1098]) ).
thf(2494,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1099]) ).
thf(2495,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1100]) ).
thf(2496,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1101]) ).
thf(2497,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1102]) ).
thf(2498,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1103]) ).
thf(2499,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1104]) ).
thf(2500,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Numeral_Onumber @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1105]) ).
thf(2501,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1106]) ).
thf(2502,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1107]) ).
thf(2503,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1108]) ).
thf(2504,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1109]) ).
thf(2505,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1110]) ).
thf(2506,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1111]) ).
thf(2507,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1112]) ).
thf(2508,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1113]) ).
thf(2509,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1114]) ).
thf(2510,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1115]) ).
thf(2511,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1116]) ).
thf(2512,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1117]) ).
thf(2513,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1118]) ).
thf(2514,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1119]) ).
thf(2515,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1120]) ).
thf(2516,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1121]) ).
thf(2517,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1122]) ).
thf(2518,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1123]) ).
thf(2519,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1124]) ).
thf(2520,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1125]) ).
thf(2521,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1126]) ).
thf(2522,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1127]) ).
thf(2523,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1128]) ).
thf(2524,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1129]) ).
thf(2525,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1130]) ).
thf(2526,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1131]) ).
thf(2527,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1132]) ).
thf(2528,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1133]) ).
thf(2529,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1134]) ).
thf(2530,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1135]) ).
thf(2531,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1136]) ).
thf(2532,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1137]) ).
thf(2533,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)],[1138]) ).
thf(2534,plain,
( ( ! [T_1: $i] : ( class_Nat_Opower @ ( tc_set @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1139]) ).
thf(2535,plain,
( ( ! [T_1: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1140]) ).
thf(2536,plain,
( ( ! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1141]) ).
thf(2537,plain,
( ( ! [T_1: $i] : ( class_Orderings_Oord @ ( tc_set @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1142]) ).
thf(2538,plain,
( ( ! [T_1: $i] : ( class_HOL_Ominus @ ( tc_set @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1143]) ).
thf(2539,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)],[1144]) ).
thf(2540,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1145]) ).
thf(2541,plain,
( ( class_Wellfounded__Recursion_Owellorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1146]) ).
thf(2542,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1147]) ).
thf(2543,plain,
( ( class_LOrder_Olorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1148]) ).
thf(2544,plain,
( ( class_LOrder_Ojoin__semilorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1149]) ).
thf(2545,plain,
( ( class_Parity_Oeven__odd @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1150]) ).
thf(2546,plain,
( ( class_Numeral_Onumber @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1151]) ).
thf(2547,plain,
( ( class_Power_Orecpower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1152]) ).
thf(2548,plain,
( ( class_Divides_Odiv @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1153]) ).
thf(2549,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1154]) ).
thf(2550,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1155]) ).
thf(2551,plain,
( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1156]) ).
thf(2552,plain,
( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1157]) ).
thf(2553,plain,
( ( class_LOrder_Omeet__semilorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1158]) ).
thf(2554,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1159]) ).
thf(2555,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1160]) ).
thf(2556,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1161]) ).
thf(2557,plain,
( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1162]) ).
thf(2558,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1163]) ).
thf(2559,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1164]) ).
thf(2560,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1165]) ).
thf(2561,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1166]) ).
thf(2562,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1167]) ).
thf(2563,plain,
( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1168]) ).
thf(2564,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1169]) ).
thf(2565,plain,
( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1170]) ).
thf(2566,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1171]) ).
thf(2567,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1172]) ).
thf(2568,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1173]) ).
thf(2569,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1174]) ).
thf(2570,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1175]) ).
thf(2571,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1176]) ).
thf(2572,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1177]) ).
thf(2573,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1178]) ).
thf(2574,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1179]) ).
thf(2575,plain,
( ( class_Orderings_Oord @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1180]) ).
thf(2576,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1181]) ).
thf(2577,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1182]) ).
thf(2578,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1183]) ).
thf(2579,plain,
( ( class_OrderedGroup_Osemigroup__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1184]) ).
thf(2580,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1185]) ).
thf(2581,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1186]) ).
thf(2582,plain,
( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1187]) ).
thf(2583,plain,
( ( class_Nat_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1188]) ).
thf(2584,plain,
( ( class_HOL_Otimes @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1189]) ).
thf(2585,plain,
( ( class_HOL_Oplus @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1190]) ).
thf(2586,plain,
( ( class_HOL_Ozero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1191]) ).
thf(2587,plain,
( ( class_HOL_Oone @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1192]) ).
thf(2588,plain,
( ( ! [T_2: $i,T_1: $i] : ( class_Nat_Opower @ ( tc_fun @ T_2 @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1193]) ).
thf(2589,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)],[1194]) ).
thf(2590,plain,
( ( class_Finite__Set_Ofinite @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[1195]) ).
thf(2591,plain,
( ( class_Finite__Set_Ofinite @ tc_Product__Type_Ounit )
= $true ),
inference(unfold_def,[status(thm)],[1196]) ).
thf(2592,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1197]) ).
thf(2593,plain,
( ( class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1198]) ).
thf(2594,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1199]) ).
thf(2595,plain,
( ( class_Parity_Oeven__odd @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1200]) ).
thf(2596,plain,
( ( class_Power_Orecpower @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1201]) ).
thf(2597,plain,
( ( class_Nat_Opower @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1202]) ).
thf(2598,plain,
( ( class_Divides_Odiv @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1203]) ).
thf(2599,plain,
( ( class_Numeral_Onumber__ring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1204]) ).
thf(2600,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1205]) ).
thf(2601,plain,
( ( class_Numeral_Onumber @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1206]) ).
thf(2602,plain,
( ( class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1207]) ).
thf(2603,plain,
( ( class_Ring__and__Field_Oidom @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1208]) ).
thf(2604,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1209]) ).
thf(2605,plain,
( ( class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1210]) ).
thf(2606,plain,
( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1211]) ).
thf(2607,plain,
( ( class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1212]) ).
thf(2608,plain,
( ( class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1213]) ).
thf(2609,plain,
( ( class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1214]) ).
thf(2610,plain,
( ( class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1215]) ).
thf(2611,plain,
( ( class_Orderings_Oord @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1216]) ).
thf(2612,plain,
( ( class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1217]) ).
thf(2613,plain,
( ( class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1218]) ).
thf(2614,plain,
( ( class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1219]) ).
thf(2615,plain,
( ( class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1220]) ).
thf(2616,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1221]) ).
thf(2617,plain,
( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1222]) ).
thf(2618,plain,
( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1223]) ).
thf(2619,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1224]) ).
thf(2620,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1225]) ).
thf(2621,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1226]) ).
thf(2622,plain,
( ( class_HOL_Ozero @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1227]) ).
thf(2623,plain,
( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1228]) ).
thf(2624,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1229]) ).
thf(2625,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1230]) ).
thf(2626,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1231]) ).
thf(2627,plain,
( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1232]) ).
thf(2628,plain,
( ( class_LOrder_Olorder @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1233]) ).
thf(2629,plain,
( ( class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1234]) ).
thf(2630,plain,
( ( class_LOrder_Omeet__semilorder @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1235]) ).
thf(2631,plain,
( ( class_Orderings_Oorder @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1236]) ).
thf(2632,plain,
( ( class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1237]) ).
thf(2633,plain,
( ( class_HOL_Otimes @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1238]) ).
thf(2634,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1239]) ).
thf(2635,plain,
( ( class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1240]) ).
thf(2636,plain,
( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1241]) ).
thf(2637,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1242]) ).
thf(2638,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1243]) ).
thf(2639,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1244]) ).
thf(2640,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1245]) ).
thf(2641,plain,
( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1246]) ).
thf(2642,plain,
( ( class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1247]) ).
thf(2643,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1248]) ).
thf(2644,plain,
( ( class_HOL_Oplus @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1249]) ).
thf(2645,plain,
( ( class_Ring__and__Field_Oring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1250]) ).
thf(2646,plain,
( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1251]) ).
thf(2647,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1252]) ).
thf(2648,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1253]) ).
thf(2649,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1254]) ).
thf(2650,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1255]) ).
thf(2651,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1256]) ).
thf(2652,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1257]) ).
thf(2653,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1258]) ).
thf(2654,plain,
( ( class_Ring__and__Field_Osemiring @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1259]) ).
thf(2655,plain,
( ( class_HOL_Oone @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1260]) ).
thf(2656,plain,
( ( class_HOL_Ominus @ tc_IntDef_Oint )
= $true ),
inference(unfold_def,[status(thm)],[1261]) ).
thf(2657,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)],[1262]) ).
thf(2658,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)],[1263]) ).
thf(2659,plain,
( ( c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1264]) ).
thf(2660,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)],[1265]) ).
thf(2661,plain,
( ( c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1266]) ).
thf(2662,plain,
( ( ! [T_a: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[1267]) ).
thf(2663,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)],[1268]) ).
thf(2664,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)],[1269]) ).
thf(2665,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)],[1270]) ).
thf(2666,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)],[1271]) ).
thf(2667,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)],[1272]) ).
thf(2668,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)],[1273]) ).
thf(2669,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)],[1274]) ).
thf(2670,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)],[1275]) ).
thf(2671,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)],[1276]) ).
thf(2672,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)],[1277]) ).
thf(2673,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1278]) ).
thf(2674,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)],[1279]) ).
thf(2675,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)],[1280]) ).
thf(2676,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)],[1281]) ).
thf(2677,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)],[1282]) ).
thf(2678,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)],[1283]) ).
thf(2679,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)],[1284]) ).
thf(2680,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)],[1285]) ).
thf(2681,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)],[1286]) ).
thf(2682,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)],[1287]) ).
thf(2683,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)],[1288]) ).
thf(2684,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1289]) ).
thf(2685,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)],[1290]) ).
thf(2686,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)],[1291]) ).
thf(2687,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ c_UNIV @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[1292]) ).
thf(2688,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)],[1293]) ).
thf(2689,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)],[1294]) ).
thf(2690,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)],[1295]) ).
thf(2691,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)],[1296]) ).
thf(2692,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)],[1297]) ).
thf(2693,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)],[1298]) ).
thf(2694,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)],[1299]) ).
thf(2695,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)],[1300]) ).
thf(2696,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)],[1301]) ).
thf(2697,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)],[1302]) ).
thf(2698,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)],[1303]) ).
thf(2699,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)],[1304]) ).
thf(2700,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)],[1305]) ).
thf(2701,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)],[1306]) ).
thf(2702,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)],[1307]) ).
thf(2703,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)],[1308]) ).
thf(2704,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)],[1309]) ).
thf(2705,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)],[1310]) ).
thf(2706,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)],[1311]) ).
thf(2707,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)],[1312]) ).
thf(2708,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)],[1313]) ).
thf(2709,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)],[1314]) ).
thf(2710,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)],[1315]) ).
thf(2711,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)],[1316]) ).
thf(2712,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)],[1317]) ).
thf(2713,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)],[1318]) ).
thf(2714,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)],[1319]) ).
thf(2715,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)],[1320]) ).
thf(2716,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)],[1321]) ).
thf(2717,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)],[1322]) ).
thf(2718,plain,
( ( ! [V_n: $i] : ( c_less @ c_0 @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1323]) ).
thf(2719,plain,
( ( ! [V_n: $i] :
~ ( c_less @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1324]) ).
thf(2720,plain,
( ( ! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1325]) ).
thf(2721,plain,
( ( ! [V_n: $i] : ( c_lessequals @ c_0 @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1326]) ).
thf(2722,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)],[1327]) ).
thf(2723,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)],[1328]) ).
thf(2724,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)],[1329]) ).
thf(2725,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)],[1330]) ).
thf(2726,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)],[1331]) ).
thf(2727,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)],[1332]) ).
thf(2728,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)],[1333]) ).
thf(2729,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)],[1334]) ).
thf(2730,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)],[1335]) ).
thf(2731,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)],[1336]) ).
thf(2732,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)],[1337]) ).
thf(2733,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)],[1338]) ).
thf(2734,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)],[1339]) ).
thf(2735,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)],[1340]) ).
thf(2736,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)],[1341]) ).
thf(2737,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)],[1342]) ).
thf(2738,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)],[1343]) ).
thf(2739,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)],[1344]) ).
thf(2740,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)],[1345]) ).
thf(2741,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)],[1346]) ).
thf(2742,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)],[1347]) ).
thf(2743,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)],[1348]) ).
thf(2744,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)],[1349]) ).
thf(2745,plain,
( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ c_1 @ V_m @ tc_IntDef_Oint ) )
= $true ),
inference(unfold_def,[status(thm)],[1350]) ).
thf(2746,plain,
( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_IntDef_Oint ) )
= $true ),
inference(unfold_def,[status(thm)],[1351]) ).
thf(2747,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)],[1352]) ).
thf(2748,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)],[1353]) ).
thf(2749,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)],[1354]) ).
thf(2750,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)],[1355]) ).
thf(2751,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)],[1356]) ).
thf(2752,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)],[1357]) ).
thf(2753,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)],[1358]) ).
thf(2754,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)],[1359]) ).
thf(2755,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)],[1360]) ).
thf(2756,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)],[1361]) ).
thf(2757,plain,
( ( ! [T_a: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1362]) ).
thf(2758,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)],[1363]) ).
thf(2759,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)],[1364]) ).
thf(2760,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)],[1365]) ).
thf(2761,plain,
( ( ! [V_k: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ V_k @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1366]) ).
thf(2762,plain,
( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1367]) ).
thf(2763,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)],[1368]) ).
thf(2764,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)],[1369]) ).
thf(2765,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)],[1370]) ).
thf(2766,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)],[1371]) ).
thf(2767,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)],[1372]) ).
thf(2768,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)],[1373]) ).
thf(2769,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)],[1374]) ).
thf(2770,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)],[1375]) ).
thf(2771,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)],[1376]) ).
thf(2772,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)],[1377]) ).
thf(2773,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)],[1378]) ).
thf(2774,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)],[1379]) ).
thf(2775,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)],[1380]) ).
thf(2776,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)],[1381]) ).
thf(2777,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)],[1382]) ).
thf(2778,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)],[1383]) ).
thf(2779,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)],[1384]) ).
thf(2780,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)],[1385]) ).
thf(2781,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)],[1386]) ).
thf(2782,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)],[1387]) ).
thf(2783,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)],[1388]) ).
thf(2784,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)],[1389]) ).
thf(2785,plain,
( ( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ v_G @ ( 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)],[1392]) ).
thf(2786,plain,
( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ v_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[1393]) ).
thf(2787,plain,
( ( c_lessequals @ v_G @ ( c_Message_Oanalz @ v_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[1394]) ).
thf(2788,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[1395]) ).
thf(2789,plain,
( ( c_lessequals @ v_G @ ( c_Message_Oanalz @ v_G_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[2787]) ).
thf(2790,plain,
( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ v_H_H ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[2786]) ).
thf(2791,plain,
( ( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
| ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[2785]) ).
thf(2792,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)],[2784]) ).
thf(2793,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)],[2783]) ).
thf(2794,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)],[2782]) ).
thf(2795,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)],[2781]) ).
thf(2796,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)],[2780]) ).
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(copy,[status(thm)],[2779]) ).
thf(2798,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)],[2778]) ).
thf(2799,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(copy,[status(thm)],[2777]) ).
thf(2800,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(copy,[status(thm)],[2776]) ).
thf(2801,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)],[2775]) ).
thf(2802,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(copy,[status(thm)],[2774]) ).
thf(2803,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(copy,[status(thm)],[2773]) ).
thf(2804,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)],[2772]) ).
thf(2805,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)],[2771]) ).
thf(2806,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)],[2770]) ).
thf(2807,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(copy,[status(thm)],[2769]) ).
thf(2808,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)],[2768]) ).
thf(2809,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(copy,[status(thm)],[2767]) ).
thf(2810,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(copy,[status(thm)],[2766]) ).
thf(2811,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)],[2765]) ).
thf(2812,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(copy,[status(thm)],[2764]) ).
thf(2813,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(copy,[status(thm)],[2763]) ).
thf(2814,plain,
( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[2762]) ).
thf(2815,plain,
( ( ! [V_k: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ V_k @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[2761]) ).
thf(2816,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)],[2760]) ).
thf(2817,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)],[2759]) ).
thf(2818,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)],[2758]) ).
thf(2819,plain,
( ( ! [T_a: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[2757]) ).
thf(2820,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(copy,[status(thm)],[2756]) ).
thf(2821,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(copy,[status(thm)],[2755]) ).
thf(2822,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(copy,[status(thm)],[2754]) ).
thf(2823,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)],[2753]) ).
thf(2824,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)],[2752]) ).
thf(2825,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)],[2751]) ).
thf(2826,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)],[2750]) ).
thf(2827,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(copy,[status(thm)],[2749]) ).
thf(2828,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)],[2748]) ).
thf(2829,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)],[2747]) ).
thf(2830,plain,
( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ V_m @ c_0 @ tc_IntDef_Oint ) )
= $true ),
inference(copy,[status(thm)],[2746]) ).
thf(2831,plain,
( ( ! [V_m: $i] : ( c_Divides_Oop_Advd @ c_1 @ V_m @ tc_IntDef_Oint ) )
= $true ),
inference(copy,[status(thm)],[2745]) ).
thf(2832,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)],[2744]) ).
thf(2833,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)],[2743]) ).
thf(2834,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)],[2742]) ).
thf(2835,plain,
( ( ! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[2741]) ).
thf(2836,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)],[2740]) ).
thf(2837,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(copy,[status(thm)],[2739]) ).
thf(2838,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)],[2738]) ).
thf(2839,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)],[2737]) ).
thf(2840,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)],[2736]) ).
thf(2841,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)],[2735]) ).
thf(2842,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)],[2734]) ).
thf(2843,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)],[2733]) ).
thf(2844,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)],[2732]) ).
thf(2845,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)],[2731]) ).
thf(2846,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)],[2730]) ).
thf(2847,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)],[2729]) ).
thf(2848,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)],[2728]) ).
thf(2849,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)],[2727]) ).
thf(2850,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)],[2726]) ).
thf(2851,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(copy,[status(thm)],[2725]) ).
thf(2852,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)],[2724]) ).
thf(2853,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)],[2723]) ).
thf(2854,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)],[2722]) ).
thf(2855,plain,
( ( ! [V_n: $i] : ( c_lessequals @ c_0 @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[2721]) ).
thf(2856,plain,
( ( ! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[2720]) ).
thf(2857,plain,
( ( ! [V_n: $i] :
~ ( c_less @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[2719]) ).
thf(2858,plain,
( ( ! [V_n: $i] : ( c_less @ c_0 @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[2718]) ).
thf(2859,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[2717]) ).
thf(2860,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)],[2716]) ).
thf(2861,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)],[2715]) ).
thf(2862,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)],[2714]) ).
thf(2863,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)],[2713]) ).
thf(2864,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)],[2712]) ).
thf(2865,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(copy,[status(thm)],[2711]) ).
thf(2866,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)],[2710]) ).
thf(2867,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)],[2709]) ).
thf(2868,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)],[2708]) ).
thf(2869,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)],[2707]) ).
thf(2870,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)],[2706]) ).
thf(2871,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)],[2705]) ).
thf(2872,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)],[2704]) ).
thf(2873,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)],[2703]) ).
thf(2874,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)],[2702]) ).
thf(2875,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)],[2701]) ).
thf(2876,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(copy,[status(thm)],[2700]) ).
thf(2877,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)],[2699]) ).
thf(2878,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)],[2698]) ).
thf(2879,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)],[2697]) ).
thf(2880,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)],[2696]) ).
thf(2881,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)],[2695]) ).
thf(2882,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)],[2694]) ).
thf(2883,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)],[2693]) ).
thf(2884,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)],[2692]) ).
thf(2885,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)],[2691]) ).
thf(2886,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)],[2690]) ).
thf(2887,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)],[2689]) ).
thf(2888,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)],[2688]) ).
thf(2889,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ c_UNIV @ T_a ) )
= $true ),
inference(copy,[status(thm)],[2687]) ).
thf(2890,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)],[2686]) ).
thf(2891,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)],[2685]) ).
thf(2892,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ c_emptyset @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[2684]) ).
thf(2893,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)],[2683]) ).
thf(2894,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)],[2682]) ).
thf(2895,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(copy,[status(thm)],[2681]) ).
thf(2896,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)],[2680]) ).
thf(2897,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)],[2679]) ).
thf(2898,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)],[2678]) ).
thf(2899,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(copy,[status(thm)],[2677]) ).
thf(2900,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)],[2676]) ).
thf(2901,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)],[2675]) ).
thf(2902,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)],[2674]) ).
thf(2903,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[2673]) ).
thf(2904,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(copy,[status(thm)],[2672]) ).
thf(2905,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(copy,[status(thm)],[2671]) ).
thf(2906,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)],[2670]) ).
thf(2907,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(copy,[status(thm)],[2669]) ).
thf(2908,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(copy,[status(thm)],[2668]) ).
thf(2909,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)],[2667]) ).
thf(2910,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)],[2666]) ).
thf(2911,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)],[2665]) ).
thf(2912,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)],[2664]) ).
thf(2913,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)],[2663]) ).
thf(2914,plain,
( ( ! [T_a: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ T_a ) )
= $true ),
inference(copy,[status(thm)],[2662]) ).
thf(2915,plain,
( ( c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2661]) ).
thf(2916,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(copy,[status(thm)],[2660]) ).
thf(2917,plain,
( ( c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2659]) ).
thf(2918,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(copy,[status(thm)],[2658]) ).
thf(2919,plain,
( ( ! [T_1: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[2657]) ).
thf(2920,plain,
( ( class_HOL_Ominus @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2656]) ).
thf(2921,plain,
( ( class_HOL_Oone @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2655]) ).
thf(2922,plain,
( ( class_Ring__and__Field_Osemiring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2654]) ).
thf(2923,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2653]) ).
thf(2924,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2652]) ).
thf(2925,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2651]) ).
thf(2926,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2650]) ).
thf(2927,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2649]) ).
thf(2928,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2648]) ).
thf(2929,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2647]) ).
thf(2930,plain,
( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2646]) ).
thf(2931,plain,
( ( class_Ring__and__Field_Oring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2645]) ).
thf(2932,plain,
( ( class_HOL_Oplus @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2644]) ).
thf(2933,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2643]) ).
thf(2934,plain,
( ( class_Ring__and__Field_Ocomm__ring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2642]) ).
thf(2935,plain,
( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2641]) ).
thf(2936,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2640]) ).
thf(2937,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2639]) ).
thf(2938,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2638]) ).
thf(2939,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2637]) ).
thf(2940,plain,
( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2636]) ).
thf(2941,plain,
( ( class_Ring__and__Field_Oring__1 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2635]) ).
thf(2942,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2634]) ).
thf(2943,plain,
( ( class_HOL_Otimes @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2633]) ).
thf(2944,plain,
( ( class_Ring__and__Field_Ocomm__ring__1 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2632]) ).
thf(2945,plain,
( ( class_Orderings_Oorder @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2631]) ).
thf(2946,plain,
( ( class_LOrder_Omeet__semilorder @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2630]) ).
thf(2947,plain,
( ( class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2629]) ).
thf(2948,plain,
( ( class_LOrder_Olorder @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2628]) ).
thf(2949,plain,
( ( class_Orderings_Olinorder @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2627]) ).
thf(2950,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2626]) ).
thf(2951,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2625]) ).
thf(2952,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2624]) ).
thf(2953,plain,
( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2623]) ).
thf(2954,plain,
( ( class_HOL_Ozero @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2622]) ).
thf(2955,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2621]) ).
thf(2956,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2620]) ).
thf(2957,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2619]) ).
thf(2958,plain,
( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2618]) ).
thf(2959,plain,
( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2617]) ).
thf(2960,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2616]) ).
thf(2961,plain,
( ( class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2615]) ).
thf(2962,plain,
( ( class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2614]) ).
thf(2963,plain,
( ( class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2613]) ).
thf(2964,plain,
( ( class_Ring__and__Field_Opordered__ring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2612]) ).
thf(2965,plain,
( ( class_Orderings_Oord @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2611]) ).
thf(2966,plain,
( ( class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2610]) ).
thf(2967,plain,
( ( class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2609]) ).
thf(2968,plain,
( ( class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2608]) ).
thf(2969,plain,
( ( class_Ring__and__Field_Olordered__ring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2607]) ).
thf(2970,plain,
( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2606]) ).
thf(2971,plain,
( ( class_Ring__and__Field_Oordered__ring__strict @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2605]) ).
thf(2972,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2604]) ).
thf(2973,plain,
( ( class_Ring__and__Field_Oidom @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2603]) ).
thf(2974,plain,
( ( class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2602]) ).
thf(2975,plain,
( ( class_Numeral_Onumber @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2601]) ).
thf(2976,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2600]) ).
thf(2977,plain,
( ( class_Numeral_Onumber__ring @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2599]) ).
thf(2978,plain,
( ( class_Divides_Odiv @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2598]) ).
thf(2979,plain,
( ( class_Nat_Opower @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2597]) ).
thf(2980,plain,
( ( class_Power_Orecpower @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2596]) ).
thf(2981,plain,
( ( class_Parity_Oeven__odd @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2595]) ).
thf(2982,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2594]) ).
thf(2983,plain,
( ( class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2593]) ).
thf(2984,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[2592]) ).
thf(2985,plain,
( ( class_Finite__Set_Ofinite @ tc_Product__Type_Ounit )
= $true ),
inference(copy,[status(thm)],[2591]) ).
thf(2986,plain,
( ( class_Finite__Set_Ofinite @ tc_bool )
= $true ),
inference(copy,[status(thm)],[2590]) ).
thf(2987,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)],[2589]) ).
thf(2988,plain,
( ( ! [T_2: $i,T_1: $i] : ( class_Nat_Opower @ ( tc_fun @ T_2 @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[2588]) ).
thf(2989,plain,
( ( class_HOL_Oone @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2587]) ).
thf(2990,plain,
( ( class_HOL_Ozero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2586]) ).
thf(2991,plain,
( ( class_HOL_Oplus @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2585]) ).
thf(2992,plain,
( ( class_HOL_Otimes @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2584]) ).
thf(2993,plain,
( ( class_Nat_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2583]) ).
thf(2994,plain,
( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2582]) ).
thf(2995,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2581]) ).
thf(2996,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2580]) ).
thf(2997,plain,
( ( class_OrderedGroup_Osemigroup__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2579]) ).
thf(2998,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2578]) ).
thf(2999,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2577]) ).
thf(3000,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2576]) ).
thf(3001,plain,
( ( class_Orderings_Oord @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2575]) ).
thf(3002,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2574]) ).
thf(3003,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2573]) ).
thf(3004,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2572]) ).
thf(3005,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2571]) ).
thf(3006,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2570]) ).
thf(3007,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2569]) ).
thf(3008,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2568]) ).
thf(3009,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2567]) ).
thf(3010,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2566]) ).
thf(3011,plain,
( ( class_Ring__and__Field_Osemiring__0__cancel @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2565]) ).
thf(3012,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2564]) ).
thf(3013,plain,
( ( class_Ring__and__Field_Osemiring__1__cancel @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2563]) ).
thf(3014,plain,
( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2562]) ).
thf(3015,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2561]) ).
thf(3016,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2560]) ).
thf(3017,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2559]) ).
thf(3018,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2558]) ).
thf(3019,plain,
( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2557]) ).
thf(3020,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2556]) ).
thf(3021,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2555]) ).
thf(3022,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2554]) ).
thf(3023,plain,
( ( class_LOrder_Omeet__semilorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2553]) ).
thf(3024,plain,
( ( class_Ring__and__Field_Opordered__comm__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2552]) ).
thf(3025,plain,
( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2551]) ).
thf(3026,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2550]) ).
thf(3027,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2549]) ).
thf(3028,plain,
( ( class_Divides_Odiv @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2548]) ).
thf(3029,plain,
( ( class_Power_Orecpower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2547]) ).
thf(3030,plain,
( ( class_Numeral_Onumber @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2546]) ).
thf(3031,plain,
( ( class_Parity_Oeven__odd @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2545]) ).
thf(3032,plain,
( ( class_LOrder_Ojoin__semilorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2544]) ).
thf(3033,plain,
( ( class_LOrder_Olorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2543]) ).
thf(3034,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2542]) ).
thf(3035,plain,
( ( class_Wellfounded__Recursion_Owellorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2541]) ).
thf(3036,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(copy,[status(thm)],[2540]) ).
thf(3037,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)],[2539]) ).
thf(3038,plain,
( ( ! [T_1: $i] : ( class_HOL_Ominus @ ( tc_set @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[2538]) ).
thf(3039,plain,
( ( ! [T_1: $i] : ( class_Orderings_Oord @ ( tc_set @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[2537]) ).
thf(3040,plain,
( ( ! [T_1: $i] : ( class_Orderings_Oorder @ ( tc_set @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[2536]) ).
thf(3041,plain,
( ( ! [T_1: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_set @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[2535]) ).
thf(3042,plain,
( ( ! [T_1: $i] : ( class_Nat_Opower @ ( tc_set @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[2534]) ).
thf(3043,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)],[2533]) ).
thf(3044,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2532]) ).
thf(3045,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2531]) ).
thf(3046,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2530]) ).
thf(3047,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2529]) ).
thf(3048,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2528]) ).
thf(3049,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Olorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2527]) ).
thf(3050,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2526]) ).
thf(3051,plain,
( ( ! [T: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2525]) ).
thf(3052,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2524]) ).
thf(3053,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2523]) ).
thf(3054,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2522]) ).
thf(3055,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2521]) ).
thf(3056,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2520]) ).
thf(3057,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2519]) ).
thf(3058,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2518]) ).
thf(3059,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2517]) ).
thf(3060,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2516]) ).
thf(3061,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2515]) ).
thf(3062,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2514]) ).
thf(3063,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2513]) ).
thf(3064,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2512]) ).
thf(3065,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2511]) ).
thf(3066,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2510]) ).
thf(3067,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2509]) ).
thf(3068,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2508]) ).
thf(3069,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2507]) ).
thf(3070,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2506]) ).
thf(3071,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2505]) ).
thf(3072,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2504]) ).
thf(3073,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2503]) ).
thf(3074,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2502]) ).
thf(3075,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2501]) ).
thf(3076,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Numeral_Onumber @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2500]) ).
thf(3077,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2499]) ).
thf(3078,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2498]) ).
thf(3079,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2497]) ).
thf(3080,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2496]) ).
thf(3081,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2495]) ).
thf(3082,plain,
( ( ! [T: $i] :
( ~ ( class_Numeral_Onumber__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2494]) ).
thf(3083,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2493]) ).
thf(3084,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2492]) ).
thf(3085,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2491]) ).
thf(3086,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2490]) ).
thf(3087,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2489]) ).
thf(3088,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2488]) ).
thf(3089,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2487]) ).
thf(3090,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2486]) ).
thf(3091,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2485]) ).
thf(3092,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2484]) ).
thf(3093,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2483]) ).
thf(3094,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2482]) ).
thf(3095,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2481]) ).
thf(3096,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2480]) ).
thf(3097,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2479]) ).
thf(3098,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2478]) ).
thf(3099,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2477]) ).
thf(3100,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2476]) ).
thf(3101,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2475]) ).
thf(3102,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2474]) ).
thf(3103,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2473]) ).
thf(3104,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2472]) ).
thf(3105,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2471]) ).
thf(3106,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2470]) ).
thf(3107,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2469]) ).
thf(3108,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2468]) ).
thf(3109,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2467]) ).
thf(3110,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2466]) ).
thf(3111,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2465]) ).
thf(3112,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2464]) ).
thf(3113,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2463]) ).
thf(3114,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2462]) ).
thf(3115,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2461]) ).
thf(3116,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2460]) ).
thf(3117,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2459]) ).
thf(3118,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2458]) ).
thf(3119,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2457]) ).
thf(3120,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2456]) ).
thf(3121,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2455]) ).
thf(3122,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2454]) ).
thf(3123,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2453]) ).
thf(3124,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2452]) ).
thf(3125,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2451]) ).
thf(3126,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2450]) ).
thf(3127,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2449]) ).
thf(3128,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2448]) ).
thf(3129,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2447]) ).
thf(3130,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2446]) ).
thf(3131,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2445]) ).
thf(3132,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2444]) ).
thf(3133,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2443]) ).
thf(3134,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2442]) ).
thf(3135,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2441]) ).
thf(3136,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2440]) ).
thf(3137,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2439]) ).
thf(3138,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2438]) ).
thf(3139,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2437]) ).
thf(3140,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2436]) ).
thf(3141,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2435]) ).
thf(3142,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2434]) ).
thf(3143,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2433]) ).
thf(3144,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2432]) ).
thf(3145,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2431]) ).
thf(3146,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2430]) ).
thf(3147,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2429]) ).
thf(3148,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2428]) ).
thf(3149,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2427]) ).
thf(3150,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2426]) ).
thf(3151,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2425]) ).
thf(3152,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2424]) ).
thf(3153,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2423]) ).
thf(3154,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2422]) ).
thf(3155,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2421]) ).
thf(3156,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2420]) ).
thf(3157,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2419]) ).
thf(3158,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2418]) ).
thf(3159,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2417]) ).
thf(3160,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2416]) ).
thf(3161,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2415]) ).
thf(3162,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2414]) ).
thf(3163,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2413]) ).
thf(3164,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2412]) ).
thf(3165,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2411]) ).
thf(3166,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2410]) ).
thf(3167,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2409]) ).
thf(3168,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2408]) ).
thf(3169,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2407]) ).
thf(3170,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2406]) ).
thf(3171,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2405]) ).
thf(3172,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2404]) ).
thf(3173,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2403]) ).
thf(3174,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2402]) ).
thf(3175,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2401]) ).
thf(3176,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2400]) ).
thf(3177,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2399]) ).
thf(3178,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2398]) ).
thf(3179,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2397]) ).
thf(3180,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2396]) ).
thf(3181,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2395]) ).
thf(3182,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2394]) ).
thf(3183,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2393]) ).
thf(3184,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2392]) ).
thf(3185,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2391]) ).
thf(3186,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2390]) ).
thf(3187,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2389]) ).
thf(3188,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2388]) ).
thf(3189,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2387]) ).
thf(3190,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2386]) ).
thf(3191,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2385]) ).
thf(3192,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2384]) ).
thf(3193,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)],[2383]) ).
thf(3194,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2382]) ).
thf(3195,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2381]) ).
thf(3196,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2380]) ).
thf(3197,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2379]) ).
thf(3198,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2378]) ).
thf(3199,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2377]) ).
thf(3200,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2376]) ).
thf(3201,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2375]) ).
thf(3202,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2374]) ).
thf(3203,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2373]) ).
thf(3204,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2372]) ).
thf(3205,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2371]) ).
thf(3206,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2370]) ).
thf(3207,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2369]) ).
thf(3208,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2368]) ).
thf(3209,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2367]) ).
thf(3210,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2366]) ).
thf(3211,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2365]) ).
thf(3212,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2364]) ).
thf(3213,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2363]) ).
thf(3214,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2362]) ).
thf(3215,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2361]) ).
thf(3216,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2360]) ).
thf(3217,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2359]) ).
thf(3218,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2358]) ).
thf(3219,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2357]) ).
thf(3220,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2356]) ).
thf(3221,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)],[2355]) ).
thf(3222,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2354]) ).
thf(3223,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2353]) ).
thf(3224,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2352]) ).
thf(3225,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2351]) ).
thf(3226,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2350]) ).
thf(3227,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2349]) ).
thf(3228,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2348]) ).
thf(3229,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2347]) ).
thf(3230,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2346]) ).
thf(3231,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2345]) ).
thf(3232,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2344]) ).
thf(3233,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2343]) ).
thf(3234,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2342]) ).
thf(3235,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2341]) ).
thf(3236,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2340]) ).
thf(3237,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2339]) ).
thf(3238,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2338]) ).
thf(3239,plain,
( ( ! [T: $i] :
( ~ ( class_OrderedGroup_Osemigroup__mult @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2337]) ).
thf(3240,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2336]) ).
thf(3241,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2335]) ).
thf(3242,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2334]) ).
thf(3243,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2333]) ).
thf(3244,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Olinorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2332]) ).
thf(3245,plain,
( ( ! [T: $i] :
( ~ ( class_Orderings_Oorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2331]) ).
thf(3246,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Nat_Opower @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2330]) ).
thf(3247,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2329]) ).
thf(3248,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2328]) ).
thf(3249,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2327]) ).
thf(3250,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2326]) ).
thf(3251,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2325]) ).
thf(3252,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2324]) ).
thf(3253,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2323]) ).
thf(3254,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2322]) ).
thf(3255,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2321]) ).
thf(3256,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2320]) ).
thf(3257,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2319]) ).
thf(3258,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2318]) ).
thf(3259,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2317]) ).
thf(3260,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2316]) ).
thf(3261,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2315]) ).
thf(3262,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2314]) ).
thf(3263,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2313]) ).
thf(3264,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2312]) ).
thf(3265,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2311]) ).
thf(3266,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2310]) ).
thf(3267,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2309]) ).
thf(3268,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2308]) ).
thf(3269,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2307]) ).
thf(3270,plain,
( ( ! [T: $i] :
( ~ ( class_Power_Orecpower @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2306]) ).
thf(3271,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2305]) ).
thf(3272,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2304]) ).
thf(3273,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2303]) ).
thf(3274,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2302]) ).
thf(3275,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2301]) ).
thf(3276,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2300]) ).
thf(3277,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2299]) ).
thf(3278,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2298]) ).
thf(3279,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2297]) ).
thf(3280,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2296]) ).
thf(3281,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2295]) ).
thf(3282,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2294]) ).
thf(3283,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2293]) ).
thf(3284,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2292]) ).
thf(3285,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2291]) ).
thf(3286,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2290]) ).
thf(3287,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2289]) ).
thf(3288,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2288]) ).
thf(3289,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2287]) ).
thf(3290,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2286]) ).
thf(3291,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2285]) ).
thf(3292,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2284]) ).
thf(3293,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2283]) ).
thf(3294,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2282]) ).
thf(3295,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2281]) ).
thf(3296,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2280]) ).
thf(3297,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2279]) ).
thf(3298,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2278]) ).
thf(3299,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2277]) ).
thf(3300,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2276]) ).
thf(3301,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2275]) ).
thf(3302,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2274]) ).
thf(3303,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2273]) ).
thf(3304,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2272]) ).
thf(3305,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2271]) ).
thf(3306,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2270]) ).
thf(3307,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2269]) ).
thf(3308,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2268]) ).
thf(3309,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2267]) ).
thf(3310,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2266]) ).
thf(3311,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2265]) ).
thf(3312,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2264]) ).
thf(3313,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)],[2263]) ).
thf(3314,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2262]) ).
thf(3315,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2261]) ).
thf(3316,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2260]) ).
thf(3317,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2259]) ).
thf(3318,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)],[2258]) ).
thf(3319,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2257]) ).
thf(3320,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)],[2256]) ).
thf(3321,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2255]) ).
thf(3322,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2254]) ).
thf(3323,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2253]) ).
thf(3324,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2252]) ).
thf(3325,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2251]) ).
thf(3326,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2250]) ).
thf(3327,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2249]) ).
thf(3328,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2248]) ).
thf(3329,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2247]) ).
thf(3330,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2246]) ).
thf(3331,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2245]) ).
thf(3332,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2244]) ).
thf(3333,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2243]) ).
thf(3334,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2242]) ).
thf(3335,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2241]) ).
thf(3336,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2240]) ).
thf(3337,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2239]) ).
thf(3338,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2238]) ).
thf(3339,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2237]) ).
thf(3340,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2236]) ).
thf(3341,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2235]) ).
thf(3342,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2234]) ).
thf(3343,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2233]) ).
thf(3344,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)],[2232]) ).
thf(3345,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2231]) ).
thf(3346,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2230]) ).
thf(3347,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2229]) ).
thf(3348,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2228]) ).
thf(3349,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2227]) ).
thf(3350,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)],[2226]) ).
thf(3351,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2225]) ).
thf(3352,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2224]) ).
thf(3353,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2223]) ).
thf(3354,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2222]) ).
thf(3355,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2221]) ).
thf(3356,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2220]) ).
thf(3357,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2219]) ).
thf(3358,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2218]) ).
thf(3359,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)],[2217]) ).
thf(3360,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2216]) ).
thf(3361,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2215]) ).
thf(3362,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2214]) ).
thf(3363,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2213]) ).
thf(3364,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2212]) ).
thf(3365,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2211]) ).
thf(3366,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2210]) ).
thf(3367,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2209]) ).
thf(3368,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2208]) ).
thf(3369,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2207]) ).
thf(3370,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2206]) ).
thf(3371,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2205]) ).
thf(3372,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2204]) ).
thf(3373,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2203]) ).
thf(3374,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2202]) ).
thf(3375,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2201]) ).
thf(3376,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)],[2200]) ).
thf(3377,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)],[2199]) ).
thf(3378,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2198]) ).
thf(3379,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2197]) ).
thf(3380,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2196]) ).
thf(3381,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2195]) ).
thf(3382,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2194]) ).
thf(3383,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2193]) ).
thf(3384,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2192]) ).
thf(3385,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2191]) ).
thf(3386,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2190]) ).
thf(3387,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2189]) ).
thf(3388,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2188]) ).
thf(3389,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)],[2187]) ).
thf(3390,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)],[2186]) ).
thf(3391,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)],[2185]) ).
thf(3392,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2184]) ).
thf(3393,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2183]) ).
thf(3394,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2182]) ).
thf(3395,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)],[2181]) ).
thf(3396,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2180]) ).
thf(3397,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2179]) ).
thf(3398,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2178]) ).
thf(3399,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2177]) ).
thf(3400,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T )
| ( class_HOL_Oinverse @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2176]) ).
thf(3401,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2175]) ).
thf(3402,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2174]) ).
thf(3403,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2173]) ).
thf(3404,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2172]) ).
thf(3405,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2171]) ).
thf(3406,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2170]) ).
thf(3407,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2169]) ).
thf(3408,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2168]) ).
thf(3409,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2167]) ).
thf(3410,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2166]) ).
thf(3411,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2165]) ).
thf(3412,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2164]) ).
thf(3413,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2163]) ).
thf(3414,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2162]) ).
thf(3415,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2161]) ).
thf(3416,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2160]) ).
thf(3417,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2159]) ).
thf(3418,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2158]) ).
thf(3419,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2157]) ).
thf(3420,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2156]) ).
thf(3421,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2155]) ).
thf(3422,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2154]) ).
thf(3423,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2153]) ).
thf(3424,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2152]) ).
thf(3425,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Oinverse @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2151]) ).
thf(3426,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2150]) ).
thf(3427,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2149]) ).
thf(3428,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2148]) ).
thf(3429,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2147]) ).
thf(3430,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2146]) ).
thf(3431,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2145]) ).
thf(3432,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2144]) ).
thf(3433,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2143]) ).
thf(3434,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2142]) ).
thf(3435,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2141]) ).
thf(3436,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2140]) ).
thf(3437,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2139]) ).
thf(3438,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2138]) ).
thf(3439,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2137]) ).
thf(3440,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2136]) ).
thf(3441,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2135]) ).
thf(3442,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2134]) ).
thf(3443,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2133]) ).
thf(3444,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2132]) ).
thf(3445,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2131]) ).
thf(3446,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2130]) ).
thf(3447,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2129]) ).
thf(3448,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2128]) ).
thf(3449,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2127]) ).
thf(3450,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2126]) ).
thf(3451,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2125]) ).
thf(3452,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2124]) ).
thf(3453,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2123]) ).
thf(3454,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2122]) ).
thf(3455,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2121]) ).
thf(3456,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2120]) ).
thf(3457,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2119]) ).
thf(3458,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2118]) ).
thf(3459,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2117]) ).
thf(3460,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2116]) ).
thf(3461,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2115]) ).
thf(3462,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2114]) ).
thf(3463,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2113]) ).
thf(3464,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2112]) ).
thf(3465,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2111]) ).
thf(3466,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2110]) ).
thf(3467,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2109]) ).
thf(3468,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2108]) ).
thf(3469,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2107]) ).
thf(3470,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2106]) ).
thf(3471,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2105]) ).
thf(3472,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2104]) ).
thf(3473,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2103]) ).
thf(3474,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2102]) ).
thf(3475,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2101]) ).
thf(3476,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2100]) ).
thf(3477,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2099]) ).
thf(3478,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2098]) ).
thf(3479,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2097]) ).
thf(3480,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2096]) ).
thf(3481,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2095]) ).
thf(3482,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2094]) ).
thf(3483,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2093]) ).
thf(3484,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2092]) ).
thf(3485,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2091]) ).
thf(3486,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2090]) ).
thf(3487,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2089]) ).
thf(3488,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2088]) ).
thf(3489,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2087]) ).
thf(3490,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2086]) ).
thf(3491,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2085]) ).
thf(3492,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2084]) ).
thf(3493,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2083]) ).
thf(3494,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2082]) ).
thf(3495,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2081]) ).
thf(3496,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)],[2080]) ).
thf(3497,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2079]) ).
thf(3498,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2078]) ).
thf(3499,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2077]) ).
thf(3500,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)],[2076]) ).
thf(3501,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2075]) ).
thf(3502,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2074]) ).
thf(3503,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2073]) ).
thf(3504,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2072]) ).
thf(3505,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)],[2071]) ).
thf(3506,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)],[2070]) ).
thf(3507,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2069]) ).
thf(3508,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2068]) ).
thf(3509,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2067]) ).
thf(3510,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2066]) ).
thf(3511,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2065]) ).
thf(3512,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2064]) ).
thf(3513,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)],[2063]) ).
thf(3514,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)],[2062]) ).
thf(3515,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)],[2061]) ).
thf(3516,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2060]) ).
thf(3517,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)],[2059]) ).
thf(3518,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)],[2058]) ).
thf(3519,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2057]) ).
thf(3520,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2056]) ).
thf(3521,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2055]) ).
thf(3522,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2054]) ).
thf(3523,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2053]) ).
thf(3524,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2052]) ).
thf(3525,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2051]) ).
thf(3526,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ofield @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2050]) ).
thf(3527,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oinverse @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2049]) ).
thf(3528,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2048]) ).
thf(3529,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2047]) ).
thf(3530,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2046]) ).
thf(3531,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2045]) ).
thf(3532,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2044]) ).
thf(3533,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2043]) ).
thf(3534,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2042]) ).
thf(3535,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2041]) ).
thf(3536,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2040]) ).
thf(3537,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2039]) ).
thf(3538,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2038]) ).
thf(3539,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2037]) ).
thf(3540,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2036]) ).
thf(3541,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2035]) ).
thf(3542,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2034]) ).
thf(3543,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2033]) ).
thf(3544,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2032]) ).
thf(3545,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2031]) ).
thf(3546,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2030]) ).
thf(3547,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2029]) ).
thf(3548,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2028]) ).
thf(3549,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2027]) ).
thf(3550,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2026]) ).
thf(3551,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2025]) ).
thf(3552,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2024]) ).
thf(3553,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2023]) ).
thf(3554,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__idom @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2022]) ).
thf(3555,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2021]) ).
thf(3556,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2020]) ).
thf(3557,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2019]) ).
thf(3558,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2018]) ).
thf(3559,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2017]) ).
thf(3560,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2016]) ).
thf(3561,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2015]) ).
thf(3562,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2014]) ).
thf(3563,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2013]) ).
thf(3564,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2012]) ).
thf(3565,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2011]) ).
thf(3566,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2010]) ).
thf(3567,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2009]) ).
thf(3568,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2008]) ).
thf(3569,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2007]) ).
thf(3570,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2006]) ).
thf(3571,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2005]) ).
thf(3572,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2004]) ).
thf(3573,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2003]) ).
thf(3574,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2002]) ).
thf(3575,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2001]) ).
thf(3576,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[2000]) ).
thf(3577,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1999]) ).
thf(3578,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1998]) ).
thf(3579,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1997]) ).
thf(3580,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1996]) ).
thf(3581,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1995]) ).
thf(3582,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1994]) ).
thf(3583,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1993]) ).
thf(3584,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1992]) ).
thf(3585,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1991]) ).
thf(3586,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1990]) ).
thf(3587,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1989]) ).
thf(3588,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1988]) ).
thf(3589,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1987]) ).
thf(3590,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1986]) ).
thf(3591,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1985]) ).
thf(3592,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1984]) ).
thf(3593,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1983]) ).
thf(3594,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1982]) ).
thf(3595,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1981]) ).
thf(3596,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1980]) ).
thf(3597,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1979]) ).
thf(3598,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1978]) ).
thf(3599,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1977]) ).
thf(3600,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1976]) ).
thf(3601,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1975]) ).
thf(3602,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1974]) ).
thf(3603,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1973]) ).
thf(3604,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1972]) ).
thf(3605,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1971]) ).
thf(3606,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1970]) ).
thf(3607,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1969]) ).
thf(3608,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1968]) ).
thf(3609,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1967]) ).
thf(3610,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1966]) ).
thf(3611,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1965]) ).
thf(3612,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1964]) ).
thf(3613,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1963]) ).
thf(3614,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1962]) ).
thf(3615,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1961]) ).
thf(3616,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1960]) ).
thf(3617,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1959]) ).
thf(3618,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1958]) ).
thf(3619,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1957]) ).
thf(3620,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1956]) ).
thf(3621,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1955]) ).
thf(3622,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1954]) ).
thf(3623,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1953]) ).
thf(3624,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1952]) ).
thf(3625,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1951]) ).
thf(3626,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1950]) ).
thf(3627,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1949]) ).
thf(3628,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1948]) ).
thf(3629,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__ring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1947]) ).
thf(3630,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1946]) ).
thf(3631,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1945]) ).
thf(3632,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1944]) ).
thf(3633,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1943]) ).
thf(3634,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1942]) ).
thf(3635,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1941]) ).
thf(3636,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1940]) ).
thf(3637,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1939]) ).
thf(3638,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oordered__semidom @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1938]) ).
thf(3639,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1937]) ).
thf(3640,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1936]) ).
thf(3641,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1935]) ).
thf(3642,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1934]) ).
thf(3643,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1933]) ).
thf(3644,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1932]) ).
thf(3645,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1931]) ).
thf(3646,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1930]) ).
thf(3647,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1929]) ).
thf(3648,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1928]) ).
thf(3649,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1927]) ).
thf(3650,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1926]) ).
thf(3651,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1925]) ).
thf(3652,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1924]) ).
thf(3653,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1923]) ).
thf(3654,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1922]) ).
thf(3655,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1921]) ).
thf(3656,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1920]) ).
thf(3657,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1919]) ).
thf(3658,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1918]) ).
thf(3659,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)],[1917]) ).
thf(3660,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1916]) ).
thf(3661,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1915]) ).
thf(3662,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1914]) ).
thf(3663,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1913]) ).
thf(3664,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1912]) ).
thf(3665,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1911]) ).
thf(3666,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Oaxclass__abs__if @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1910]) ).
thf(3667,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1909]) ).
thf(3668,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1908]) ).
thf(3669,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1907]) ).
thf(3670,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Olordered__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1906]) ).
thf(3671,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Opordered__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1905]) ).
thf(3672,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1904]) ).
thf(3673,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__meet @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1903]) ).
thf(3674,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Olordered__ab__group__join @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1902]) ).
thf(3675,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)],[1901]) ).
thf(3676,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1900]) ).
thf(3677,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1899]) ).
thf(3678,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1898]) ).
thf(3679,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1897]) ).
thf(3680,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1896]) ).
thf(3681,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1895]) ).
thf(3682,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1894]) ).
thf(3683,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1893]) ).
thf(3684,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1892]) ).
thf(3685,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1891]) ).
thf(3686,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1890]) ).
thf(3687,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1889]) ).
thf(3688,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1888]) ).
thf(3689,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1887]) ).
thf(3690,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1886]) ).
thf(3691,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1885]) ).
thf(3692,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1884]) ).
thf(3693,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1883]) ).
thf(3694,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocomm__monoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1882]) ).
thf(3695,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1881]) ).
thf(3696,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1880]) ).
thf(3697,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1879]) ).
thf(3698,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1878]) ).
thf(3699,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1877]) ).
thf(3700,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Oordered__semiring__strict @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1876]) ).
thf(3701,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1875]) ).
thf(3702,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1874]) ).
thf(3703,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1873]) ).
thf(3704,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1872]) ).
thf(3705,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1871]) ).
thf(3706,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1870]) ).
thf(3707,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1869]) ).
thf(3708,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1868]) ).
thf(3709,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1867]) ).
thf(3710,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1866]) ).
thf(3711,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1865]) ).
thf(3712,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1864]) ).
thf(3713,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1863]) ).
thf(3714,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1862]) ).
thf(3715,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1861]) ).
thf(3716,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1860]) ).
thf(3717,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1859]) ).
thf(3718,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1858]) ).
thf(3719,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1857]) ).
thf(3720,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1856]) ).
thf(3721,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1855]) ).
thf(3722,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1854]) ).
thf(3723,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1853]) ).
thf(3724,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1852]) ).
thf(3725,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1851]) ).
thf(3726,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1850]) ).
thf(3727,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1849]) ).
thf(3728,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)],[1848]) ).
thf(3729,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1847]) ).
thf(3730,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1846]) ).
thf(3731,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1845]) ).
thf(3732,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1844]) ).
thf(3733,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1843]) ).
thf(3734,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1842]) ).
thf(3735,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1841]) ).
thf(3736,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1840]) ).
thf(3737,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1839]) ).
thf(3738,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1838]) ).
thf(3739,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1837]) ).
thf(3740,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1836]) ).
thf(3741,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1835]) ).
thf(3742,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1834]) ).
thf(3743,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1833]) ).
thf(3744,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1832]) ).
thf(3745,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1831]) ).
thf(3746,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)],[1830]) ).
thf(3747,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)],[1829]) ).
thf(3748,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1828]) ).
thf(3749,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1827]) ).
thf(3750,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1826]) ).
thf(3751,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1825]) ).
thf(3752,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1824]) ).
thf(3753,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1823]) ).
thf(3754,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1822]) ).
thf(3755,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1821]) ).
thf(3756,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1820]) ).
thf(3757,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)],[1819]) ).
thf(3758,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1818]) ).
thf(3759,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)],[1817]) ).
thf(3760,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1816]) ).
thf(3761,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1815]) ).
thf(3762,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1814]) ).
thf(3763,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1813]) ).
thf(3764,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1812]) ).
thf(3765,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1811]) ).
thf(3766,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1810]) ).
thf(3767,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1809]) ).
thf(3768,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1808]) ).
thf(3769,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1807]) ).
thf(3770,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1806]) ).
thf(3771,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1805]) ).
thf(3772,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1804]) ).
thf(3773,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1803]) ).
thf(3774,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1802]) ).
thf(3775,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1801]) ).
thf(3776,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1800]) ).
thf(3777,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1799]) ).
thf(3778,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1798]) ).
thf(3779,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1797]) ).
thf(3780,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1796]) ).
thf(3781,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1795]) ).
thf(3782,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1794]) ).
thf(3783,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1793]) ).
thf(3784,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1792]) ).
thf(3785,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1791]) ).
thf(3786,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1790]) ).
thf(3787,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1789]) ).
thf(3788,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1788]) ).
thf(3789,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1787]) ).
thf(3790,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1786]) ).
thf(3791,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1785]) ).
thf(3792,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1784]) ).
thf(3793,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1783]) ).
thf(3794,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1782]) ).
thf(3795,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1781]) ).
thf(3796,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Opordered__comm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1780]) ).
thf(3797,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1779]) ).
thf(3798,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1778]) ).
thf(3799,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1777]) ).
thf(3800,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1776]) ).
thf(3801,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1775]) ).
thf(3802,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)],[1774]) ).
thf(3803,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1773]) ).
thf(3804,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1772]) ).
thf(3805,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1771]) ).
thf(3806,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1770]) ).
thf(3807,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1769]) ).
thf(3808,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1768]) ).
thf(3809,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Ocomm__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1767]) ).
thf(3810,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1766]) ).
thf(3811,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1765]) ).
thf(3812,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1764]) ).
thf(3813,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1763]) ).
thf(3814,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1762]) ).
thf(3815,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1761]) ).
thf(3816,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1760]) ).
thf(3817,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1759]) ).
thf(3818,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1758]) ).
thf(3819,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1757]) ).
thf(3820,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1756]) ).
thf(3821,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1755]) ).
thf(3822,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1754]) ).
thf(3823,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1753]) ).
thf(3824,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1752]) ).
thf(3825,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1751]) ).
thf(3826,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1750]) ).
thf(3827,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1749]) ).
thf(3828,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1748]) ).
thf(3829,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1747]) ).
thf(3830,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1746]) ).
thf(3831,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Opordered__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1745]) ).
thf(3832,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1744]) ).
thf(3833,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1743]) ).
thf(3834,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1742]) ).
thf(3835,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1741]) ).
thf(3836,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1740]) ).
thf(3837,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1739]) ).
thf(3838,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1738]) ).
thf(3839,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1737]) ).
thf(3840,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1736]) ).
thf(3841,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1735]) ).
thf(3842,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1734]) ).
thf(3843,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1733]) ).
thf(3844,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1732]) ).
thf(3845,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1731]) ).
thf(3846,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1730]) ).
thf(3847,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1729]) ).
thf(3848,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1728]) ).
thf(3849,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1727]) ).
thf(3850,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1726]) ).
thf(3851,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1725]) ).
thf(3852,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1724]) ).
thf(3853,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1723]) ).
thf(3854,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1722]) ).
thf(3855,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1721]) ).
thf(3856,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1720]) ).
thf(3857,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1719]) ).
thf(3858,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1718]) ).
thf(3859,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1717]) ).
thf(3860,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1716]) ).
thf(3861,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1715]) ).
thf(3862,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1714]) ).
thf(3863,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1713]) ).
thf(3864,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1712]) ).
thf(3865,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1711]) ).
thf(3866,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1710]) ).
thf(3867,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1709]) ).
thf(3868,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1708]) ).
thf(3869,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1707]) ).
thf(3870,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1706]) ).
thf(3871,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1705]) ).
thf(3872,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1704]) ).
thf(3873,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Oring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1703]) ).
thf(3874,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1702]) ).
thf(3875,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1701]) ).
thf(3876,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1700]) ).
thf(3877,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1699]) ).
thf(3878,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1698]) ).
thf(3879,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1697]) ).
thf(3880,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1696]) ).
thf(3881,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1695]) ).
thf(3882,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1694]) ).
thf(3883,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1693]) ).
thf(3884,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__1__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1692]) ).
thf(3885,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Ominus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1691]) ).
thf(3886,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1690]) ).
thf(3887,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1689]) ).
thf(3888,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1688]) ).
thf(3889,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1687]) ).
thf(3890,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1686]) ).
thf(3891,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1685]) ).
thf(3892,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1684]) ).
thf(3893,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1683]) ).
thf(3894,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1682]) ).
thf(3895,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1681]) ).
thf(3896,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1680]) ).
thf(3897,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1679]) ).
thf(3898,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1678]) ).
thf(3899,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1677]) ).
thf(3900,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1676]) ).
thf(3901,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1675]) ).
thf(3902,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1674]) ).
thf(3903,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1673]) ).
thf(3904,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1672]) ).
thf(3905,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1671]) ).
thf(3906,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1670]) ).
thf(3907,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1669]) ).
thf(3908,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1668]) ).
thf(3909,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1667]) ).
thf(3910,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1666]) ).
thf(3911,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1665]) ).
thf(3912,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1664]) ).
thf(3913,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1663]) ).
thf(3914,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1662]) ).
thf(3915,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1661]) ).
thf(3916,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1660]) ).
thf(3917,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1659]) ).
thf(3918,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1658]) ).
thf(3919,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1657]) ).
thf(3920,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1656]) ).
thf(3921,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1655]) ).
thf(3922,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1654]) ).
thf(3923,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1653]) ).
thf(3924,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1652]) ).
thf(3925,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1651]) ).
thf(3926,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1650]) ).
thf(3927,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1649]) ).
thf(3928,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1648]) ).
thf(3929,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1647]) ).
thf(3930,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)],[1646]) ).
thf(3931,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Oone @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1645]) ).
thf(3932,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1644]) ).
thf(3933,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Otimes @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1643]) ).
thf(3934,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1642]) ).
thf(3935,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1641]) ).
thf(3936,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0__cancel @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1640]) ).
thf(3937,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1639]) ).
thf(3938,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_Ring__and__Field_Osemiring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1638]) ).
thf(3939,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1637]) ).
thf(3940,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Ozero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1636]) ).
thf(3941,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1635]) ).
thf(3942,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Osemigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1634]) ).
thf(3943,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_HOL_Oplus @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1633]) ).
thf(3944,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1632]) ).
thf(3945,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Oord @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1631]) ).
thf(3946,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1630]) ).
thf(3947,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Omeet__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1629]) ).
thf(3948,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Ojoin__semilorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1628]) ).
thf(3949,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_LOrder_Olorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1627]) ).
thf(3950,plain,
( ( ! [T: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ T )
| ( class_Orderings_Olinorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[1626]) ).
thf(3951,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)],[1625]) ).
thf(3952,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)],[1624]) ).
thf(3953,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(copy,[status(thm)],[1623]) ).
thf(3954,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(copy,[status(thm)],[1622]) ).
thf(3955,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)],[1621]) ).
thf(3956,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)],[1620]) ).
thf(3957,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)],[1619]) ).
thf(3958,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)],[1618]) ).
thf(3959,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)],[1617]) ).
thf(3960,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)],[1616]) ).
thf(3961,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)],[1615]) ).
thf(3962,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)],[1614]) ).
thf(3963,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)],[1613]) ).
thf(3964,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)],[1612]) ).
thf(3965,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)],[1611]) ).
thf(3966,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)],[1610]) ).
thf(3967,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)],[1609]) ).
thf(3968,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)],[1608]) ).
thf(3969,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)],[1607]) ).
thf(3970,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)],[1606]) ).
thf(3971,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)],[1605]) ).
thf(3972,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)],[1604]) ).
thf(3973,plain,
( ( ! [V_m: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_nat )
| ( V_m = c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[1603]) ).
thf(3974,plain,
( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1602]) ).
thf(3975,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)],[1601]) ).
thf(3976,plain,
( ( ! [V_r: $i,T_a: $i] :
( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1600]) ).
thf(3977,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)],[1599]) ).
thf(3978,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Equiv__Relations_Oquotient @ c_emptyset @ V_r @ T_a )
= c_emptyset ) )
= $true ),
inference(copy,[status(thm)],[1598]) ).
thf(3979,plain,
( ( c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight )
= $true ),
inference(copy,[status(thm)],[1597]) ).
thf(3980,plain,
( ( c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft )
= $true ),
inference(copy,[status(thm)],[1596]) ).
thf(3981,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)],[1595]) ).
thf(3982,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(copy,[status(thm)],[1594]) ).
thf(3983,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)],[1593]) ).
thf(3984,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)],[1592]) ).
thf(3985,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)],[1591]) ).
thf(3986,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)],[1590]) ).
thf(3987,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(copy,[status(thm)],[1589]) ).
thf(3988,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)],[1588]) ).
thf(3989,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)],[1587]) ).
thf(3990,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)],[1586]) ).
thf(3991,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)],[1585]) ).
thf(3992,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(copy,[status(thm)],[1584]) ).
thf(3993,plain,
( ( ~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1583]) ).
thf(3994,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)],[1582]) ).
thf(3995,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)],[1581]) ).
thf(3996,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)],[1580]) ).
thf(3997,plain,
( ( ! [V_m: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ V_m @ tc_IntDef_Oint )
| ( V_m = c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[1579]) ).
thf(3998,plain,
( ( c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint )
= $true ),
inference(copy,[status(thm)],[1578]) ).
thf(3999,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)],[1577]) ).
thf(4000,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)],[1576]) ).
thf(4001,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)],[1575]) ).
thf(4002,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)],[1574]) ).
thf(4003,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)],[1573]) ).
thf(4004,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)],[1572]) ).
thf(4005,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)],[1571]) ).
thf(4006,plain,
( ( ! [T_a: $i] :
( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1570]) ).
thf(4007,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)],[1569]) ).
thf(4008,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)],[1568]) ).
thf(4009,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)],[1567]) ).
thf(4010,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)],[1566]) ).
thf(4011,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)],[1565]) ).
thf(4012,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(copy,[status(thm)],[1564]) ).
thf(4013,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)],[1563]) ).
thf(4014,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)],[1562]) ).
thf(4015,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)],[1561]) ).
thf(4016,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)],[1560]) ).
thf(4017,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)],[1559]) ).
thf(4018,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_append @ c_List_Olist_ONil @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[1558]) ).
thf(4019,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)],[1557]) ).
thf(4020,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_append @ V_xs @ c_List_Olist_ONil @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1556]) ).
thf(4021,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)],[1555]) ).
thf(4022,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)],[1554]) ).
thf(4023,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)],[1553]) ).
thf(4024,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ T_a ) )
= c_0 ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(4025,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)],[1551]) ).
thf(4026,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(copy,[status(thm)],[1550]) ).
thf(4027,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)],[1549]) ).
thf(4028,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)],[1548]) ).
thf(4029,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)],[1547]) ).
thf(4030,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)],[1546]) ).
thf(4031,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)],[1545]) ).
thf(4032,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)],[1544]) ).
thf(4033,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)],[1543]) ).
thf(4034,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)],[1542]) ).
thf(4035,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)],[1541]) ).
thf(4036,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ c_List_Olist_ONil @ T_a )
= c_List_Olist_ONil ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(4037,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)],[1539]) ).
thf(4038,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)],[1538]) ).
thf(4039,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)],[1537]) ).
thf(4040,plain,
( ( ! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_append @ c_List_Olist_ONil @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1536]) ).
thf(4041,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)],[1535]) ).
thf(4042,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_append @ V_xs @ c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1534]) ).
thf(4043,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)],[1533]) ).
thf(4044,plain,
( ( ! [T_a: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1532]) ).
thf(4045,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)],[1531]) ).
thf(4046,plain,
( ( ! [T_a: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ T_a )
= c_emptyset ) )
= $true ),
inference(copy,[status(thm)],[1530]) ).
thf(4047,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ V_m )
!= ( c_Suc @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1529]) ).
thf(4048,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)],[1528]) ).
thf(4049,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)],[1527]) ).
thf(4050,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)],[1526]) ).
thf(4051,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)],[1525]) ).
thf(4052,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= c_0 ) )
= $true ),
inference(copy,[status(thm)],[1524]) ).
thf(4053,plain,
( ( ! [V_m: $i] :
( c_0
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1523]) ).
thf(4054,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)],[1522]) ).
thf(4055,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(copy,[status(thm)],[1521]) ).
thf(4056,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(copy,[status(thm)],[1520]) ).
thf(4057,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)],[1519]) ).
thf(4058,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)],[1518]) ).
thf(4059,plain,
( ( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 )
= $true ),
inference(copy,[status(thm)],[1517]) ).
thf(4060,plain,
( ( ! [V_i: $i] :
( ~ ( c_lessequals @ V_i @ c_0 @ tc_nat )
| ( V_i = c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[1516]) ).
thf(4061,plain,
( ( c_lessequals @ c_0 @ c_0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1515]) ).
thf(4062,plain,
( ( ! [V_n: $i] :
( ~ ( c_less @ V_n @ ( c_Suc @ c_0 ) @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[1514]) ).
thf(4063,plain,
( ( c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1513]) ).
thf(4064,plain,
( ( ! [V_n: $i] :
( ~ ( c_less @ V_n @ c_1 @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[1512]) ).
thf(4065,plain,
( ( c_less @ c_0 @ c_1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1511]) ).
thf(4066,plain,
( ( ! [V_n: $i] :
( ( c_less @ c_0 @ V_n @ tc_nat )
| ( V_n = c_0 ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(4067,plain,
( ( ~ ( c_less @ c_0 @ c_0 @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1509]) ).
thf(4068,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)],[1508]) ).
thf(4069,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)],[1507]) ).
thf(4070,plain,
( ( ! [V_n: $i] :
~ ( c_less @ V_n @ c_0 @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1506]) ).
thf(4071,plain,
( ( c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 )
= $true ),
inference(copy,[status(thm)],[1505]) ).
thf(4072,plain,
( ( c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0 )
= $true ),
inference(copy,[status(thm)],[1504]) ).
thf(4073,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_less @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1503]) ).
thf(4074,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)],[1502]) ).
thf(4075,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)],[1501]) ).
thf(4076,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)],[1500]) ).
thf(4077,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)],[1499]) ).
thf(4078,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)],[1498]) ).
thf(4079,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)],[1497]) ).
thf(4080,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)],[1496]) ).
thf(4081,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)],[1495]) ).
thf(4082,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(copy,[status(thm)],[1494]) ).
thf(4083,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(copy,[status(thm)],[1493]) ).
thf(4084,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(copy,[status(thm)],[1492]) ).
thf(4085,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(copy,[status(thm)],[1491]) ).
thf(4086,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(copy,[status(thm)],[1490]) ).
thf(4087,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(copy,[status(thm)],[1489]) ).
thf(4088,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(copy,[status(thm)],[1488]) ).
thf(4089,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(copy,[status(thm)],[1487]) ).
thf(4090,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(copy,[status(thm)],[1486]) ).
thf(4091,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(copy,[status(thm)],[1485]) ).
thf(4092,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(copy,[status(thm)],[1484]) ).
thf(4093,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(copy,[status(thm)],[1483]) ).
thf(4094,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(copy,[status(thm)],[1482]) ).
thf(4095,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(copy,[status(thm)],[1481]) ).
thf(4096,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(copy,[status(thm)],[1480]) ).
thf(4097,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(copy,[status(thm)],[1479]) ).
thf(4098,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(copy,[status(thm)],[1478]) ).
thf(4099,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(copy,[status(thm)],[1477]) ).
thf(4100,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(copy,[status(thm)],[1476]) ).
thf(4101,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(copy,[status(thm)],[1475]) ).
thf(4102,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)],[1474]) ).
thf(4103,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)],[1473]) ).
thf(4104,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)],[1472]) ).
thf(4105,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)],[1471]) ).
thf(4106,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)],[1470]) ).
thf(4107,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(copy,[status(thm)],[1469]) ).
thf(4108,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)],[1468]) ).
thf(4109,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(copy,[status(thm)],[1467]) ).
thf(4110,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)],[1466]) ).
thf(4111,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)],[1465]) ).
thf(4112,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(copy,[status(thm)],[1464]) ).
thf(4113,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(copy,[status(thm)],[1463]) ).
thf(4114,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)],[1462]) ).
thf(4115,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)],[1461]) ).
thf(4116,plain,
( ( c_UNIV != c_emptyset )
= $true ),
inference(copy,[status(thm)],[1460]) ).
thf(4117,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(copy,[status(thm)],[1459]) ).
thf(4118,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(copy,[status(thm)],[1458]) ).
thf(4119,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)],[1457]) ).
thf(4120,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)],[1456]) ).
thf(4121,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)],[1455]) ).
thf(4122,plain,
( ( ! [T_a: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ T_a )
= c_emptyset ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(4123,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(copy,[status(thm)],[1453]) ).
thf(4124,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ c_emptyset @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1452]) ).
thf(4125,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(copy,[status(thm)],[1451]) ).
thf(4126,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)],[1450]) ).
thf(4127,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(copy,[status(thm)],[1449]) ).
thf(4128,plain,
( ( ! [V_A: $i,T_a: $i] :
~ ( c_less @ V_A @ c_emptyset @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(4129,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)],[1447]) ).
thf(4130,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)],[1446]) ).
thf(4131,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)],[1445]) ).
thf(4132,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)],[1444]) ).
thf(4133,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)],[1443]) ).
thf(4134,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)],[1442]) ).
thf(4135,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)],[1441]) ).
thf(4136,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)],[1440]) ).
thf(4137,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)],[1439]) ).
thf(4138,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)],[1438]) ).
thf(4139,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)],[1437]) ).
thf(4140,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)],[1436]) ).
thf(4141,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)],[1435]) ).
thf(4142,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)],[1434]) ).
thf(4143,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(copy,[status(thm)],[1433]) ).
thf(4144,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)],[1432]) ).
thf(4145,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)],[1431]) ).
thf(4146,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(copy,[status(thm)],[1430]) ).
thf(4147,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)],[1429]) ).
thf(4148,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)],[1428]) ).
thf(4149,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)],[1427]) ).
thf(4150,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)],[1426]) ).
thf(4151,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)],[1425]) ).
thf(4152,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)],[1424]) ).
thf(4153,plain,
( ( ! [V_nat_H: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(4154,plain,
( ( ! [V_nat_H: $i] :
( ( c_Message_Oagent_OFriend @ V_nat_H )
!= c_Message_Oagent_OServer ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(4155,plain,
( ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(4156,plain,
( ( c_Message_Oagent_OSpy != c_Message_Oagent_OServer )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(4157,plain,
( ( ! [V_nat: $i] :
( ( c_Message_Oagent_OFriend @ V_nat )
!= c_Message_Oagent_OSpy ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(4158,plain,
( ( ! [V_nat: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(4159,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)],[1417]) ).
thf(4160,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)],[1416]) ).
thf(4161,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)],[1415]) ).
thf(4162,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)],[1414]) ).
thf(4163,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ V_G ) @ ( c_Message_Oanalz @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(copy,[status(thm)],[1413]) ).
thf(4164,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)],[1412]) ).
thf(4165,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)],[1411]) ).
thf(4166,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)],[1410]) ).
thf(4167,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)],[1409]) ).
thf(4168,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)],[1408]) ).
thf(4169,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)],[1407]) ).
thf(4170,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)],[1406]) ).
thf(4171,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)],[1405]) ).
thf(4172,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)],[1404]) ).
thf(4173,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)],[1403]) ).
thf(4174,plain,
( ( ! [V_K: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( 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)],[1402]) ).
thf(4175,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)],[1401]) ).
thf(4176,plain,
( ( ! [V_X: $i] :
~ ( c_in @ V_X @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[1400]) ).
thf(4177,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)],[1399]) ).
thf(4178,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1398]) ).
thf(4179,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_union @ V_A @ V_B @ T_a ) @ ( tc_set @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1397]) ).
thf(4180,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_A @ V_C @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1396]) ).
thf(4181,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[2788]) ).
thf(4182,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Datatype__Universe_OIn0 @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OIn1 @ SX3 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3961]) ).
thf(4183,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Message_Omsg_OCrypt @ SX0 @ SX1 )
!= ( c_Message_Omsg_OCrypt @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4172]) ).
thf(4184,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= c_List_Olist_ONil )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4035]) ).
thf(4185,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_append @ SX0 @ ( c_List_Olist_OCons @ SX1 @ c_List_Olist_ONil @ SX2 ) @ SX2 )
!= ( c_append @ SX3 @ ( c_List_Olist_OCons @ SX4 @ c_List_Olist_ONil @ SX2 ) @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4009]) ).
thf(4186,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( c_Datatype__Universe_OScons @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Datatype__Universe_ONumb @ SX4 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3972]) ).
thf(4187,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Oset @ SX0 @ SX1 )
!= c_emptyset )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4045]) ).
thf(4188,plain,
( ( ! [SX0: $i,SX1: $i] :
( c_Datatype_Ooption_ONone
!= ( c_Datatype_Ooption_OSome @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3955]) ).
thf(4189,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OLeaf @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2792]) ).
thf(4190,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Datatype__Universe_OIn1 @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OIn0 @ SX3 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3963]) ).
thf(4191,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Oremdups @ SX0 @ SX1 )
!= SX0 )
| ( ( c_Nat_Osize @ ( c_List_Oremdups @ SX0 @ SX1 ) @ ( tc_List_Olist @ SX1 ) )
= ( c_Nat_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4028]) ).
thf(4192,plain,
( ( ! [SX0: $i] :
( ( c_Message_Oagent_OFriend @ SX0 )
!= c_Message_Oagent_OSpy ) )
= $true ),
inference(unfold_def,[status(thm)],[4157]) ).
thf(4193,plain,
( ( c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight )
= $true ),
inference(unfold_def,[status(thm)],[3979]) ).
thf(4194,plain,
( ( c_UNIV != c_emptyset )
= $true ),
inference(unfold_def,[status(thm)],[4116]) ).
thf(4195,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Datatype__Universe_ONumb @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_ONumb @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2793]) ).
thf(4196,plain,
( ( ! [SX0: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4158]) ).
thf(4197,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Equiv__Relations_Oquotient @ SX0 @ SX1 @ SX2 )
!= c_emptyset )
| ( SX0 = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3977]) ).
thf(4198,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Nat_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) )
!= c_0 )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4023]) ).
thf(4199,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Message_Omsg_OMPair @ SX0 @ SX1 )
!= ( c_Message_Omsg_OMPair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4170]) ).
thf(4200,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4032]) ).
thf(4201,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Sum__Type_OInr @ SX0 @ SX1 @ SX2 )
!= ( c_Sum__Type_OInl @ SX3 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4138]) ).
thf(4202,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Message_Omsg_OHash @ SX0 )
!= ( c_Message_Omsg_OHash @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4169]) ).
thf(4203,plain,
( ( c_Message_Oagent_OSpy != c_Message_Oagent_OServer )
= $true ),
inference(unfold_def,[status(thm)],[4156]) ).
thf(4204,plain,
( ( c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft )
= $true ),
inference(unfold_def,[status(thm)],[3980]) ).
thf(4205,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_append @ SX0 @ ( c_List_Olist_OCons @ SX1 @ c_List_Olist_ONil @ SX2 ) @ SX2 )
!= ( c_append @ SX3 @ ( c_List_Olist_OCons @ SX4 @ c_List_Olist_ONil @ SX2 ) @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4008]) ).
thf(4206,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Datatype__Universe_OAtom @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OAtom @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3958]) ).
thf(4207,plain,
( ( ! [SX0: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4153]) ).
thf(4208,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_append @ SX0 @ SX1 @ SX2 )
!= c_List_Olist_ONil )
| ( SX1 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4014]) ).
thf(4209,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Datatype__Universe_OIn1 @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OIn1 @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3962]) ).
thf(4210,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_union @ SX0 @ SX1 @ SX2 )
!= c_emptyset )
| ( SX1 = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4121]) ).
thf(4211,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_SetInterval_OlessThan @ SX1 @ SX0 )
!= ( c_SetInterval_OlessThan @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4097]) ).
thf(4212,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_Pair @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Pair @ SX4 @ SX5 @ SX2 @ SX3 ) )
| ( SX0 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4074]) ).
thf(4213,plain,
( ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )
= $true ),
inference(unfold_def,[status(thm)],[4155]) ).
thf(4214,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4029]) ).
thf(4215,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Message_Omsg_OKey @ SX0 )
!= ( c_Message_Omsg_OKey @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4168]) ).
thf(4216,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ochar_OChar @ SX0 @ SX1 )
!= ( c_List_Ochar_OChar @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4022]) ).
thf(4217,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_plus @ SX0 @ SX1 @ tc_nat )
!= c_0 )
| ( SX1 = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4058]) ).
thf(4218,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( c_Datatype__Universe_OLeaf @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OScons @ SX3 @ SX4 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3965]) ).
thf(4219,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ SX0 @ SX1 @ SX2 ) )
| ( SX1 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4003]) ).
thf(4220,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_append @ SX0 @ SX1 @ SX2 )
!= ( c_append @ SX0 @ SX3 @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4038]) ).
thf(4221,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_union @ SX0 @ SX1 @ SX2 )
!= c_emptyset )
| ( SX0 = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4120]) ).
thf(4222,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= c_0 ) )
= $true ),
inference(unfold_def,[status(thm)],[4052]) ).
thf(4223,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Datatype__Universe_OIn0 @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OIn0 @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3960]) ).
thf(4224,plain,
( ( c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 )
= $true ),
inference(unfold_def,[status(thm)],[4071]) ).
thf(4225,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_Pair @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Pair @ SX4 @ SX5 @ SX2 @ SX3 ) )
| ( SX1 = SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4075]) ).
thf(4226,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( c_Datatype__Universe_OAtom @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OScons @ SX3 @ SX4 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3959]) ).
thf(4227,plain,
( ( ! [SX0: $i] :
( ( c_Message_Oagent_OFriend @ SX0 )
!= c_Message_Oagent_OServer ) )
= $true ),
inference(unfold_def,[status(thm)],[4154]) ).
thf(4228,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ SX3 @ SX1 ) )
| ( SX0
= ( c_append @ ( c_List_Orev @ SX3 @ SX1 ) @ ( c_List_Olist_OCons @ SX2 @ c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4033]) ).
thf(4229,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_SetInterval_OatLeast @ SX1 @ SX0 )
!= ( c_SetInterval_OatLeast @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4082]) ).
thf(4230,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_uminus @ SX0 @ ( tc_set @ SX1 ) )
!= ( c_uminus @ SX2 @ ( tc_set @ SX1 ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4104]) ).
thf(4231,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( c_Datatype__Universe_ONumb @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OScons @ SX3 @ SX4 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3967]) ).
thf(4232,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_insert @ SX0 @ c_emptyset @ SX1 )
!= ( c_insert @ SX2 @ SX3 @ SX1 ) )
| ( SX2 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4132]) ).
thf(4233,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_append @ SX1 @ SX0 @ SX2 ) )
| ( SX1 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4039]) ).
thf(4234,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Message_Oagent_OFriend @ SX0 )
!= ( c_Message_Oagent_OFriend @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4159]) ).
thf(4235,plain,
( ( ! [SX0: $i] :
( c_0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4053]) ).
thf(4236,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ SX0 @ SX1 @ SX2 ) )
| ( SX0 = c_emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3975]) ).
thf(4237,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ SX0 @ SX1 @ SX2 ) )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4002]) ).
thf(4238,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Datatype_Ooption_OSome @ SX0 @ SX1 )
!= c_Datatype_Ooption_ONone ) )
= $true ),
inference(unfold_def,[status(thm)],[3956]) ).
thf(4239,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_append @ SX0 @ SX1 @ SX2 )
!= SX0 )
| ( SX1 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4019]) ).
thf(4240,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_SetInterval_OgreaterThan @ SX1 @ SX0 )
!= ( c_SetInterval_OgreaterThan @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4092]) ).
thf(4241,plain,
( ( c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0 )
= $true ),
inference(unfold_def,[status(thm)],[4072]) ).
thf(4242,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Message_Omsg_OCrypt @ SX0 @ SX1 )
!= ( c_Message_Omsg_OCrypt @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4173]) ).
thf(4243,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Message_Omsg_OAgent @ SX0 )
!= ( c_Message_Omsg_OAgent @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4165]) ).
thf(4244,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Datatype_Ooption_OSome @ SX0 @ SX1 )
!= ( c_Datatype_Ooption_OSome @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3957]) ).
thf(4245,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Message_Omsg_ONonce @ SX0 )
!= ( c_Message_Omsg_ONonce @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4167]) ).
thf(4246,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_append @ SX0 @ SX1 @ SX2 )
!= SX1 )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4017]) ).
thf(4247,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_append @ SX0 @ SX1 @ SX2 ) )
| ( SX1 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4041]) ).
thf(4248,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Message_Omsg_ONumber @ SX0 )
!= ( c_Message_Omsg_ONumber @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4166]) ).
thf(4249,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_emptyset
!= ( c_List_Oset @ SX0 @ SX1 ) )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4043]) ).
thf(4250,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_insert @ SX0 @ c_emptyset @ SX1 )
!= ( c_insert @ SX2 @ c_emptyset @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2898]) ).
thf(4251,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Divides_Oop_Amod @ SX0 @ SX1 @ tc_nat )
!= c_0 )
| ( SX0
= ( c_times @ SX1 @ ( c_Main_Omod__eq__0D__dest__1 @ SX1 @ SX0 ) @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2818]) ).
thf(4252,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Sum__Type_OInl @ SX0 @ SX1 @ SX2 )
!= ( c_Sum__Type_OInr @ SX3 @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4136]) ).
thf(4253,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SX0 @ SX1 ) @ ( tc_List_Olist @ SX1 ) )
!= ( c_Nat_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) )
| ( ( c_List_Oremdups @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4027]) ).
thf(4254,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( c_Datatype__Universe_OScons @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Datatype__Universe_OLeaf @ SX4 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3971]) ).
thf(4255,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4031]) ).
thf(4256,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4047]) ).
thf(4257,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Datatype__Universe_ONumb @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_OLeaf @ SX3 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3966]) ).
thf(4258,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= c_List_Olist_ONil ) )
= $true ),
inference(unfold_def,[status(thm)],[4030]) ).
thf(4259,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_plus @ SX0 @ SX1 @ tc_nat )
!= c_0 )
| ( SX0 = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4057]) ).
thf(4260,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Sum__Type_OInl @ SX0 @ SX1 @ SX2 )
!= ( c_Sum__Type_OInl @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4135]) ).
thf(4261,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_Datatype__Universe_OScons @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Datatype__Universe_OScons @ SX4 @ SX5 @ SX2 @ SX3 ) )
| ( SX0 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3968]) ).
thf(4262,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_append @ SX0 @ SX1 @ SX2 )
!= ( c_append @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4016]) ).
thf(4263,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Orev @ SX0 @ SX1 ) )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4005]) ).
thf(4264,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( c_Datatype__Universe_OScons @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Datatype__Universe_OAtom @ SX4 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3970]) ).
thf(4265,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_Datatype__Universe_OLeaf @ SX0 @ SX1 @ SX2 )
!= ( c_Datatype__Universe_ONumb @ SX3 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3964]) ).
thf(4266,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ochar_OChar @ SX0 @ SX1 )
!= ( c_List_Ochar_OChar @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4021]) ).
thf(4267,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_append @ SX0 @ SX1 @ SX2 )
!= c_List_Olist_ONil )
| ( SX0 = c_List_Olist_ONil ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4013]) ).
thf(4268,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_Datatype__Universe_OScons @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Datatype__Universe_OScons @ SX4 @ SX5 @ SX2 @ SX3 ) )
| ( SX1 = SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3969]) ).
thf(4269,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_SetInterval_OatMost @ SX1 @ SX0 )
!= ( c_SetInterval_OatMost @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4087]) ).
thf(4270,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Divides_Oop_Amod @ SX0 @ SX1 @ tc_IntDef_Oint )
!= c_0 )
| ( SX0
= ( c_times @ SX1 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SX1 @ SX0 ) @ tc_IntDef_Oint ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2834]) ).
thf(4271,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4037]) ).
thf(4272,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Message_Omsg_OMPair @ SX0 @ SX1 )
!= ( c_Message_Omsg_OMPair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4171]) ).
thf(4273,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_insert @ SX0 @ c_emptyset @ SX1 )
!= ( c_insert @ SX2 @ SX3 @ SX1 ) )
| ( c_lessequals @ SX3 @ ( c_insert @ SX0 @ c_emptyset @ SX1 ) @ ( tc_set @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4133]) ).
thf(4274,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_IntDef_Oint @ SX0 )
!= ( c_IntDef_Oint @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3994]) ).
thf(4275,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Sum__Type_OInr @ SX0 @ SX1 @ SX2 )
!= ( c_Sum__Type_OInr @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4137]) ).
thf(4276,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_insert @ SX0 @ SX1 @ SX2 )
!= ( c_insert @ SX3 @ c_emptyset @ SX2 ) )
| ( c_lessequals @ SX1 @ ( c_insert @ SX3 @ c_emptyset @ SX2 ) @ ( tc_set @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4130]) ).
thf(4277,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_insert @ SX0 @ SX1 @ SX2 )
!= ( c_insert @ SX3 @ c_emptyset @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4129]) ).
thf(4278,plain,
( ( ( ~ ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2791]) ).
thf(4279,plain,
! [SV1: $i] :
( ( ! [SY1982: $i,SY1983: $i,SY1984: $i,SY1985: $i] :
( ~ ( c_in @ SV1 @ ( c_Datatype__Universe_Odprod @ SY1982 @ SY1983 @ SY1984 @ SY1985 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1984 @ SY1985 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1984 @ SY1985 ) ) ) )
| ( SV1
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV1 @ SY1982 @ SY1983 @ SY1984 @ SY1985 ) @ ( c_Main_OdprodE__2 @ SV1 @ SY1982 @ SY1983 @ SY1984 @ SY1985 ) @ SY1984 @ SY1985 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV1 @ SY1982 @ SY1983 @ SY1984 @ SY1985 ) @ ( c_Main_OdprodE__4 @ SV1 @ SY1982 @ SY1983 @ SY1984 @ SY1985 ) @ SY1984 @ SY1985 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1984 @ SY1985 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1984 @ SY1985 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(4280,plain,
! [SV2: $i] :
( ( ! [SY1986: $i,SY1987: $i,SY1988: $i,SY1989: $i] :
( ~ ( c_in @ SV2 @ ( c_Datatype__Universe_Odprod @ SY1986 @ SY1987 @ SY1988 @ SY1989 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1988 @ SY1989 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1988 @ SY1989 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV2 @ SY1986 @ SY1987 @ SY1988 @ SY1989 ) @ ( c_Main_OdprodE__4 @ SV2 @ SY1986 @ SY1987 @ SY1988 @ SY1989 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1988 @ SY1989 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1988 @ SY1989 ) ) ) @ SY1987 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1988 @ SY1989 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1988 @ SY1989 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(4281,plain,
! [SV3: $i] :
( ( ! [SY1990: $i,SY1991: $i,SY1992: $i,SY1993: $i] :
( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SY1990 @ SY1991 @ SY1992 @ SY1993 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1992 @ SY1993 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1992 @ SY1993 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV3 @ SY1990 @ SY1991 @ SY1992 @ SY1993 ) @ ( c_Main_OdprodE__3 @ SV3 @ SY1990 @ SY1991 @ SY1992 @ SY1993 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1992 @ SY1993 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1992 @ SY1993 ) ) ) @ SY1990 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1992 @ SY1993 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1992 @ SY1993 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(4282,plain,
! [SV4: $i] :
( ( ! [SY1994: $i,SY1995: $i,SY1996: $i,SY1997: $i,SY1998: $i,SY1999: $i,SY2000: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ SY1994 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) ) @ SY1997 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SY1998 @ SY1999 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) ) @ SY2000 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY1998 @ SV4 @ SY1995 @ SY1996 ) @ ( c_Datatype__Universe_OScons @ SY1999 @ SY1994 @ SY1995 @ SY1996 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY2000 @ SY1997 @ SY1995 @ SY1996 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY1995 @ SY1996 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(4283,plain,
! [SV5: $i] :
( ( ! [SY2001: $i,SY2002: $i,SY2003: $i,SY2004: $i] :
( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SY2001 @ SY2002 @ SY2003 @ SY2004 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2003 @ SY2004 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2003 @ SY2004 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SY2001 @ SV5 @ SY2003 @ SY2004 ) @ SY2003 @ SY2004 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SY2001 @ SV5 @ SY2003 @ SY2004 ) @ SY2003 @ SY2004 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2003 @ SY2004 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2003 @ SY2004 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2002 @ SV5 @ SY2003 @ SY2004 ) @ SY2003 @ SY2004 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2002 @ SV5 @ SY2003 @ SY2004 ) @ SY2003 @ SY2004 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2003 @ SY2004 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2003 @ SY2004 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(4284,plain,
! [SV6: $i] :
( ( ! [SY2005: $i,SY2006: $i,SY2007: $i,SY2008: $i] :
( ~ ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SY2005 @ SY2006 @ SY2007 @ SY2008 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2006 @ SV6 @ SY2007 @ SY2008 ) @ ( c_Main_OdsumE__4 @ SY2006 @ SV6 @ SY2007 @ SY2008 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) ) @ SY2006 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) ) )
| ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SY2005 @ SV6 @ SY2007 @ SY2008 ) @ SY2007 @ SY2008 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SY2005 @ SV6 @ SY2007 @ SY2008 ) @ SY2007 @ SY2008 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2007 @ SY2008 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(4285,plain,
! [SV7: $i] :
( ( ! [SY2009: $i,SY2010: $i,SY2011: $i,SY2012: $i] :
( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SY2009 @ SY2010 @ SY2011 @ SY2012 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SY2009 @ SV7 @ SY2011 @ SY2012 ) @ ( c_Main_OdsumE__2 @ SY2009 @ SV7 @ SY2011 @ SY2012 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) ) @ SY2009 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) ) )
| ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2010 @ SV7 @ SY2011 @ SY2012 ) @ SY2011 @ SY2012 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2010 @ SV7 @ SY2011 @ SY2012 ) @ SY2011 @ SY2012 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2011 @ SY2012 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(4286,plain,
! [SV8: $i] :
( ( ! [SY2013: $i,SY2014: $i,SY2015: $i,SY2016: $i] :
( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SY2013 @ SY2014 @ SY2015 @ SY2016 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SY2013 @ SV8 @ SY2015 @ SY2016 ) @ ( c_Main_OdsumE__2 @ SY2013 @ SV8 @ SY2015 @ SY2016 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) ) @ SY2013 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2014 @ SV8 @ SY2015 @ SY2016 ) @ ( c_Main_OdsumE__4 @ SY2014 @ SV8 @ SY2015 @ SY2016 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) ) @ SY2014 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2015 @ SY2016 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(4287,plain,
! [SV9: $i] :
( ( ! [SY2017: $i,SY2018: $i,SY2019: $i,SY2020: $i,SY2021: $i] :
( ~ ( c_in @ ( c_Pair @ SV9 @ SY2017 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) ) @ SY2020 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SY2018 @ SY2019 ) @ ( c_Datatype__Universe_OIn0 @ SY2017 @ SY2018 @ SY2019 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2020 @ SY2021 @ SY2018 @ SY2019 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2018 @ SY2019 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(4288,plain,
! [SV10: $i] :
( ( ! [SY2022: $i,SY2023: $i,SY2024: $i,SY2025: $i,SY2026: $i] :
( ~ ( c_in @ ( c_Pair @ SV10 @ SY2022 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) ) @ SY2025 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SY2023 @ SY2024 ) @ ( c_Datatype__Universe_OIn1 @ SY2022 @ SY2023 @ SY2024 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2026 @ SY2025 @ SY2023 @ SY2024 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2023 @ SY2024 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(4289,plain,
! [SV11: $i] :
( ( ! [SY2027: $i,SY2028: $i,SY2029: $i,SY2030: $i] :
( ~ ( c_in @ SV11 @ ( c_Datatype__Universe_Ouprod @ SY2027 @ SY2028 @ SY2029 @ SY2030 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2029 @ SY2030 ) ) )
| ( SV11
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SY2027 @ SY2028 @ SV11 @ SY2029 @ SY2030 ) @ ( c_Main_OuprodE__2 @ SY2027 @ SY2028 @ SV11 @ SY2029 @ SY2030 ) @ SY2029 @ SY2030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(4290,plain,
! [SV12: $i] :
( ( ! [SY2031: $i,SY2032: $i,SY2033: $i,SY2034: $i] :
( ~ ( c_in @ SV12 @ ( c_Datatype__Universe_Ouprod @ SY2031 @ SY2032 @ SY2033 @ SY2034 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2033 @ SY2034 ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ SY2031 @ SY2032 @ SV12 @ SY2033 @ SY2034 ) @ SY2032 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2033 @ SY2034 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(4291,plain,
! [SV13: $i] :
( ( ! [SY2035: $i,SY2036: $i,SY2037: $i,SY2038: $i] :
( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SY2035 @ SY2036 @ SY2037 @ SY2038 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2037 @ SY2038 ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ SY2035 @ SY2036 @ SV13 @ SY2037 @ SY2038 ) @ SY2035 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2037 @ SY2038 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(4292,plain,
! [SV14: $i] :
( ( ! [SY2039: $i,SY2040: $i,SY2041: $i,SY2042: $i,SY2043: $i] :
( ~ ( c_in @ SV14 @ SY2039 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) )
| ~ ( c_in @ SY2042 @ SY2043 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SY2042 @ SV14 @ SY2040 @ SY2041 ) @ ( c_Datatype__Universe_Ouprod @ SY2043 @ SY2039 @ SY2040 @ SY2041 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2040 @ SY2041 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(4293,plain,
! [SV15: $i] :
( ( ! [SY2044: $i,SY2045: $i,SY2046: $i,SY2047: $i] :
( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SY2044 @ SY2045 @ SY2046 @ SY2047 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2046 @ SY2047 ) ) )
| ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SY2044 @ SV15 @ SY2046 @ SY2047 ) @ SY2046 @ SY2047 ) )
| ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2045 @ SV15 @ SY2046 @ SY2047 ) @ SY2046 @ SY2047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(4294,plain,
! [SV16: $i] :
( ( ! [SY2048: $i,SY2049: $i,SY2050: $i,SY2051: $i] :
( ~ ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SY2048 @ SY2049 @ SY2050 @ SY2051 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2050 @ SY2051 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SY2049 @ SV16 @ SY2050 @ SY2051 ) @ SY2049 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2050 @ SY2051 ) ) )
| ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SY2048 @ SV16 @ SY2050 @ SY2051 ) @ SY2050 @ SY2051 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(4295,plain,
! [SV17: $i] :
( ( ! [SY2052: $i,SY2053: $i,SY2054: $i,SY2055: $i] :
( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SY2052 @ SY2053 @ SY2054 @ SY2055 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2054 @ SY2055 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SY2052 @ SV17 @ SY2054 @ SY2055 ) @ SY2052 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2054 @ SY2055 ) ) )
| ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2053 @ SV17 @ SY2054 @ SY2055 ) @ SY2054 @ SY2055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(4296,plain,
! [SV18: $i] :
( ( ! [SY2056: $i,SY2057: $i,SY2058: $i,SY2059: $i] :
( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SY2056 @ SY2057 @ SY2058 @ SY2059 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2058 @ SY2059 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SY2056 @ SV18 @ SY2058 @ SY2059 ) @ SY2056 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2058 @ SY2059 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SY2057 @ SV18 @ SY2058 @ SY2059 ) @ SY2057 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2058 @ SY2059 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(4297,plain,
! [SV19: $i] :
( ( ! [SY2060: $i,SY2061: $i,SY2062: $i,SY2063: $i] :
( ~ ( c_in @ SV19 @ SY2060 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2061 @ SY2062 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn0 @ SV19 @ SY2061 @ SY2062 ) @ ( c_Datatype__Universe_Ousum @ SY2060 @ SY2063 @ SY2061 @ SY2062 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2061 @ SY2062 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(4298,plain,
! [SV20: $i] :
( ( ! [SY2064: $i,SY2065: $i,SY2066: $i,SY2067: $i] :
( ~ ( c_in @ SV20 @ SY2064 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2065 @ SY2066 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn1 @ SV20 @ SY2065 @ SY2066 ) @ ( c_Datatype__Universe_Ousum @ SY2067 @ SY2064 @ SY2065 @ SY2066 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2065 @ SY2066 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(4299,plain,
! [SV21: $i] :
( ( c_Divides_Oop_Advd @ SV21 @ c_0 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(4300,plain,
! [SV22: $i] :
( ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ SV22 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(4301,plain,
! [SV23: $i] :
( ( ! [SY2068: $i] : ( c_Divides_Oop_Advd @ SV23 @ ( c_times @ SV23 @ SY2068 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(4302,plain,
! [SV24: $i] :
( ( ! [SY2069: $i] : ( c_Divides_Oop_Advd @ SV24 @ ( c_times @ SY2069 @ SV24 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(4303,plain,
! [SV25: $i] :
( ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(4304,plain,
! [SV26: $i] :
( ( ! [SY2070: $i,SY2071: $i] :
( ~ ( c_in @ SV26 @ c_Finite__Set_OFinites @ ( tc_set @ SY2070 ) )
| ( c_in @ ( c_insert @ SY2071 @ SV26 @ SY2070 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(4305,plain,
! [SV27: $i] :
( ( ! [SY2072: $i,SY2073: $i] :
( ~ ( c_in @ SV27 @ c_Finite__Set_OFinites @ ( tc_set @ SY2072 ) )
| ( c_in @ ( c_inter @ SV27 @ SY2073 @ SY2072 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(4306,plain,
! [SV28: $i] :
( ( ! [SY2074: $i,SY2075: $i] :
( ~ ( c_in @ SV28 @ c_Finite__Set_OFinites @ ( tc_set @ SY2074 ) )
| ( c_in @ ( c_inter @ SY2075 @ SV28 @ SY2074 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(4307,plain,
! [SV29: $i] :
( ( ! [SY2076: $i] :
( ~ ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2076 ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ SV29 @ SY2076 ) @ SV29 @ ( tc_set @ SY2076 ) )
| ( c_in @ ( c_Union @ SV29 @ SY2076 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(4308,plain,
! [SV30: $i] :
( ( ! [SY2077: $i] :
( ~ ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2077 ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV30 @ SY2077 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2077 ) )
| ( c_in @ ( c_Union @ SV30 @ SY2077 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(4309,plain,
! [SV31: $i] :
( ( ! [SY2078: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV31 @ SY2078 @ tc_nat @ tc_nat ) ) @ SV31 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(4310,plain,
! [SV32: $i] :
( ( ! [SY2079: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV32 @ SY2079 @ tc_nat @ tc_nat ) ) @ SY2079 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(4311,plain,
! [SV33: $i] :
( ( ! [SY2080: $i,SY2081: $i,SY2082: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ SV33 @ SY2080 )
| ~ ( c_in @ SY2081 @ SV33 @ SY2080 )
| ~ ( c_in @ SY2082 @ SV33 @ SY2080 )
| ( SY2081 = SY2082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(4312,plain,
! [SV34: $i] :
( ( ! [SY2083: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ SV34 ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SY2083 ) @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(4313,plain,
! [SV35: $i] :
( ( ! [SY2084: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ SV35 ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SY2084 ) @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(4314,plain,
! [SV36: $i] :
( ( c_Divides_Oop_Advd @ SV36 @ c_0 @ tc_IntDef_Oint )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(4315,plain,
! [SV37: $i] :
( ( c_Divides_Oop_Advd @ c_1 @ SV37 @ tc_IntDef_Oint )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(4316,plain,
! [SV38: $i] :
( ( ! [SY2085: $i] : ( c_Divides_Oop_Advd @ SV38 @ ( c_times @ SV38 @ SY2085 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(4317,plain,
! [SV39: $i] :
( ( ! [SY2086: $i] : ( c_Divides_Oop_Advd @ SV39 @ ( c_times @ SY2086 @ SV39 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(4318,plain,
! [SV40: $i] :
( ( ! [SY2087: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ SV40 @ SY2087 ) @ SY2087 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(4319,plain,
! [SV41: $i] :
( ( ! [SY2088: $i] : ( c_in @ ( c_List_Oset @ SV41 @ SY2088 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(4320,plain,
! [SV42: $i] :
( ( ! [SY2089: $i,SY2090: $i,SY2091: $i] :
( ~ ( c_in @ SV42 @ ( c_List_Olists @ SY2089 @ SY2090 ) @ ( tc_List_Olist @ SY2090 ) )
| ~ ( c_in @ SY2091 @ ( c_List_Oset @ SV42 @ SY2090 ) @ SY2090 )
| ( c_in @ SY2091 @ SY2089 @ SY2090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(4321,plain,
! [SV43: $i] :
( ( ! [SY2092: $i,SY2093: $i] :
( ( c_in @ SV43 @ ( c_List_Olists @ SY2092 @ SY2093 ) @ ( tc_List_Olist @ SY2093 ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ SY2092 @ SV43 @ SY2093 ) @ ( c_List_Oset @ SV43 @ SY2093 ) @ SY2093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(4322,plain,
! [SV44: $i] :
( ( ! [SY2094: $i,SY2095: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV44 @ SY2094 @ SY2095 ) @ SV44 @ SY2095 )
| ( c_in @ SY2094 @ ( c_List_Olists @ SV44 @ SY2095 ) @ ( tc_List_Olist @ SY2095 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(4323,plain,
! [SV45: $i] :
( ( ! [SY2096: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ SV45 @ SY2096 ) @ ( tc_List_Olist @ SY2096 ) ) @ ( c_Nat_Osize @ SV45 @ ( tc_List_Olist @ SY2096 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(4324,plain,
! [SV46: $i] :
( ( ! [SY2097: $i,SY2098: $i,SY2099: $i,SY2100: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV46 @ SY2097 @ SY2098 ) @ SY2099 @ ( tc_List_Olist @ SY2098 ) @ ( tc_List_Olist @ SY2098 ) ) @ ( c_List_Olistrel @ SY2100 @ SY2098 ) @ ( tc_prod @ ( tc_List_Olist @ SY2098 ) @ ( tc_List_Olist @ SY2098 ) ) )
| ( SY2099
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY2100 @ SY2099 @ SV46 @ SY2097 @ SY2098 ) @ ( c_Main_Olistrel__Cons1__2 @ SY2100 @ SY2099 @ SV46 @ SY2097 @ SY2098 ) @ SY2098 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(4325,plain,
! [SV47: $i] :
( ( ! [SY2101: $i,SY2102: $i,SY2103: $i,SY2104: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV47 @ SY2101 @ SY2102 ) @ SY2103 @ ( tc_List_Olist @ SY2102 ) @ ( tc_List_Olist @ SY2102 ) ) @ ( c_List_Olistrel @ SY2104 @ SY2102 ) @ ( tc_prod @ ( tc_List_Olist @ SY2102 ) @ ( tc_List_Olist @ SY2102 ) ) )
| ( c_in @ ( c_Pair @ SY2101 @ ( c_Main_Olistrel__Cons1__2 @ SY2104 @ SY2103 @ SV47 @ SY2101 @ SY2102 ) @ ( tc_List_Olist @ SY2102 ) @ ( tc_List_Olist @ SY2102 ) ) @ ( c_List_Olistrel @ SY2104 @ SY2102 ) @ ( tc_prod @ ( tc_List_Olist @ SY2102 ) @ ( tc_List_Olist @ SY2102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(4326,plain,
! [SV48: $i] :
( ( ! [SY2105: $i,SY2106: $i,SY2107: $i,SY2108: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV48 @ SY2105 @ SY2106 ) @ SY2107 @ ( tc_List_Olist @ SY2106 ) @ ( tc_List_Olist @ SY2106 ) ) @ ( c_List_Olistrel @ SY2108 @ SY2106 ) @ ( tc_prod @ ( tc_List_Olist @ SY2106 ) @ ( tc_List_Olist @ SY2106 ) ) )
| ( c_in @ ( c_Pair @ SV48 @ ( c_Main_Olistrel__Cons1__1 @ SY2108 @ SY2107 @ SV48 @ SY2105 @ SY2106 ) @ SY2106 @ SY2106 ) @ SY2108 @ ( tc_prod @ SY2106 @ SY2106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(4327,plain,
! [SV49: $i] :
( ( ! [SY2109: $i,SY2110: $i,SY2111: $i,SY2112: $i] :
( ~ ( c_in @ ( c_Pair @ SV49 @ ( c_List_Olist_OCons @ SY2109 @ SY2110 @ SY2111 ) @ ( tc_List_Olist @ SY2111 ) @ ( tc_List_Olist @ SY2111 ) ) @ ( c_List_Olistrel @ SY2112 @ SY2111 ) @ ( tc_prod @ ( tc_List_Olist @ SY2111 ) @ ( tc_List_Olist @ SY2111 ) ) )
| ( SV49
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY2112 @ SV49 @ SY2109 @ SY2110 @ SY2111 ) @ ( c_Main_Olistrel__Cons2__2 @ SY2112 @ SV49 @ SY2109 @ SY2110 @ SY2111 ) @ SY2111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(4328,plain,
! [SV50: $i] :
( ( ! [SY2113: $i,SY2114: $i,SY2115: $i,SY2116: $i] :
( ~ ( c_in @ ( c_Pair @ SV50 @ ( c_List_Olist_OCons @ SY2113 @ SY2114 @ SY2115 ) @ ( tc_List_Olist @ SY2115 ) @ ( tc_List_Olist @ SY2115 ) ) @ ( c_List_Olistrel @ SY2116 @ SY2115 ) @ ( tc_prod @ ( tc_List_Olist @ SY2115 ) @ ( tc_List_Olist @ SY2115 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY2116 @ SV50 @ SY2113 @ SY2114 @ SY2115 ) @ SY2114 @ ( tc_List_Olist @ SY2115 ) @ ( tc_List_Olist @ SY2115 ) ) @ ( c_List_Olistrel @ SY2116 @ SY2115 ) @ ( tc_prod @ ( tc_List_Olist @ SY2115 ) @ ( tc_List_Olist @ SY2115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(4329,plain,
! [SV51: $i] :
( ( ! [SY2117: $i,SY2118: $i,SY2119: $i,SY2120: $i] :
( ~ ( c_in @ ( c_Pair @ SV51 @ ( c_List_Olist_OCons @ SY2117 @ SY2118 @ SY2119 ) @ ( tc_List_Olist @ SY2119 ) @ ( tc_List_Olist @ SY2119 ) ) @ ( c_List_Olistrel @ SY2120 @ SY2119 ) @ ( tc_prod @ ( tc_List_Olist @ SY2119 ) @ ( tc_List_Olist @ SY2119 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY2120 @ SV51 @ SY2117 @ SY2118 @ SY2119 ) @ SY2117 @ SY2119 @ SY2119 ) @ SY2120 @ ( tc_prod @ SY2119 @ SY2119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(4330,plain,
! [SV52: $i] :
( ( ! [SY2121: $i,SY2122: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV52 @ ( tc_List_Olist @ SY2121 ) @ ( tc_List_Olist @ SY2121 ) ) @ ( c_List_Olistrel @ SY2122 @ SY2121 ) @ ( tc_prod @ ( tc_List_Olist @ SY2121 ) @ ( tc_List_Olist @ SY2121 ) ) )
| ( SV52 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(4331,plain,
! [SV53: $i] :
( ( ! [SY2123: $i,SY2124: $i] :
( ~ ( c_in @ ( c_Pair @ SV53 @ c_List_Olist_ONil @ ( tc_List_Olist @ SY2123 ) @ ( tc_List_Olist @ SY2123 ) ) @ ( c_List_Olistrel @ SY2124 @ SY2123 ) @ ( tc_prod @ ( tc_List_Olist @ SY2123 ) @ ( tc_List_Olist @ SY2123 ) ) )
| ( SV53 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(4332,plain,
! [SV54: $i] :
( ( ! [SY2125: $i,SY2126: $i,SY2127: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ SV54 @ SY2125 @ SY2126 ) @ ( c_List_Olists @ SY2127 @ SY2126 ) @ ( tc_List_Olist @ SY2126 ) )
| ( c_in @ SY2125 @ ( c_List_Olists @ SY2127 @ SY2126 ) @ ( tc_List_Olist @ SY2126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(4333,plain,
! [SV55: $i] :
( ( ! [SY2128: $i,SY2129: $i,SY2130: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ SV55 @ SY2128 @ SY2129 ) @ ( c_List_Olists @ SY2130 @ SY2129 ) @ ( tc_List_Olist @ SY2129 ) )
| ( c_in @ SV55 @ SY2130 @ SY2129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(4334,plain,
! [SV56: $i] :
( ( ! [SY2131: $i,SY2132: $i,SY2133: $i] :
( ~ ( c_in @ SV56 @ SY2131 @ SY2132 )
| ~ ( c_in @ SY2133 @ ( c_List_Olists @ SY2131 @ SY2132 ) @ ( tc_List_Olist @ SY2132 ) )
| ( c_in @ ( c_List_Olist_OCons @ SV56 @ SY2133 @ SY2132 ) @ ( c_List_Olists @ SY2131 @ SY2132 ) @ ( tc_List_Olist @ SY2132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(4335,plain,
! [SV57: $i] :
( ( ! [SY2134: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ SV57 @ SY2134 ) @ ( tc_List_Olist @ SY2134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(4336,plain,
! [SV58: $i] :
( ( ! [SY2135: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV58 @ SY2135 )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV58 @ SY2135 ) @ ( tc_List_Olist @ SY2135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(4337,plain,
! [SV59: $i] :
( ( ! [SY2136: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV59 @ SY2136 )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV59 @ SY2136 ) @ ( tc_List_Olist @ SY2136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(4338,plain,
! [SV60: $i] :
( ( c_lessequals @ c_0 @ SV60 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(4339,plain,
! [SV61: $i] :
( ( c_less @ SV61 @ ( c_Suc @ SV61 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(4340,plain,
! [SV62: $i] :
( ( ~ ( c_less @ SV62 @ SV62 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(4341,plain,
! [SV63: $i] :
( ( c_less @ c_0 @ ( c_Suc @ SV63 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(4342,plain,
! [SV64: $i] :
( ( ! [SY2137: $i] :
( ~ ( class_Orderings_Oorder @ SV64 )
| ( c_lessequals @ SY2137 @ SY2137 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(4343,plain,
! [SV65: $i] :
( ( ! [SY2138: $i,SY2139: $i,SY2140: $i] :
( ~ ( c_in @ SV65 @ ( c_Relation_ODomain @ SY2138 @ SY2139 @ SY2140 ) @ SY2139 )
| ( c_in @ ( c_Pair @ SV65 @ ( c_Main_ODomainE__1 @ SV65 @ SY2138 @ SY2139 @ SY2140 ) @ SY2139 @ SY2140 ) @ SY2138 @ ( tc_prod @ SY2139 @ SY2140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(4344,plain,
! [SV66: $i] :
( ( ! [SY2141: $i,SY2142: $i,SY2143: $i,SY2144: $i] :
( ~ ( c_in @ ( c_Pair @ SV66 @ SY2141 @ SY2142 @ SY2143 ) @ SY2144 @ ( tc_prod @ SY2142 @ SY2143 ) )
| ( c_in @ SV66 @ ( c_Relation_ODomain @ SY2144 @ SY2142 @ SY2143 ) @ SY2142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(4345,plain,
! [SV67: $i] :
( ( ! [SY2145: $i] :
( ~ ( c_in @ SV67 @ c_Relation_OId @ ( tc_prod @ SY2145 @ SY2145 ) )
| ( SV67
= ( c_Pair @ ( c_Main_OIdE__1 @ SV67 @ SY2145 ) @ ( c_Main_OIdE__1 @ SV67 @ SY2145 ) @ SY2145 @ SY2145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(4346,plain,
! [SV68: $i] :
( ( ! [SY2146: $i,SY2147: $i,SY2148: $i,SY2149: $i] :
( ~ ( c_in @ SV68 @ ( c_Relation_OImage @ SY2146 @ SY2147 @ SY2148 @ SY2149 ) @ SY2149 )
| ( c_in @ ( c_Main_OImageE__1 @ SY2147 @ SV68 @ SY2146 @ SY2148 @ SY2149 ) @ SY2147 @ SY2148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(4347,plain,
! [SV69: $i] :
( ( ! [SY2150: $i,SY2151: $i,SY2152: $i,SY2153: $i] :
( ~ ( c_in @ SV69 @ ( c_Relation_OImage @ SY2150 @ SY2151 @ SY2152 @ SY2153 ) @ SY2153 )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SY2151 @ SV69 @ SY2150 @ SY2152 @ SY2153 ) @ SV69 @ SY2152 @ SY2153 ) @ SY2150 @ ( tc_prod @ SY2152 @ SY2153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(4348,plain,
! [SV70: $i] :
( ( ! [SY2154: $i,SY2155: $i,SY2156: $i,SY2157: $i,SY2158: $i] :
( ~ ( c_in @ SV70 @ SY2154 @ SY2155 )
| ~ ( c_in @ ( c_Pair @ SV70 @ SY2156 @ SY2155 @ SY2157 ) @ SY2158 @ ( tc_prod @ SY2155 @ SY2157 ) )
| ( c_in @ SY2156 @ ( c_Relation_OImage @ SY2158 @ SY2154 @ SY2155 @ SY2157 ) @ SY2157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(4349,plain,
! [SV71: $i] :
( ( ! [SY2159: $i,SY2160: $i,SY2161: $i] :
( ~ ( c_in @ SV71 @ ( c_Relation_ORange @ SY2159 @ SY2160 @ SY2161 ) @ SY2161 )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV71 @ SY2159 @ SY2161 @ SY2160 ) @ SV71 @ SY2160 @ SY2161 ) @ SY2159 @ ( tc_prod @ SY2160 @ SY2161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(4350,plain,
! [SV72: $i] :
( ( ! [SY2162: $i,SY2163: $i,SY2164: $i,SY2165: $i] :
( ~ ( c_in @ ( c_Pair @ SV72 @ SY2162 @ SY2163 @ SY2164 ) @ SY2165 @ ( tc_prod @ SY2163 @ SY2164 ) )
| ( c_in @ SY2162 @ ( c_Relation_ORange @ SY2165 @ SY2163 @ SY2164 ) @ SY2164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(4351,plain,
! [SV73: $i] :
( ( ! [SY2166: $i,SY2167: $i,SY2168: $i] :
( ~ ( c_in @ SV73 @ ( c_Relation_Oconverse @ SY2166 @ SY2167 @ SY2168 ) @ ( tc_prod @ SY2168 @ SY2167 ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SY2166 @ SV73 @ SY2167 @ SY2168 ) @ ( c_Main_OconverseE__2 @ SY2166 @ SV73 @ SY2167 @ SY2168 ) @ SY2167 @ SY2168 ) @ SY2166 @ ( tc_prod @ SY2167 @ SY2168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(4352,plain,
! [SV74: $i] :
( ( ! [SY2169: $i,SY2170: $i,SY2171: $i] :
( ~ ( c_in @ SV74 @ ( c_Relation_Oconverse @ SY2169 @ SY2170 @ SY2171 ) @ ( tc_prod @ SY2171 @ SY2170 ) )
| ( SV74
= ( c_Pair @ ( c_Main_OconverseE__2 @ SY2169 @ SV74 @ SY2170 @ SY2171 ) @ ( c_Main_OconverseE__1 @ SY2169 @ SV74 @ SY2170 @ SY2171 ) @ SY2171 @ SY2170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(4353,plain,
! [SV75: $i] :
( ( ! [SY2172: $i,SY2173: $i] :
( ~ ( c_in @ SV75 @ ( c_Relation_Odiag @ SY2172 @ SY2173 ) @ ( tc_prod @ SY2173 @ SY2173 ) )
| ( SV75
= ( c_Pair @ ( c_Main_OdiagE__1 @ SY2172 @ SV75 @ SY2173 ) @ ( c_Main_OdiagE__1 @ SY2172 @ SV75 @ SY2173 ) @ SY2173 @ SY2173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(4354,plain,
! [SV76: $i] :
( ( ! [SY2174: $i,SY2175: $i] :
( ~ ( c_in @ SV76 @ ( c_Relation_Odiag @ SY2174 @ SY2175 ) @ ( tc_prod @ SY2175 @ SY2175 ) )
| ( c_in @ ( c_Main_OdiagE__1 @ SY2174 @ SV76 @ SY2175 ) @ SY2174 @ SY2175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(4355,plain,
! [SV77: $i] :
( ( ! [SY2176: $i,SY2177: $i] :
( ~ ( c_in @ SV77 @ SY2176 @ SY2177 )
| ( c_in @ ( c_Pair @ SV77 @ SV77 @ SY2177 @ SY2177 ) @ ( c_Relation_Odiag @ SY2176 @ SY2177 ) @ ( tc_prod @ SY2177 @ SY2177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(4356,plain,
! [SV78: $i] :
( ( ! [SY2178: $i,SY2179: $i,SY2180: $i,SY2181: $i,SY2182: $i] :
( ~ ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SY2178 @ SY2179 @ SY2180 @ SY2181 @ SY2182 ) @ ( tc_prod @ SY2182 @ SY2181 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SY2178 @ SY2179 @ SV78 @ SY2180 @ SY2181 @ SY2182 ) @ ( c_Main_Orel__compE__3 @ SY2178 @ SY2179 @ SV78 @ SY2180 @ SY2181 @ SY2182 ) @ SY2180 @ SY2181 ) @ SY2178 @ ( tc_prod @ SY2180 @ SY2181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(4357,plain,
! [SV79: $i] :
( ( ! [SY2183: $i,SY2184: $i,SY2185: $i,SY2186: $i,SY2187: $i] :
( ~ ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SY2183 @ SY2184 @ SY2185 @ SY2186 @ SY2187 ) @ ( tc_prod @ SY2187 @ SY2186 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SY2183 @ SY2184 @ SV79 @ SY2185 @ SY2186 @ SY2187 ) @ ( c_Main_Orel__compE__2 @ SY2183 @ SY2184 @ SV79 @ SY2185 @ SY2186 @ SY2187 ) @ SY2187 @ SY2185 ) @ SY2184 @ ( tc_prod @ SY2187 @ SY2185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(4358,plain,
! [SV80: $i] :
( ( ! [SY2188: $i,SY2189: $i,SY2190: $i,SY2191: $i,SY2192: $i] :
( ~ ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SY2188 @ SY2189 @ SY2190 @ SY2191 @ SY2192 ) @ ( tc_prod @ SY2192 @ SY2191 ) )
| ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SY2188 @ SY2189 @ SV80 @ SY2190 @ SY2191 @ SY2192 ) @ ( c_Main_Orel__compE__3 @ SY2188 @ SY2189 @ SV80 @ SY2190 @ SY2191 @ SY2192 ) @ SY2192 @ SY2191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(4359,plain,
! [SV81: $i] :
( ( ! [SY2193: $i,SY2194: $i,SY2195: $i,SY2196: $i,SY2197: $i,SY2198: $i,SY2199: $i] :
( ~ ( c_in @ ( c_Pair @ SV81 @ SY2193 @ SY2194 @ SY2195 ) @ SY2196 @ ( tc_prod @ SY2194 @ SY2195 ) )
| ~ ( c_in @ ( c_Pair @ SY2197 @ SV81 @ SY2198 @ SY2194 ) @ SY2199 @ ( tc_prod @ SY2198 @ SY2194 ) )
| ( c_in @ ( c_Pair @ SY2197 @ SY2193 @ SY2198 @ SY2195 ) @ ( c_Relation_Orel__comp @ SY2196 @ SY2199 @ SY2194 @ SY2195 @ SY2198 ) @ ( tc_prod @ SY2198 @ SY2195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(4360,plain,
! [SV82: $i] :
( ( ! [SY2200: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV82 @ SY2200 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(4361,plain,
! [SV83: $i] :
( ( ! [SY2201: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV83 @ SY2201 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(4362,plain,
! [SV84: $i] :
( ( ! [SY2202: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV84 @ SY2202 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(4363,plain,
! [SV85: $i] :
( ( ! [SY2203: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV85 @ SY2203 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(4364,plain,
! [SV86: $i] :
( ( c_in @ ( c_SetInterval_OatMost @ SV86 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(4365,plain,
! [SV87: $i] :
( ( ! [SY2204: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV87 @ SY2204 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(4366,plain,
! [SV88: $i] :
( ( ! [SY2205: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV88 @ SY2205 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(4367,plain,
! [SV89: $i] :
( ( ! [SY2206: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV89 @ SY2206 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(4368,plain,
! [SV90: $i] :
( ( ! [SY2207: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV90 @ SY2207 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(4369,plain,
! [SV91: $i] :
( ( c_in @ ( c_SetInterval_OlessThan @ SV91 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(4370,plain,
! [SV92: $i] :
( ( ! [SY2208: $i,SY2209: $i] :
( ( c_in @ SV92 @ ( c_Inter @ SY2208 @ SY2209 ) @ SY2209 )
| ( c_in @ ( c_Main_OInterI__1 @ SV92 @ SY2208 @ SY2209 ) @ SY2208 @ ( tc_set @ SY2209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(4371,plain,
! [SV93: $i] :
( ( ! [SY2210: $i,SY2211: $i] :
( ~ ( c_in @ SV93 @ ( c_Main_OInterI__1 @ SV93 @ SY2210 @ SY2211 ) @ SY2211 )
| ( c_in @ SV93 @ ( c_Inter @ SY2210 @ SY2211 ) @ SY2211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(4372,plain,
! [SV94: $i] :
( ( ! [SY2212: $i] : ( c_in @ SV94 @ c_UNIV @ SY2212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(4373,plain,
! [SV95: $i] :
( ( ! [SY2213: $i,SY2214: $i] :
( ~ ( c_in @ SV95 @ ( c_Union @ SY2213 @ SY2214 ) @ SY2214 )
| ( c_in @ ( c_Main_OUnionE__1 @ SV95 @ SY2213 @ SY2214 ) @ SY2213 @ ( tc_set @ SY2214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(4374,plain,
! [SV96: $i] :
( ( ! [SY2215: $i,SY2216: $i] :
( ~ ( c_in @ SV96 @ ( c_Union @ SY2215 @ SY2216 ) @ SY2216 )
| ( c_in @ SV96 @ ( c_Main_OUnionE__1 @ SV96 @ SY2215 @ SY2216 ) @ SY2216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(4375,plain,
! [SV97: $i] :
( ( ! [SY2217: $i] : ( c_lessequals @ c_emptyset @ SV97 @ ( tc_set @ SY2217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(4376,plain,
! [SV98: $i] :
( ( ! [SY2218: $i,SY2219: $i] :
( ~ ( c_less @ SV98 @ SY2218 @ ( tc_set @ SY2219 ) )
| ~ ( c_lessequals @ SY2218 @ SV98 @ ( tc_set @ SY2219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(4377,plain,
! [SV99: $i] :
( ( ! [SY2220: $i,SY2221: $i] :
( ~ ( c_less @ SV99 @ SY2220 @ ( tc_set @ SY2221 ) )
| ( c_lessequals @ SV99 @ SY2220 @ ( tc_set @ SY2221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(4378,plain,
! [SV100: $i] :
( ( ! [SY2222: $i,SY2223: $i] :
( ~ ( c_lessequals @ SV100 @ SY2222 @ ( tc_set @ SY2223 ) )
| ( c_less @ SV100 @ SY2222 @ ( tc_set @ SY2223 ) )
| ( SV100 = SY2222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(4379,plain,
! [SV101: $i] :
( ( ! [SY2224: $i,SY2225: $i] :
( ~ ( c_in @ SV101 @ ( c_insert @ SY2224 @ c_emptyset @ SY2225 ) @ SY2225 )
| ( SV101 = SY2224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(4380,plain,
! [SV102: $i] :
( ( ! [SY2226: $i] : ( c_in @ SV102 @ ( c_insert @ SV102 @ c_emptyset @ SY2226 ) @ SY2226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(4381,plain,
! [SV103: $i] :
( ( ! [SY2227: $i,SY2228: $i,SY2229: $i] :
( ~ ( c_in @ SV103 @ SY2227 @ SY2228 )
| ~ ( c_lessequals @ SY2227 @ SY2229 @ ( tc_set @ SY2228 ) )
| ( c_in @ SV103 @ SY2229 @ SY2228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(4382,plain,
! [SV104: $i] :
( ( ! [SY2230: $i,SY2231: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV104 @ SY2230 @ SY2231 ) @ SV104 @ SY2231 )
| ( c_lessequals @ SV104 @ SY2230 @ ( tc_set @ SY2231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(4383,plain,
! [SV105: $i] :
( ( ! [SY2232: $i,SY2233: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV105 @ SY2232 @ SY2233 ) @ SY2232 @ SY2233 )
| ( c_lessequals @ SV105 @ SY2232 @ ( tc_set @ SY2233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(4384,plain,
! [SV106: $i] :
( ( ! [SY2234: $i,SY2235: $i] :
( ~ ( c_lessequals @ SV106 @ SY2234 @ ( tc_set @ SY2235 ) )
| ~ ( c_lessequals @ SY2234 @ SV106 @ ( tc_set @ SY2235 ) )
| ( SY2234 = SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(4385,plain,
! [SV107: $i] :
( ( ! [SY2236: $i] : ( c_lessequals @ SV107 @ SV107 @ ( tc_set @ SY2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(4386,plain,
! [SV108: $i] :
( ( ! [SY2237: $i,SY2238: $i,SY2239: $i,SY2240: $i] :
( ~ ( c_in @ SV108 @ SY2237 @ SY2238 )
| ( c_in @ ( c_Sum__Type_OInl @ SV108 @ SY2238 @ SY2239 ) @ ( c_Sum__Type_OPlus @ SY2237 @ SY2240 @ SY2238 @ SY2239 ) @ ( tc_sum @ SY2238 @ SY2239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(4387,plain,
! [SV109: $i] :
( ( ! [SY2241: $i,SY2242: $i,SY2243: $i,SY2244: $i] :
( ~ ( c_in @ SV109 @ SY2241 @ SY2242 )
| ( c_in @ ( c_Sum__Type_OInr @ SV109 @ SY2242 @ SY2243 ) @ ( c_Sum__Type_OPlus @ SY2244 @ SY2241 @ SY2243 @ SY2242 ) @ ( tc_sum @ SY2243 @ SY2242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(4388,plain,
! [SV110: $i] :
( ( ! [SY2245: $i,SY2246: $i,SY2247: $i,SY2248: $i] :
( ~ ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SY2245 @ SY2246 @ SY2247 @ SY2248 ) @ ( tc_sum @ SY2247 @ SY2248 ) )
| ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SY2245 @ SV110 @ SY2247 @ SY2248 ) @ SY2247 @ SY2248 ) )
| ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2246 @ SV110 @ SY2248 @ SY2247 ) @ SY2248 @ SY2247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(4389,plain,
! [SV111: $i] :
( ( ! [SY2249: $i,SY2250: $i,SY2251: $i,SY2252: $i] :
( ~ ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SY2249 @ SY2250 @ SY2251 @ SY2252 ) @ ( tc_sum @ SY2251 @ SY2252 ) )
| ( c_in @ ( c_Main_OPlusE__2 @ SY2250 @ SV111 @ SY2252 @ SY2251 ) @ SY2250 @ SY2252 )
| ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SY2249 @ SV111 @ SY2251 @ SY2252 ) @ SY2251 @ SY2252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(4390,plain,
! [SV112: $i] :
( ( ! [SY2253: $i,SY2254: $i,SY2255: $i,SY2256: $i] :
( ~ ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SY2253 @ SY2254 @ SY2255 @ SY2256 ) @ ( tc_sum @ SY2255 @ SY2256 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SY2253 @ SV112 @ SY2255 @ SY2256 ) @ SY2253 @ SY2255 )
| ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2254 @ SV112 @ SY2256 @ SY2255 ) @ SY2256 @ SY2255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(4391,plain,
! [SV113: $i] :
( ( ! [SY2257: $i,SY2258: $i,SY2259: $i,SY2260: $i] :
( ~ ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SY2257 @ SY2258 @ SY2259 @ SY2260 ) @ ( tc_sum @ SY2259 @ SY2260 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SY2257 @ SV113 @ SY2259 @ SY2260 ) @ SY2257 @ SY2259 )
| ( c_in @ ( c_Main_OPlusE__2 @ SY2258 @ SV113 @ SY2260 @ SY2259 ) @ SY2258 @ SY2260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(4392,plain,
! [SV114: $i] :
( ( ! [SY2261: $i,SY2262: $i] :
( ~ ( c_in @ SV114 @ SY2261 @ ( tc_prod @ SY2262 @ SY2262 ) )
| ( c_in @ SV114 @ ( c_Transitive__Closure_Ortrancl @ SY2261 @ SY2262 ) @ ( tc_prod @ SY2262 @ SY2262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(4393,plain,
! [SV115: $i] :
( ( ! [SY2263: $i,SY2264: $i] : ( c_in @ ( c_Pair @ SV115 @ SV115 @ SY2263 @ SY2263 ) @ ( c_Transitive__Closure_Ortrancl @ SY2264 @ SY2263 ) @ ( tc_prod @ SY2263 @ SY2263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(4394,plain,
! [SV116: $i] :
( ( ! [SY2265: $i,SY2266: $i,SY2267: $i] :
( ~ ( c_in @ ( c_Pair @ SV116 @ SY2265 @ SY2266 @ SY2266 ) @ SY2267 @ ( tc_prod @ SY2266 @ SY2266 ) )
| ( c_in @ ( c_Pair @ SV116 @ SY2265 @ SY2266 @ SY2266 ) @ ( c_Transitive__Closure_Otrancl @ SY2267 @ SY2266 ) @ ( tc_prod @ SY2266 @ SY2266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(4395,plain,
! [SV117: $i] :
( ( ! [SY2268: $i,SY2269: $i,SY2270: $i] :
( ~ ( c_in @ ( c_Pair @ SV117 @ SY2268 @ SY2269 @ SY2269 ) @ ( c_Transitive__Closure_Otrancl @ SY2270 @ SY2269 ) @ ( tc_prod @ SY2269 @ SY2269 ) )
| ( c_in @ ( c_Pair @ SV117 @ SY2268 @ SY2269 @ SY2269 ) @ ( c_Transitive__Closure_Ortrancl @ SY2270 @ SY2269 ) @ ( tc_prod @ SY2269 @ SY2269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(4396,plain,
! [SV118: $i] :
( ( c_Wellfounded__Recursion_Owf @ c_emptyset @ SV118 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(4397,plain,
! [SV119: $i] :
( ( ! [SY2271: $i,SY2272: $i,SY2273: $i] :
( ~ ( c_Relation_Otrans @ SV119 @ SY2271 )
| ~ ( c_Relation_Otrans @ SY2272 @ SY2273 )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SY2272 @ SV119 @ SY2273 @ SY2271 ) @ ( tc_prod @ SY2273 @ SY2271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(4398,plain,
! [SV120: $i] :
( ( ! [SY2274: $i,SY2275: $i,SY2276: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV120 @ SY2274 )
| ~ ( c_Wellfounded__Recursion_Owf @ SY2275 @ SY2276 )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SY2275 @ SV120 @ SY2276 @ SY2274 ) @ ( tc_prod @ SY2276 @ SY2274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(4399,plain,
! [SV121: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ SV121 ) )
| ~ ( class_Finite__Set_Ofinite @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(4400,plain,
! [SV122: $i] :
( ( ! [SY2277: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV122 @ SY2277 ) )
| ~ ( class_Finite__Set_Ofinite @ SY2277 )
| ~ ( class_Finite__Set_Ofinite @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(4401,plain,
! [SV123: $i] :
( ( ! [SY2278: $i] : ( class_Nat_Opower @ ( tc_fun @ SV123 @ SY2278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(4402,plain,
! [SV124: $i] :
( ( ! [SY2279: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV124 @ SY2279 ) )
| ~ ( class_Finite__Set_Ofinite @ SY2279 )
| ~ ( class_Finite__Set_Ofinite @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(4403,plain,
! [SV125: $i] :
( ( class_HOL_Ominus @ ( tc_set @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(4404,plain,
! [SV126: $i] :
( ( class_Orderings_Oord @ ( tc_set @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(4405,plain,
! [SV127: $i] :
( ( class_Orderings_Oorder @ ( tc_set @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(4406,plain,
! [SV128: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_set @ SV128 ) )
| ~ ( class_Finite__Set_Ofinite @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(4407,plain,
! [SV129: $i] :
( ( class_Nat_Opower @ ( tc_set @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(4408,plain,
! [SV130: $i] :
( ( ! [SY2280: $i] :
( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV130 @ SY2280 ) )
| ~ ( class_Finite__Set_Ofinite @ SY2280 )
| ~ ( class_Finite__Set_Ofinite @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(4409,plain,
! [SV131: $i] :
( ( ~ ( class_LOrder_Ojoin__semilorder @ SV131 )
| ( class_Orderings_Oord @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(4410,plain,
! [SV132: $i] :
( ( ~ ( class_LOrder_Ojoin__semilorder @ SV132 )
| ( class_Orderings_Oorder @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(4411,plain,
! [SV133: $i] :
( ( ~ ( class_LOrder_Olorder @ SV133 )
| ( class_LOrder_Omeet__semilorder @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(4412,plain,
! [SV134: $i] :
( ( ~ ( class_LOrder_Olorder @ SV134 )
| ( class_Orderings_Oord @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(4413,plain,
! [SV135: $i] :
( ( ~ ( class_LOrder_Olorder @ SV135 )
| ( class_Orderings_Oorder @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(4414,plain,
! [SV136: $i] :
( ( ~ ( class_LOrder_Olorder @ SV136 )
| ( class_LOrder_Ojoin__semilorder @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(4415,plain,
! [SV137: $i] :
( ( ~ ( class_LOrder_Omeet__semilorder @ SV137 )
| ( class_Orderings_Oord @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(4416,plain,
! [SV138: $i] :
( ( ~ ( class_LOrder_Omeet__semilorder @ SV138 )
| ( class_Orderings_Oorder @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(4417,plain,
! [SV139: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV139 )
| ( class_HOL_Oplus @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(4418,plain,
! [SV140: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV140 )
| ( class_OrderedGroup_Osemigroup__add @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(4419,plain,
! [SV141: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV141 )
| ( class_Ring__and__Field_Osemiring__0 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(4420,plain,
! [SV142: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV142 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(4421,plain,
! [SV143: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV143 )
| ( class_HOL_Ominus @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(4422,plain,
! [SV144: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV144 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(4423,plain,
! [SV145: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV145 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(4424,plain,
! [SV146: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV146 )
| ( class_OrderedGroup_Oab__group__add @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(4425,plain,
! [SV147: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV147 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(4426,plain,
! [SV148: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV148 )
| ( class_Ring__and__Field_Oring @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(4427,plain,
! [SV149: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV149 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(4428,plain,
! [SV150: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV150 )
| ( class_Ring__and__Field_Ocomm__ring @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(4429,plain,
! [SV151: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV151 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(4430,plain,
! [SV152: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV152 )
| ( class_HOL_Oone @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(4431,plain,
! [SV153: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV153 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(4432,plain,
! [SV154: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV154 )
| ( class_OrderedGroup_Omonoid__mult @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(4433,plain,
! [SV155: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV155 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(4434,plain,
! [SV156: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV156 )
| ( class_Ring__and__Field_Osemiring__1 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(4435,plain,
! [SV157: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV157 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(4436,plain,
! [SV158: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV158 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(4437,plain,
! [SV159: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV159 )
| ( class_Ring__and__Field_Oring__1 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(4438,plain,
! [SV160: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV160 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(4439,plain,
! [SV161: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV161 )
| ( class_Ring__and__Field_Ocomm__ring__1 @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(4440,plain,
! [SV162: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV162 )
| ( class_HOL_Otimes @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(4441,plain,
! [SV163: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV163 )
| ( class_Numeral_Onumber @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(4442,plain,
! [SV164: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV164 )
| ( class_OrderedGroup_Osemigroup__mult @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(4443,plain,
! [SV165: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV165 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(4444,plain,
! [SV166: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV166 )
| ( class_Ring__and__Field_Osemiring @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(4445,plain,
! [SV167: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV167 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(4446,plain,
! [SV168: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV168 )
| ( class_HOL_Ozero @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(4447,plain,
! [SV169: $i] :
( ( ~ ( class_Numeral_Onumber__ring @ SV169 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(4448,plain,
! [SV170: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV170 )
| ( class_HOL_Ominus @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(4449,plain,
! [SV171: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV171 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(4450,plain,
! [SV172: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV172 )
| ( class_HOL_Ozero @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(4451,plain,
! [SV173: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV173 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(4452,plain,
! [SV174: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV174 )
| ( class_OrderedGroup_Osemigroup__add @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(4453,plain,
! [SV175: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV175 )
| ( class_HOL_Oplus @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(4454,plain,
! [SV176: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV176 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(4455,plain,
! [SV177: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV177 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(4456,plain,
! [SV178: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV178 )
| ( class_OrderedGroup_Osemigroup__add @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(4457,plain,
! [SV179: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV179 )
| ( class_HOL_Oplus @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(4458,plain,
! [SV180: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV180 )
| ( class_OrderedGroup_Osemigroup__mult @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(4459,plain,
! [SV181: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV181 )
| ( class_HOL_Otimes @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(4460,plain,
! [SV182: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV182 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(4461,plain,
! [SV183: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV183 )
| ( class_OrderedGroup_Osemigroup__add @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(4462,plain,
! [SV184: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV184 )
| ( class_HOL_Oplus @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(4463,plain,
! [SV185: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV185 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(4464,plain,
! [SV186: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV186 )
| ( class_OrderedGroup_Osemigroup__add @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(4465,plain,
! [SV187: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV187 )
| ( class_HOL_Oplus @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(4466,plain,
! [SV188: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV188 )
| ( class_HOL_Ozero @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(4467,plain,
! [SV189: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV189 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(4468,plain,
! [SV190: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV190 )
| ( class_OrderedGroup_Osemigroup__add @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(4469,plain,
! [SV191: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV191 )
| ( class_HOL_Oplus @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(4470,plain,
! [SV192: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV192 )
| ( class_HOL_Oone @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(4471,plain,
! [SV193: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV193 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(4472,plain,
! [SV194: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV194 )
| ( class_OrderedGroup_Osemigroup__mult @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(4473,plain,
! [SV195: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV195 )
| ( class_HOL_Otimes @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(4474,plain,
! [SV196: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV196 )
| ( class_OrderedGroup_Omonoid__mult @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(4475,plain,
! [SV197: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV197 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(4476,plain,
! [SV198: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV198 )
| ( class_OrderedGroup_Oab__group__add @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(4477,plain,
! [SV199: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV199 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(4478,plain,
! [SV200: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV200 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(4479,plain,
! [SV201: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV201 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(4480,plain,
! [SV202: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV202 )
| ( class_OrderedGroup_Osemigroup__add @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(4481,plain,
! [SV203: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV203 )
| ( class_HOL_Oplus @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(4482,plain,
! [SV204: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV204 )
| ( class_LOrder_Olorder @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(4483,plain,
! [SV205: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV205 )
| ( class_LOrder_Ojoin__semilorder @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(4484,plain,
! [SV206: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV206 )
| ( class_LOrder_Omeet__semilorder @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(4485,plain,
! [SV207: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV207 )
| ( class_HOL_Ominus @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(4486,plain,
! [SV208: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV208 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(4487,plain,
! [SV209: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV209 )
| ( class_HOL_Ozero @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(4488,plain,
! [SV210: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV210 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(4489,plain,
! [SV211: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV211 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(4490,plain,
! [SV212: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV212 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(4491,plain,
! [SV213: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV213 )
| ( class_Orderings_Oorder @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(4492,plain,
! [SV214: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV214 )
| ( class_Orderings_Oord @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(4493,plain,
! [SV215: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV215 )
| ( class_OrderedGroup_Olordered__ab__group @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(4494,plain,
! [SV216: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV216 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(4495,plain,
! [SV217: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV217 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(4496,plain,
! [SV218: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV218 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(4497,plain,
! [SV219: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV219 )
| ( class_OrderedGroup_Osemigroup__add @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(4498,plain,
! [SV220: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV220 )
| ( class_HOL_Oplus @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(4499,plain,
! [SV221: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV221 )
| ( class_LOrder_Olorder @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(4500,plain,
! [SV222: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV222 )
| ( class_LOrder_Ojoin__semilorder @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(4501,plain,
! [SV223: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV223 )
| ( class_LOrder_Omeet__semilorder @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(4502,plain,
! [SV224: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV224 )
| ( class_Orderings_Oorder @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(4503,plain,
! [SV225: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV225 )
| ( class_Orderings_Oord @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(4504,plain,
! [SV226: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV226 )
| ( class_OrderedGroup_Oab__group__add @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(4505,plain,
! [SV227: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV227 )
| ( class_HOL_Ominus @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(4506,plain,
! [SV228: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV228 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(4507,plain,
! [SV229: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV229 )
| ( class_HOL_Ozero @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(4508,plain,
! [SV230: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV230 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(4509,plain,
! [SV231: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV231 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(4510,plain,
! [SV232: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV232 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(4511,plain,
! [SV233: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV233 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(4512,plain,
! [SV234: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV234 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(4513,plain,
! [SV235: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV235 )
| ( class_OrderedGroup_Oab__group__add @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(4514,plain,
! [SV236: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV236 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(4515,plain,
! [SV237: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV237 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(4516,plain,
! [SV238: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV238 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(4517,plain,
! [SV239: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV239 )
| ( class_OrderedGroup_Osemigroup__add @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(4518,plain,
! [SV240: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV240 )
| ( class_HOL_Oplus @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(4519,plain,
! [SV241: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV241 )
| ( class_LOrder_Ojoin__semilorder @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(4520,plain,
! [SV242: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV242 )
| ( class_OrderedGroup_Olordered__ab__group @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(4521,plain,
! [SV243: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV243 )
| ( class_LOrder_Olorder @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(4522,plain,
! [SV244: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV244 )
| ( class_LOrder_Omeet__semilorder @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(4523,plain,
! [SV245: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV245 )
| ( class_HOL_Ominus @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(4524,plain,
! [SV246: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV246 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(4525,plain,
! [SV247: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV247 )
| ( class_HOL_Ozero @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(4526,plain,
! [SV248: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV248 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(4527,plain,
! [SV249: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV249 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(4528,plain,
! [SV250: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV250 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(4529,plain,
! [SV251: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV251 )
| ( class_Orderings_Oorder @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(4530,plain,
! [SV252: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV252 )
| ( class_Orderings_Oord @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(4531,plain,
! [SV253: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV253 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(4532,plain,
! [SV254: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV254 )
| ( class_OrderedGroup_Oab__group__add @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(4533,plain,
! [SV255: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV255 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(4534,plain,
! [SV256: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV256 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(4535,plain,
! [SV257: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV257 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(4536,plain,
! [SV258: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV258 )
| ( class_OrderedGroup_Osemigroup__add @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(4537,plain,
! [SV259: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV259 )
| ( class_HOL_Oplus @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(4538,plain,
! [SV260: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV260 )
| ( class_LOrder_Omeet__semilorder @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(4539,plain,
! [SV261: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV261 )
| ( class_OrderedGroup_Olordered__ab__group @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(4540,plain,
! [SV262: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV262 )
| ( class_LOrder_Olorder @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(4541,plain,
! [SV263: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV263 )
| ( class_LOrder_Ojoin__semilorder @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(4542,plain,
! [SV264: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV264 )
| ( class_HOL_Ominus @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(4543,plain,
! [SV265: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV265 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(4544,plain,
! [SV266: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV266 )
| ( class_HOL_Ozero @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(4545,plain,
! [SV267: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV267 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(4546,plain,
! [SV268: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV268 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(4547,plain,
! [SV269: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV269 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(4548,plain,
! [SV270: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV270 )
| ( class_Orderings_Oorder @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(4549,plain,
! [SV271: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV271 )
| ( class_Orderings_Oord @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(4550,plain,
! [SV272: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV272 )
| ( class_HOL_Oone @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(4551,plain,
! [SV273: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV273 )
| ( class_OrderedGroup_Osemigroup__mult @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(4552,plain,
! [SV274: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV274 )
| ( class_HOL_Otimes @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(4553,plain,
! [SV275: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV275 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(4554,plain,
! [SV276: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV276 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(4555,plain,
! [SV277: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV277 )
| ( class_LOrder_Olorder @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(4556,plain,
! [SV278: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV278 )
| ( class_LOrder_Ojoin__semilorder @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(4557,plain,
! [SV279: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV279 )
| ( class_LOrder_Omeet__semilorder @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(4558,plain,
! [SV280: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV280 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(4559,plain,
! [SV281: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV281 )
| ( class_Orderings_Oorder @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(4560,plain,
! [SV282: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV282 )
| ( class_Orderings_Oord @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(4561,plain,
! [SV283: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV283 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(4562,plain,
! [SV284: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV284 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(4563,plain,
! [SV285: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV285 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(4564,plain,
! [SV286: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV286 )
| ( class_OrderedGroup_Osemigroup__add @ SV286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(4565,plain,
! [SV287: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV287 )
| ( class_HOL_Oplus @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(4566,plain,
! [SV288: $i] :
( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV288 )
| ( class_Orderings_Olinorder @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(4567,plain,
! [SV289: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV289 )
| ( class_OrderedGroup_Oab__group__add @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(4568,plain,
! [SV290: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV290 )
| ( class_HOL_Ominus @ SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(4569,plain,
! [SV291: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV291 )
| ( class_Orderings_Oorder @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(4570,plain,
! [SV292: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV292 )
| ( class_Orderings_Oord @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(4571,plain,
! [SV293: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV293 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(4572,plain,
! [SV294: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV294 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(4573,plain,
! [SV295: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV295 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(4574,plain,
! [SV296: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV296 )
| ( class_HOL_Ozero @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(4575,plain,
! [SV297: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV297 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(4576,plain,
! [SV298: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV298 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(4577,plain,
! [SV299: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV299 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(4578,plain,
! [SV300: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV300 )
| ( class_OrderedGroup_Osemigroup__add @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(4579,plain,
! [SV301: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV301 )
| ( class_HOL_Oplus @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(4580,plain,
! [SV302: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV302 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(4581,plain,
! [SV303: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV303 )
| ( class_Orderings_Oorder @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(4582,plain,
! [SV304: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV304 )
| ( class_Orderings_Oord @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(4583,plain,
! [SV305: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV305 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(4584,plain,
! [SV306: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV306 )
| ( class_OrderedGroup_Osemigroup__add @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(4585,plain,
! [SV307: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV307 )
| ( class_HOL_Oplus @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(4586,plain,
! [SV308: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV308 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(4587,plain,
! [SV309: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV309 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(4588,plain,
! [SV310: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV310 )
| ( class_Orderings_Oorder @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(4589,plain,
! [SV311: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV311 )
| ( class_Orderings_Oord @ SV311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(4590,plain,
! [SV312: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV312 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(4591,plain,
! [SV313: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV313 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(4592,plain,
! [SV314: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV314 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(4593,plain,
! [SV315: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV315 )
| ( class_OrderedGroup_Osemigroup__add @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(4594,plain,
! [SV316: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV316 )
| ( class_HOL_Oplus @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(4595,plain,
! [SV317: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV317 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(4596,plain,
! [SV318: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV318 )
| ( class_Orderings_Oorder @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(4597,plain,
! [SV319: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV319 )
| ( class_Orderings_Oord @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(4598,plain,
! [SV320: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(4599,plain,
! [SV321: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV321 )
| ( class_OrderedGroup_Osemigroup__add @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(4600,plain,
! [SV322: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV322 )
| ( class_HOL_Oplus @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(4601,plain,
! [SV323: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV323 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(4602,plain,
! [SV324: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV324 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(4603,plain,
! [SV325: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV325 )
| ( class_HOL_Oplus @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(4604,plain,
! [SV326: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV326 )
| ( class_HOL_Otimes @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(4605,plain,
! [SV327: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV327 )
| ( class_LOrder_Olorder @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(4606,plain,
! [SV328: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV328 )
| ( class_LOrder_Ojoin__semilorder @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(4607,plain,
! [SV329: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV329 )
| ( class_LOrder_Omeet__semilorder @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(4608,plain,
! [SV330: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV330 )
| ( class_Orderings_Oord @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(4609,plain,
! [SV331: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV331 )
| ( class_Orderings_Oorder @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(4610,plain,
! [SV332: $i] :
( ( ~ ( class_Orderings_Oorder @ SV332 )
| ( class_Orderings_Oord @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(4611,plain,
! [SV333: $i] :
( ( ~ ( class_Power_Orecpower @ SV333 )
| ( class_Nat_Opower @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(4612,plain,
! [SV334: $i] :
( ( ~ ( class_Power_Orecpower @ SV334 )
| ( class_HOL_Ozero @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(4613,plain,
! [SV335: $i] :
( ( ~ ( class_Power_Orecpower @ SV335 )
| ( class_Ring__and__Field_Osemiring @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(4614,plain,
! [SV336: $i] :
( ( ~ ( class_Power_Orecpower @ SV336 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(4615,plain,
! [SV337: $i] :
( ( ~ ( class_Power_Orecpower @ SV337 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(4616,plain,
! [SV338: $i] :
( ( ~ ( class_Power_Orecpower @ SV338 )
| ( class_Ring__and__Field_Osemiring__0 @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(4617,plain,
! [SV339: $i] :
( ( ~ ( class_Power_Orecpower @ SV339 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(4618,plain,
! [SV340: $i] :
( ( ~ ( class_Power_Orecpower @ SV340 )
| ( class_OrderedGroup_Omonoid__mult @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(4619,plain,
! [SV341: $i] :
( ( ~ ( class_Power_Orecpower @ SV341 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(4620,plain,
! [SV342: $i] :
( ( ~ ( class_Power_Orecpower @ SV342 )
| ( class_Ring__and__Field_Osemiring__1 @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(4621,plain,
! [SV343: $i] :
( ( ~ ( class_Power_Orecpower @ SV343 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(4622,plain,
! [SV344: $i] :
( ( ~ ( class_Power_Orecpower @ SV344 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(4623,plain,
! [SV345: $i] :
( ( ~ ( class_Power_Orecpower @ SV345 )
| ( class_HOL_Oone @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3258]) ).
thf(4624,plain,
! [SV346: $i] :
( ( ~ ( class_Power_Orecpower @ SV346 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(4625,plain,
! [SV347: $i] :
( ( ~ ( class_Power_Orecpower @ SV347 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(4626,plain,
! [SV348: $i] :
( ( ~ ( class_Power_Orecpower @ SV348 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(4627,plain,
! [SV349: $i] :
( ( ~ ( class_Power_Orecpower @ SV349 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(4628,plain,
! [SV350: $i] :
( ( ~ ( class_Power_Orecpower @ SV350 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(4629,plain,
! [SV351: $i] :
( ( ~ ( class_Power_Orecpower @ SV351 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(4630,plain,
! [SV352: $i] :
( ( ~ ( class_Power_Orecpower @ SV352 )
| ( class_HOL_Oplus @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(4631,plain,
! [SV353: $i] :
( ( ~ ( class_Power_Orecpower @ SV353 )
| ( class_OrderedGroup_Osemigroup__add @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(4632,plain,
! [SV354: $i] :
( ( ~ ( class_Power_Orecpower @ SV354 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(4633,plain,
! [SV355: $i] :
( ( ~ ( class_Power_Orecpower @ SV355 )
| ( class_HOL_Otimes @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(4634,plain,
! [SV356: $i] :
( ( ~ ( class_Power_Orecpower @ SV356 )
| ( class_OrderedGroup_Osemigroup__mult @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(4635,plain,
! [SV357: $i] :
( ( ~ ( class_Power_Orecpower @ SV357 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(4636,plain,
! [SV358: $i] :
( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV358 )
| ( class_HOL_Ozero @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(4637,plain,
! [SV359: $i] :
( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV359 )
| ( class_HOL_Oone @ SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(4638,plain,
! [SV360: $i] :
( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV360 )
| ( class_HOL_Ominus @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(4639,plain,
! [SV361: $i] :
( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV361 )
| ( class_Orderings_Oord @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(4640,plain,
! [SV362: $i] :
( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV362 )
| ( class_HOL_Ozero @ SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(4641,plain,
! [SV363: $i] :
( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV363 )
| ( class_HOL_Ozero @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(4642,plain,
! [SV364: $i] :
( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV364 )
| ( class_HOL_Otimes @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(4643,plain,
! [SV365: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV365 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(4644,plain,
! [SV366: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV366 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(4645,plain,
! [SV367: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV367 )
| ( class_HOL_Oplus @ SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(4646,plain,
! [SV368: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV368 )
| ( class_HOL_Ozero @ SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(4647,plain,
! [SV369: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV369 )
| ( class_OrderedGroup_Oab__group__add @ SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(4648,plain,
! [SV370: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV370 )
| ( class_HOL_Ominus @ SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(4649,plain,
! [SV371: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV371 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(4650,plain,
! [SV372: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV372 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(4651,plain,
! [SV373: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV373 )
| ( class_Ring__and__Field_Oring @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(4652,plain,
! [SV374: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV374 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(4653,plain,
! [SV375: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV375 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(4654,plain,
! [SV376: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV376 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(4655,plain,
! [SV377: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV377 )
| ( class_Ring__and__Field_Osemiring__0 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(4656,plain,
! [SV378: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV378 )
| ( class_Ring__and__Field_Osemiring @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3291]) ).
thf(4657,plain,
! [SV379: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV379 )
| ( class_OrderedGroup_Osemigroup__mult @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(4658,plain,
! [SV380: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV380 )
| ( class_HOL_Otimes @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3293]) ).
thf(4659,plain,
! [SV381: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV381 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(4660,plain,
! [SV382: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV382 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(4661,plain,
! [SV383: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV383 )
| ( class_OrderedGroup_Osemigroup__add @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(4662,plain,
! [SV384: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV384 )
| ( class_Ring__and__Field_Ocomm__ring @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(4663,plain,
! [SV385: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV385 )
| ( class_Ring__and__Field_Oring @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(4664,plain,
! [SV386: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV386 )
| ( class_Ring__and__Field_Osemiring @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(4665,plain,
! [SV387: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV387 )
| ( class_OrderedGroup_Osemigroup__mult @ SV387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(4666,plain,
! [SV388: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV388 )
| ( class_HOL_Otimes @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(4667,plain,
! [SV389: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV389 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(4668,plain,
! [SV390: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV390 )
| ( class_HOL_Ozero @ SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(4669,plain,
! [SV391: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV391 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(4670,plain,
! [SV392: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV392 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV392 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(4671,plain,
! [SV393: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV393 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(4672,plain,
! [SV394: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV394 )
| ( class_OrderedGroup_Osemigroup__add @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(4673,plain,
! [SV395: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV395 )
| ( class_HOL_Oplus @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(4674,plain,
! [SV396: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV396 )
| ( class_OrderedGroup_Oab__group__add @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(4675,plain,
! [SV397: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV397 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(4676,plain,
! [SV398: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV398 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV398 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(4677,plain,
! [SV399: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV399 )
| ( class_Ring__and__Field_Osemiring__1 @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(4678,plain,
! [SV400: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV400 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(4679,plain,
! [SV401: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV401 )
| ( class_OrderedGroup_Omonoid__mult @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(4680,plain,
! [SV402: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV402 )
| ( class_HOL_Oone @ SV402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(4681,plain,
! [SV403: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV403 )
| ( class_Ring__and__Field_Oring__1 @ SV403 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(4682,plain,
! [SV404: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV404 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(4683,plain,
! [SV405: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV405 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(4684,plain,
! [SV406: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV406 )
| ( class_HOL_Ominus @ SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(4685,plain,
! [SV407: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV407 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(4686,plain,
! [SV408: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV408 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV408 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(4687,plain,
! [SV409: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV409 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(4688,plain,
! [SV410: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV410 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(4689,plain,
! [SV411: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV411 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(4690,plain,
! [SV412: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV412 )
| ( class_Ring__and__Field_Osemiring__0 @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(4691,plain,
! [SV413: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV413 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(4692,plain,
! [SV414: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV414 )
| ( class_OrderedGroup_Osemigroup__add @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3327]) ).
thf(4693,plain,
! [SV415: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV415 )
| ( class_HOL_Oplus @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3328]) ).
thf(4694,plain,
! [SV416: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV416 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(4695,plain,
! [SV417: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV417 )
| ( class_OrderedGroup_Osemigroup__mult @ SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(4696,plain,
! [SV418: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV418 )
| ( class_HOL_Otimes @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(4697,plain,
! [SV419: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV419 )
| ( class_Ring__and__Field_Osemiring @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(4698,plain,
! [SV420: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV420 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3333]) ).
thf(4699,plain,
! [SV421: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV421 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(4700,plain,
! [SV422: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV422 )
| ( class_Ring__and__Field_Osemiring__0 @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(4701,plain,
! [SV423: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV423 )
| ( class_Ring__and__Field_Osemiring @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(4702,plain,
! [SV424: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV424 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(4703,plain,
! [SV425: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV425 )
| ( class_OrderedGroup_Osemigroup__add @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(4704,plain,
! [SV426: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV426 )
| ( class_HOL_Oplus @ SV426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(4705,plain,
! [SV427: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV427 )
| ( class_OrderedGroup_Osemigroup__mult @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(4706,plain,
! [SV428: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV428 )
| ( class_HOL_Otimes @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(4707,plain,
! [SV429: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV429 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(4708,plain,
! [SV430: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV430 )
| ( class_HOL_Ozero @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(4709,plain,
! [SV431: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV431 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(4710,plain,
! [SV432: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV432 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(4711,plain,
! [SV433: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV433 )
| ( class_HOL_Oplus @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(4712,plain,
! [SV434: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV434 )
| ( class_HOL_Ozero @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(4713,plain,
! [SV435: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV435 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(4714,plain,
! [SV436: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV436 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(4715,plain,
! [SV437: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV437 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(4716,plain,
! [SV438: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV438 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(4717,plain,
! [SV439: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV439 )
| ( class_Ring__and__Field_Osemiring__0 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(4718,plain,
! [SV440: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV440 )
| ( class_Ring__and__Field_Osemiring @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(4719,plain,
! [SV441: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV441 )
| ( class_OrderedGroup_Osemigroup__mult @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(4720,plain,
! [SV442: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV442 )
| ( class_HOL_Otimes @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(4721,plain,
! [SV443: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV443 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(4722,plain,
! [SV444: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV444 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(4723,plain,
! [SV445: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV445 )
| ( class_OrderedGroup_Osemigroup__add @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(4724,plain,
! [SV446: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV446 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(4725,plain,
! [SV447: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV447 )
| ( class_HOL_Ozero @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(4726,plain,
! [SV448: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV448 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(4727,plain,
! [SV449: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(4728,plain,
! [SV450: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 )
| ( class_OrderedGroup_Osemigroup__add @ SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(4729,plain,
! [SV451: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV451 )
| ( class_HOL_Oplus @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(4730,plain,
! [SV452: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV452 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(4731,plain,
! [SV453: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV453 )
| ( class_OrderedGroup_Omonoid__mult @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(4732,plain,
! [SV454: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV454 )
| ( class_Ring__and__Field_Osemiring__1 @ SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(4733,plain,
! [SV455: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV455 )
| ( class_HOL_Oone @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(4734,plain,
! [SV456: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV456 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(4735,plain,
! [SV457: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV457 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(4736,plain,
! [SV458: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV458 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(4737,plain,
! [SV459: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV459 )
| ( class_Ring__and__Field_Osemiring__0 @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(4738,plain,
! [SV460: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV460 )
| ( class_Ring__and__Field_Osemiring @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(4739,plain,
! [SV461: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV461 )
| ( class_OrderedGroup_Osemigroup__mult @ SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(4740,plain,
! [SV462: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV462 )
| ( class_HOL_Otimes @ SV462 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(4741,plain,
! [SV463: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV463 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(4742,plain,
! [SV464: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV464 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV464 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(4743,plain,
! [SV465: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV465 )
| ( class_HOL_Ozero @ SV465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(4744,plain,
! [SV466: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV466 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(4745,plain,
! [SV467: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV467 )
| ( class_OrderedGroup_Osemigroup__add @ SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(4746,plain,
! [SV468: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV468 )
| ( class_HOL_Oplus @ SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(4747,plain,
! [SV469: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV469 )
| ( class_OrderedGroup_Omonoid__mult @ SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(4748,plain,
! [SV470: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV470 )
| ( class_HOL_Oone @ SV470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(4749,plain,
! [SV471: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV471 )
| ( class_OrderedGroup_Osemigroup__mult @ SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(4750,plain,
! [SV472: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV472 )
| ( class_HOL_Otimes @ SV472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(4751,plain,
! [SV473: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV473 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(4752,plain,
! [SV474: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV474 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(4753,plain,
! [SV475: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV475 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(4754,plain,
! [SV476: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV476 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(4755,plain,
! [SV477: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV477 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(4756,plain,
! [SV478: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV478 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(4757,plain,
! [SV479: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV479 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(4758,plain,
! [SV480: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV480 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(4759,plain,
! [SV481: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV481 )
| ( class_Ring__and__Field_Osemiring__1 @ SV481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(4760,plain,
! [SV482: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV482 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(4761,plain,
! [SV483: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV483 )
| ( class_Ring__and__Field_Osemiring__0 @ SV483 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(4762,plain,
! [SV484: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV484 )
| ( class_Ring__and__Field_Osemiring @ SV484 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(4763,plain,
! [SV485: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV485 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(4764,plain,
! [SV486: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV486 )
| ( class_HOL_Ozero @ SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(4765,plain,
! [SV487: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV487 )
| ( class_HOL_Oinverse @ SV487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(4766,plain,
! [SV488: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV488 )
| ( class_Ring__and__Field_Ocomm__ring__1 @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(4767,plain,
! [SV489: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV489 )
| ( class_Ring__and__Field_Ocomm__ring @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(4768,plain,
! [SV490: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV490 )
| ( class_Ring__and__Field_Osemiring__1 @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(4769,plain,
! [SV491: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV491 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(4770,plain,
! [SV492: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV492 )
| ( class_OrderedGroup_Omonoid__mult @ SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(4771,plain,
! [SV493: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV493 )
| ( class_HOL_Oone @ SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(4772,plain,
! [SV494: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV494 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(4773,plain,
! [SV495: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV495 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(4774,plain,
! [SV496: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV496 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(4775,plain,
! [SV497: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV497 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV497 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4776,plain,
! [SV498: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV498 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4777,plain,
! [SV499: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV499 )
| ( class_Ring__and__Field_Osemiring__0 @ SV499 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(4778,plain,
! [SV500: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV500 )
| ( class_Ring__and__Field_Oring__1 @ SV500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(4779,plain,
! [SV501: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV501 )
| ( class_Ring__and__Field_Osemiring @ SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(4780,plain,
! [SV502: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV502 )
| ( class_OrderedGroup_Osemigroup__mult @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(4781,plain,
! [SV503: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV503 )
| ( class_HOL_Otimes @ SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(4782,plain,
! [SV504: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV504 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(4783,plain,
! [SV505: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV505 )
| ( class_HOL_Ozero @ SV505 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4784,plain,
! [SV506: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV506 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4785,plain,
! [SV507: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV507 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(4786,plain,
! [SV508: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV508 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4787,plain,
! [SV509: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV509 )
| ( class_OrderedGroup_Osemigroup__add @ SV509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(4788,plain,
! [SV510: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV510 )
| ( class_HOL_Oplus @ SV510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(4789,plain,
! [SV511: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV511 )
| ( class_Ring__and__Field_Oring @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(4790,plain,
! [SV512: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV512 )
| ( class_HOL_Oinverse @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(4791,plain,
! [SV513: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV513 )
| ( class_Ring__and__Field_Oidom @ SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(4792,plain,
! [SV514: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV514 )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(4793,plain,
! [SV515: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV515 )
| ( class_OrderedGroup_Oab__group__add @ SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4794,plain,
! [SV516: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV516 )
| ( class_HOL_Ominus @ SV516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(4795,plain,
! [SV517: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV517 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(4796,plain,
! [SV518: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV518 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(4797,plain,
! [SV519: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV519 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(4798,plain,
! [SV520: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV520 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(4799,plain,
! [SV521: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV521 )
| ( class_Ring__and__Field_Ocomm__ring__1 @ SV521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4800,plain,
! [SV522: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV522 )
| ( class_Ring__and__Field_Ocomm__ring @ SV522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4801,plain,
! [SV523: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV523 )
| ( class_Ring__and__Field_Osemiring__1 @ SV523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4802,plain,
! [SV524: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV524 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(4803,plain,
! [SV525: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV525 )
| ( class_OrderedGroup_Omonoid__mult @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(4804,plain,
! [SV526: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV526 )
| ( class_HOL_Oone @ SV526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(4805,plain,
! [SV527: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV527 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(4806,plain,
! [SV528: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV528 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(4807,plain,
! [SV529: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV529 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(4808,plain,
! [SV530: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV530 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(4809,plain,
! [SV531: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV531 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3444]) ).
thf(4810,plain,
! [SV532: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV532 )
| ( class_Ring__and__Field_Osemiring__0 @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(4811,plain,
! [SV533: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV533 )
| ( class_Ring__and__Field_Oring__1 @ SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3446]) ).
thf(4812,plain,
! [SV534: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV534 )
| ( class_Ring__and__Field_Osemiring @ SV534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(4813,plain,
! [SV535: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV535 )
| ( class_OrderedGroup_Osemigroup__mult @ SV535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(4814,plain,
! [SV536: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV536 )
| ( class_HOL_Otimes @ SV536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(4815,plain,
! [SV537: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV537 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(4816,plain,
! [SV538: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV538 )
| ( class_HOL_Ozero @ SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(4817,plain,
! [SV539: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV539 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4818,plain,
! [SV540: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV540 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(4819,plain,
! [SV541: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV541 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(4820,plain,
! [SV542: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV542 )
| ( class_OrderedGroup_Osemigroup__add @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(4821,plain,
! [SV543: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV543 )
| ( class_HOL_Oplus @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(4822,plain,
! [SV544: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV544 )
| ( class_Ring__and__Field_Oring @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(4823,plain,
! [SV545: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV545 )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(4824,plain,
! [SV546: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV546 )
| ( class_OrderedGroup_Oab__group__add @ SV546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(4825,plain,
! [SV547: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV547 )
| ( class_HOL_Ominus @ SV547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4826,plain,
! [SV548: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV548 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(4827,plain,
! [SV549: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV549 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(4828,plain,
! [SV550: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV550 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(4829,plain,
! [SV551: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV551 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(4830,plain,
! [SV552: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV552 )
| ( class_Ring__and__Field_Opordered__ring @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(4831,plain,
! [SV553: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV553 )
| ( class_Ring__and__Field_Oring @ SV553 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(4832,plain,
! [SV554: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV554 )
| ( class_Orderings_Oorder @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(4833,plain,
! [SV555: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV555 )
| ( class_Orderings_Oord @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(4834,plain,
! [SV556: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV556 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4835,plain,
! [SV557: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV557 )
| ( class_Ring__and__Field_Osemiring__0 @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(4836,plain,
! [SV558: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV558 )
| ( class_Ring__and__Field_Osemiring @ SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(4837,plain,
! [SV559: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV559 )
| ( class_OrderedGroup_Osemigroup__mult @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(4838,plain,
! [SV560: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV560 )
| ( class_HOL_Otimes @ SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(4839,plain,
! [SV561: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV561 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(4840,plain,
! [SV562: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV562 )
| ( class_HOL_Ozero @ SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(4841,plain,
! [SV563: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV563 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4842,plain,
! [SV564: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV564 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(4843,plain,
! [SV565: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV565 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(4844,plain,
! [SV566: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV566 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(4845,plain,
! [SV567: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV567 )
| ( class_OrderedGroup_Osemigroup__add @ SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4846,plain,
! [SV568: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV568 )
| ( class_HOL_Oplus @ SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4847,plain,
! [SV569: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV569 )
| ( class_OrderedGroup_Olordered__ab__group__abs @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(4848,plain,
! [SV570: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV570 )
| ( class_OrderedGroup_Olordered__ab__group @ SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(4849,plain,
! [SV571: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV571 )
| ( class_LOrder_Olorder @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(4850,plain,
! [SV572: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV572 )
| ( class_LOrder_Ojoin__semilorder @ SV572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(4851,plain,
! [SV573: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV573 )
| ( class_LOrder_Omeet__semilorder @ SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(4852,plain,
! [SV574: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV574 )
| ( class_OrderedGroup_Olordered__ab__group__meet @ SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(4853,plain,
! [SV575: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV575 )
| ( class_OrderedGroup_Oab__group__add @ SV575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(4854,plain,
! [SV576: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV576 )
| ( class_OrderedGroup_Olordered__ab__group__join @ SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4855,plain,
! [SV577: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV577 )
| ( class_HOL_Ominus @ SV577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(4856,plain,
! [SV578: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV578 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(4857,plain,
! [SV579: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV579 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(4858,plain,
! [SV580: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV580 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV580 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4859,plain,
! [SV581: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV581 )
| ( class_Ring__and__Field_Opordered__semiring @ SV581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(4860,plain,
! [SV582: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV582 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4861,plain,
! [SV583: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV583 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV583 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4862,plain,
! [SV584: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV584 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4863,plain,
! [SV585: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV585 )
| ( class_HOL_Oplus @ SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(4864,plain,
! [SV586: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV586 )
| ( class_HOL_Ozero @ SV586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(4865,plain,
! [SV587: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV587 )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV587 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(4866,plain,
! [SV588: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV588 )
| ( class_Orderings_Olinorder @ SV588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4867,plain,
! [SV589: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV589 )
| ( class_LOrder_Olorder @ SV589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4868,plain,
! [SV590: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV590 )
| ( class_LOrder_Ojoin__semilorder @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(4869,plain,
! [SV591: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV591 )
| ( class_LOrder_Omeet__semilorder @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4870,plain,
! [SV592: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV592 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(4871,plain,
! [SV593: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV593 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV593 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(4872,plain,
! [SV594: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV594 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(4873,plain,
! [SV595: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV595 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(4874,plain,
! [SV596: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV596 )
| ( class_Orderings_Oorder @ SV596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(4875,plain,
! [SV597: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV597 )
| ( class_Orderings_Oord @ SV597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(4876,plain,
! [SV598: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV598 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(4877,plain,
! [SV599: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV599 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV599 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(4878,plain,
! [SV600: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV600 )
| ( class_Ring__and__Field_Oordered__semiring__strict @ SV600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4879,plain,
! [SV601: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV601 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV601 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(4880,plain,
! [SV602: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV602 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(4881,plain,
! [SV603: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV603 )
| ( class_Ring__and__Field_Opordered__semiring @ SV603 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3516]) ).
thf(4882,plain,
! [SV604: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV604 )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4883,plain,
! [SV605: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV605 )
| ( class_Ring__and__Field_Opordered__comm__semiring @ SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4884,plain,
! [SV606: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV606 )
| ( class_Ring__and__Field_Osemiring__0 @ SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4885,plain,
! [SV607: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV607 )
| ( class_Ring__and__Field_Osemiring @ SV607 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(4886,plain,
! [SV608: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV608 )
| ( class_OrderedGroup_Osemigroup__mult @ SV608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4887,plain,
! [SV609: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV609 )
| ( class_HOL_Otimes @ SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4888,plain,
! [SV610: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV610 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV610 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(4889,plain,
! [SV611: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV611 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV611 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4890,plain,
! [SV612: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV612 )
| ( class_OrderedGroup_Osemigroup__add @ SV612 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4891,plain,
! [SV613: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV613 )
| ( class_Ring__and__Field_Ofield @ SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4892,plain,
! [SV614: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV614 )
| ( class_HOL_Oinverse @ SV614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4893,plain,
! [SV615: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV615 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(4894,plain,
! [SV616: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV616 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4895,plain,
! [SV617: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV617 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4896,plain,
! [SV618: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV618 )
| ( class_Ring__and__Field_Osemiring__1 @ SV618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(4897,plain,
! [SV619: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV619 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(4898,plain,
! [SV620: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV620 )
| ( class_OrderedGroup_Omonoid__mult @ SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4899,plain,
! [SV621: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV621 )
| ( class_HOL_Oone @ SV621 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(4900,plain,
! [SV622: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV622 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(4901,plain,
! [SV623: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV623 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(4902,plain,
! [SV624: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV624 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4903,plain,
! [SV625: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV625 )
| ( class_Ring__and__Field_Oidom @ SV625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(4904,plain,
! [SV626: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV626 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4905,plain,
! [SV627: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV627 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV627 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(4906,plain,
! [SV628: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV628 )
| ( class_Ring__and__Field_Osemiring__0 @ SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4907,plain,
! [SV629: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV629 )
| ( class_Ring__and__Field_Osemiring @ SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(4908,plain,
! [SV630: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV630 )
| ( class_OrderedGroup_Osemigroup__mult @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4909,plain,
! [SV631: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV631 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV631 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4910,plain,
! [SV632: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV632 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4911,plain,
! [SV633: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV633 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV633 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4912,plain,
! [SV634: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV634 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4913,plain,
! [SV635: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV635 )
| ( class_OrderedGroup_Osemigroup__add @ SV635 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4914,plain,
! [SV636: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV636 )
| ( class_Ring__and__Field_Ocomm__ring__1 @ SV636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4915,plain,
! [SV637: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV637 )
| ( class_HOL_Oplus @ SV637 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(4916,plain,
! [SV638: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV638 )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV638 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4917,plain,
! [SV639: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV639 )
| ( class_HOL_Ozero @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(4918,plain,
! [SV640: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV640 )
| ( class_HOL_Otimes @ SV640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(4919,plain,
! [SV641: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV641 )
| ( class_Ring__and__Field_Oordered__idom @ SV641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(4920,plain,
! [SV642: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV642 )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(4921,plain,
! [SV643: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV643 )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(4922,plain,
! [SV644: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV644 )
| ( class_Ring__and__Field_Opordered__comm__semiring @ SV644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4923,plain,
! [SV645: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV645 )
| ( class_Ring__and__Field_Oordered__ring__strict @ SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4924,plain,
! [SV646: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV646 )
| ( class_Ring__and__Field_Oordered__semiring__strict @ SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(4925,plain,
! [SV647: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV647 )
| ( class_Ring__and__Field_Ocomm__ring @ SV647 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(4926,plain,
! [SV648: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV648 )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV648 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(4927,plain,
! [SV649: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV649 )
| ( class_Orderings_Olinorder @ SV649 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(4928,plain,
! [SV650: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV650 )
| ( class_Ring__and__Field_Oaxclass__abs__if @ SV650 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(4929,plain,
! [SV651: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV651 )
| ( class_Ring__and__Field_Olordered__ring @ SV651 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(4930,plain,
! [SV652: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV652 )
| ( class_Ring__and__Field_Opordered__ring @ SV652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(4931,plain,
! [SV653: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV653 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV653 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3566]) ).
thf(4932,plain,
! [SV654: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV654 )
| ( class_Ring__and__Field_Opordered__semiring @ SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(4933,plain,
! [SV655: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV655 )
| ( class_OrderedGroup_Olordered__ab__group__abs @ SV655 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(4934,plain,
! [SV656: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV656 )
| ( class_OrderedGroup_Olordered__ab__group__meet @ SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(4935,plain,
! [SV657: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV657 )
| ( class_OrderedGroup_Olordered__ab__group__join @ SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(4936,plain,
! [SV658: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV658 )
| ( class_Ring__and__Field_Oring__1 @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(4937,plain,
! [SV659: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV659 )
| ( class_OrderedGroup_Olordered__ab__group @ SV659 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3572]) ).
thf(4938,plain,
! [SV660: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV660 )
| ( class_LOrder_Olorder @ SV660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3573]) ).
thf(4939,plain,
! [SV661: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV661 )
| ( class_LOrder_Ojoin__semilorder @ SV661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4940,plain,
! [SV662: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV662 )
| ( class_LOrder_Omeet__semilorder @ SV662 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4941,plain,
! [SV663: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV663 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(4942,plain,
! [SV664: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV664 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(4943,plain,
! [SV665: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV665 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV665 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4944,plain,
! [SV666: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV666 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(4945,plain,
! [SV667: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV667 )
| ( class_Orderings_Oorder @ SV667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(4946,plain,
! [SV668: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV668 )
| ( class_Orderings_Oord @ SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(4947,plain,
! [SV669: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV669 )
| ( class_Ring__and__Field_Oring @ SV669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(4948,plain,
! [SV670: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV670 )
| ( class_Ring__and__Field_Oordered__semidom @ SV670 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(4949,plain,
! [SV671: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV671 )
| ( class_OrderedGroup_Oab__group__add @ SV671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4950,plain,
! [SV672: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV672 )
| ( class_HOL_Ominus @ SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4951,plain,
! [SV673: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV673 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(4952,plain,
! [SV674: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV674 )
| ( class_Ring__and__Field_Ocomm__ring__1 @ SV674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(4953,plain,
! [SV675: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV675 )
| ( class_Ring__and__Field_Ocomm__ring @ SV675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(4954,plain,
! [SV676: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV676 )
| ( class_Ring__and__Field_Osemiring__1 @ SV676 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(4955,plain,
! [SV677: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV677 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV677 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4956,plain,
! [SV678: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV678 )
| ( class_OrderedGroup_Omonoid__mult @ SV678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(4957,plain,
! [SV679: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV679 )
| ( class_HOL_Oone @ SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(4958,plain,
! [SV680: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV680 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV680 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(4959,plain,
! [SV681: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV681 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3594]) ).
thf(4960,plain,
! [SV682: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV682 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(4961,plain,
! [SV683: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV683 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV683 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(4962,plain,
! [SV684: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(4963,plain,
! [SV685: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV685 )
| ( class_Ring__and__Field_Osemiring__0 @ SV685 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(4964,plain,
! [SV686: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV686 )
| ( class_Ring__and__Field_Oring__1 @ SV686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4965,plain,
! [SV687: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV687 )
| ( class_Ring__and__Field_Osemiring @ SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(4966,plain,
! [SV688: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV688 )
| ( class_OrderedGroup_Osemigroup__mult @ SV688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4967,plain,
! [SV689: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV689 )
| ( class_HOL_Otimes @ SV689 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(4968,plain,
! [SV690: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV690 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV690 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4969,plain,
! [SV691: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV691 )
| ( class_HOL_Ozero @ SV691 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(4970,plain,
! [SV692: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV692 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4971,plain,
! [SV693: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV693 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(4972,plain,
! [SV694: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV694 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV694 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(4973,plain,
! [SV695: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV695 )
| ( class_OrderedGroup_Osemigroup__add @ SV695 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4974,plain,
! [SV696: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV696 )
| ( class_HOL_Oplus @ SV696 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4975,plain,
! [SV697: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV697 )
| ( class_Ring__and__Field_Oring @ SV697 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4976,plain,
! [SV698: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV698 )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV698 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4977,plain,
! [SV699: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV699 )
| ( class_Ring__and__Field_Oordered__semiring__strict @ SV699 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(4978,plain,
! [SV700: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV700 )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4979,plain,
! [SV701: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV701 )
| ( class_Orderings_Olinorder @ SV701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(4980,plain,
! [SV702: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV702 )
| ( class_LOrder_Olorder @ SV702 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(4981,plain,
! [SV703: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV703 )
| ( class_LOrder_Ojoin__semilorder @ SV703 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4982,plain,
! [SV704: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV704 )
| ( class_LOrder_Omeet__semilorder @ SV704 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4983,plain,
! [SV705: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV705 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV705 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4984,plain,
! [SV706: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV706 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV706 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(4985,plain,
! [SV707: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV707 )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4986,plain,
! [SV708: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV708 )
| ( class_OrderedGroup_Oab__group__add @ SV708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4987,plain,
! [SV709: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV709 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV709 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4988,plain,
! [SV710: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV710 )
| ( class_Ring__and__Field_Opordered__comm__semiring @ SV710 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(4989,plain,
! [SV711: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV711 )
| ( class_Ring__and__Field_Opordered__semiring @ SV711 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(4990,plain,
! [SV712: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV712 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(4991,plain,
! [SV713: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV713 )
| ( class_Orderings_Oorder @ SV713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(4992,plain,
! [SV714: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV714 )
| ( class_Orderings_Oord @ SV714 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(4993,plain,
! [SV715: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV715 )
| ( class_Ring__and__Field_Oaxclass__abs__if @ SV715 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(4994,plain,
! [SV716: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV716 )
| ( class_Ring__and__Field_Oordered__ring__strict @ SV716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(4995,plain,
! [SV717: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV717 )
| ( class_Ring__and__Field_Olordered__ring @ SV717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(4996,plain,
! [SV718: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV718 )
| ( class_Ring__and__Field_Opordered__ring @ SV718 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(4997,plain,
! [SV719: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV719 )
| ( class_HOL_Ominus @ SV719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4998,plain,
! [SV720: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV720 )
| ( class_OrderedGroup_Olordered__ab__group__abs @ SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(4999,plain,
! [SV721: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV721 )
| ( class_OrderedGroup_Olordered__ab__group__meet @ SV721 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(5000,plain,
! [SV722: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV722 )
| ( class_OrderedGroup_Olordered__ab__group__join @ SV722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(5001,plain,
! [SV723: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV723 )
| ( class_OrderedGroup_Olordered__ab__group @ SV723 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3636]) ).
thf(5002,plain,
! [SV724: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV724 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV724 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(5003,plain,
! [SV725: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV725 )
| ( class_Ring__and__Field_Oordered__semidom @ SV725 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(5004,plain,
! [SV726: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV726 )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(5005,plain,
! [SV727: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV727 )
| ( class_Ring__and__Field_Oidom @ SV727 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(5006,plain,
! [SV728: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV728 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(5007,plain,
! [SV729: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV729 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV729 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(5008,plain,
! [SV730: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV730 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV730 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(5009,plain,
! [SV731: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV731 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV731 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(5010,plain,
! [SV732: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV732 )
| ( class_Ring__and__Field_Oring @ SV732 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(5011,plain,
! [SV733: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV733 )
| ( class_OrderedGroup_Oab__group__add @ SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(5012,plain,
! [SV734: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV734 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV734 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(5013,plain,
! [SV735: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV735 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV735 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3648]) ).
thf(5014,plain,
! [SV736: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV736 )
| ( class_OrderedGroup_Osemigroup__add @ SV736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3649]) ).
thf(5015,plain,
! [SV737: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV737 )
| ( class_HOL_Oplus @ SV737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3650]) ).
thf(5016,plain,
! [SV738: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV738 )
| ( class_HOL_Ozero @ SV738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3651]) ).
thf(5017,plain,
! [SV739: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV739 )
| ( class_Ring__and__Field_Oordered__semiring__strict @ SV739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(5018,plain,
! [SV740: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV740 )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV740 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(5019,plain,
! [SV741: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV741 )
| ( class_Orderings_Olinorder @ SV741 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(5020,plain,
! [SV742: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV742 )
| ( class_LOrder_Olorder @ SV742 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(5021,plain,
! [SV743: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV743 )
| ( class_LOrder_Ojoin__semilorder @ SV743 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3656]) ).
thf(5022,plain,
! [SV744: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV744 )
| ( class_HOL_Ominus @ SV744 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3657]) ).
thf(5023,plain,
! [SV745: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV745 )
| ( class_LOrder_Omeet__semilorder @ SV745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(5024,plain,
! [SV746: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV746 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV746 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(5025,plain,
! [SV747: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(5026,plain,
! [SV748: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV748 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV748 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(5027,plain,
! [SV749: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV749 )
| ( class_Ring__and__Field_Opordered__semiring @ SV749 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(5028,plain,
! [SV750: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV750 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3663]) ).
thf(5029,plain,
! [SV751: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV751 )
| ( class_Orderings_Oorder @ SV751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(5030,plain,
! [SV752: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV752 )
| ( class_Orderings_Oord @ SV752 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(5031,plain,
! [SV753: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV753 )
| ( class_Ring__and__Field_Oaxclass__abs__if @ SV753 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(5032,plain,
! [SV754: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV754 )
| ( class_OrderedGroup_Olordered__ab__group @ SV754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(5033,plain,
! [SV755: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV755 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(5034,plain,
! [SV756: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV756 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3669]) ).
thf(5035,plain,
! [SV757: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV757 )
| ( class_Ring__and__Field_Olordered__ring @ SV757 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(5036,plain,
! [SV758: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV758 )
| ( class_Ring__and__Field_Opordered__ring @ SV758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(5037,plain,
! [SV759: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV759 )
| ( class_OrderedGroup_Olordered__ab__group__abs @ SV759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(5038,plain,
! [SV760: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV760 )
| ( class_OrderedGroup_Olordered__ab__group__meet @ SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(5039,plain,
! [SV761: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV761 )
| ( class_OrderedGroup_Olordered__ab__group__join @ SV761 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(5040,plain,
! [SV762: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV762 )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3675]) ).
thf(5041,plain,
! [SV763: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV763 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(5042,plain,
! [SV764: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV764 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV764 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(5043,plain,
! [SV765: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV765 )
| ( class_Ring__and__Field_Osemiring__0 @ SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3678]) ).
thf(5044,plain,
! [SV766: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV766 )
| ( class_Ring__and__Field_Osemiring @ SV766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(5045,plain,
! [SV767: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV767 )
| ( class_OrderedGroup_Osemigroup__mult @ SV767 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3680]) ).
thf(5046,plain,
! [SV768: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV768 )
| ( class_HOL_Otimes @ SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3681]) ).
thf(5047,plain,
! [SV769: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV769 )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV769 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3682]) ).
thf(5048,plain,
! [SV770: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV770 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV770 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(5049,plain,
! [SV771: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV771 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(5050,plain,
! [SV772: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV772 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV772 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(5051,plain,
! [SV773: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV773 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV773 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(5052,plain,
! [SV774: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV774 )
| ( class_Ring__and__Field_Osemiring__0 @ SV774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(5053,plain,
! [SV775: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV775 )
| ( class_Ring__and__Field_Osemiring @ SV775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(5054,plain,
! [SV776: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV776 )
| ( class_OrderedGroup_Osemigroup__mult @ SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(5055,plain,
! [SV777: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV777 )
| ( class_HOL_Otimes @ SV777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3690]) ).
thf(5056,plain,
! [SV778: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV778 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV778 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(5057,plain,
! [SV779: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV779 )
| ( class_HOL_Ozero @ SV779 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(5058,plain,
! [SV780: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV780 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV780 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(5059,plain,
! [SV781: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV781 )
| ( class_OrderedGroup_Ocomm__monoid__mult @ SV781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(5060,plain,
! [SV782: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV782 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV782 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(5061,plain,
! [SV783: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV783 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV783 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(5062,plain,
! [SV784: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV784 )
| ( class_OrderedGroup_Osemigroup__add @ SV784 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(5063,plain,
! [SV785: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV785 )
| ( class_HOL_Oplus @ SV785 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(5064,plain,
! [SV786: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV786 )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV786 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(5065,plain,
! [SV787: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV787 )
| ( class_Ring__and__Field_Oordered__semiring__strict @ SV787 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3700]) ).
thf(5066,plain,
! [SV788: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV788 )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV788 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3701]) ).
thf(5067,plain,
! [SV789: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV789 )
| ( class_Orderings_Olinorder @ SV789 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(5068,plain,
! [SV790: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV790 )
| ( class_LOrder_Olorder @ SV790 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(5069,plain,
! [SV791: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV791 )
| ( class_LOrder_Ojoin__semilorder @ SV791 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(5070,plain,
! [SV792: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV792 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV792 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3705]) ).
thf(5071,plain,
! [SV793: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV793 )
| ( class_LOrder_Omeet__semilorder @ SV793 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(5072,plain,
! [SV794: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV794 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV794 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3707]) ).
thf(5073,plain,
! [SV795: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV795 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV795 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(5074,plain,
! [SV796: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV796 )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3709]) ).
thf(5075,plain,
! [SV797: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV797 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(5076,plain,
! [SV798: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV798 )
| ( class_Ring__and__Field_Opordered__comm__semiring @ SV798 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(5077,plain,
! [SV799: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV799 )
| ( class_Ring__and__Field_Opordered__semiring @ SV799 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(5078,plain,
! [SV800: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV800 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV800 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(5079,plain,
! [SV801: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV801 )
| ( class_Orderings_Oorder @ SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3714]) ).
thf(5080,plain,
! [SV802: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV802 )
| ( class_Orderings_Oord @ SV802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(5081,plain,
! [SV803: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV803 )
| ( class_Ring__and__Field_Osemiring__1 @ SV803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3716]) ).
thf(5082,plain,
! [SV804: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV804 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(5083,plain,
! [SV805: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV805 )
| ( class_OrderedGroup_Omonoid__mult @ SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(5084,plain,
! [SV806: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV806 )
| ( class_HOL_Oone @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3719]) ).
thf(5085,plain,
! [SV807: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV807 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(5086,plain,
! [SV808: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV808 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(5087,plain,
! [SV809: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV809 )
| ( class_Ring__and__Field_Osemiring__0 @ SV809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3722]) ).
thf(5088,plain,
! [SV810: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV810 )
| ( class_Ring__and__Field_Osemiring @ SV810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(5089,plain,
! [SV811: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV811 )
| ( class_Orderings_Olinorder @ SV811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(5090,plain,
! [SV812: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV812 )
| ( class_LOrder_Olorder @ SV812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(5091,plain,
! [SV813: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV813 )
| ( class_LOrder_Ojoin__semilorder @ SV813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(5092,plain,
! [SV814: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV814 )
| ( class_LOrder_Omeet__semilorder @ SV814 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3727]) ).
thf(5093,plain,
! [SV815: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV815 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(5094,plain,
! [SV816: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV816 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV816 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(5095,plain,
! [SV817: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV817 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV817 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(5096,plain,
! [SV818: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV818 )
| ( class_Orderings_Oorder @ SV818 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(5097,plain,
! [SV819: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV819 )
| ( class_Orderings_Oord @ SV819 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(5098,plain,
! [SV820: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV820 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV820 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(5099,plain,
! [SV821: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV821 )
| ( class_OrderedGroup_Osemigroup__mult @ SV821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(5100,plain,
! [SV822: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV822 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV822 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(5101,plain,
! [SV823: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV823 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV823 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(5102,plain,
! [SV824: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV824 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV824 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(5103,plain,
! [SV825: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV825 )
| ( class_Ring__and__Field_Opordered__semiring @ SV825 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(5104,plain,
! [SV826: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV826 )
| ( class_HOL_Otimes @ SV826 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3739]) ).
thf(5105,plain,
! [SV827: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV827 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3740]) ).
thf(5106,plain,
! [SV828: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV828 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV828 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3741]) ).
thf(5107,plain,
! [SV829: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV829 )
| ( class_OrderedGroup_Osemigroup__add @ SV829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(5108,plain,
! [SV830: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV830 )
| ( class_HOL_Oplus @ SV830 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3743]) ).
thf(5109,plain,
! [SV831: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV831 )
| ( class_HOL_Ozero @ SV831 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3744]) ).
thf(5110,plain,
! [SV832: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV832 )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3745]) ).
thf(5111,plain,
! [SV833: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV833 )
| ( class_Ring__and__Field_Opordered__comm__semiring @ SV833 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(5112,plain,
! [SV834: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV834 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV834 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(5113,plain,
! [SV835: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV835 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV835 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(5114,plain,
! [SV836: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV836 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV836 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(5115,plain,
! [SV837: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV837 )
| ( class_OrderedGroup_Osemigroup__add @ SV837 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3750]) ).
thf(5116,plain,
! [SV838: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV838 )
| ( class_HOL_Oplus @ SV838 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3751]) ).
thf(5117,plain,
! [SV839: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV839 )
| ( class_Orderings_Oorder @ SV839 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3752]) ).
thf(5118,plain,
! [SV840: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV840 )
| ( class_Orderings_Oord @ SV840 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(5119,plain,
! [SV841: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV841 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV841 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3754]) ).
thf(5120,plain,
! [SV842: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV842 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3755]) ).
thf(5121,plain,
! [SV843: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV843 )
| ( class_Ring__and__Field_Opordered__semiring @ SV843 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3756]) ).
thf(5122,plain,
! [SV844: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV844 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV844 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(5123,plain,
! [SV845: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV845 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV845 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3758]) ).
thf(5124,plain,
! [SV846: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV846 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV846 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3759]) ).
thf(5125,plain,
! [SV847: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV847 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(5126,plain,
! [SV848: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV848 )
| ( class_Ring__and__Field_Osemiring__0 @ SV848 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(5127,plain,
! [SV849: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV849 )
| ( class_Ring__and__Field_Osemiring @ SV849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(5128,plain,
! [SV850: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV850 )
| ( class_OrderedGroup_Osemigroup__mult @ SV850 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3763]) ).
thf(5129,plain,
! [SV851: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV851 )
| ( class_HOL_Otimes @ SV851 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(5130,plain,
! [SV852: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV852 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV852 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3765]) ).
thf(5131,plain,
! [SV853: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV853 )
| ( class_HOL_Ozero @ SV853 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3766]) ).
thf(5132,plain,
! [SV854: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV854 )
| ( class_Ring__and__Field_Opordered__semiring @ SV854 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(5133,plain,
! [SV855: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV855 )
| ( class_Ring__and__Field_Osemiring__0 @ SV855 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(5134,plain,
! [SV856: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV856 )
| ( class_HOL_Oplus @ SV856 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3769]) ).
thf(5135,plain,
! [SV857: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV857 )
| ( class_Orderings_Oorder @ SV857 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(5136,plain,
! [SV858: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV858 )
| ( class_Orderings_Oord @ SV858 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3771]) ).
thf(5137,plain,
! [SV859: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV859 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV859 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3772]) ).
thf(5138,plain,
! [SV860: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV860 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3773]) ).
thf(5139,plain,
! [SV861: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV861 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV861 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(5140,plain,
! [SV862: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV862 )
| ( class_Ring__and__Field_Osemiring @ SV862 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(5141,plain,
! [SV863: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV863 )
| ( class_OrderedGroup_Osemigroup__mult @ SV863 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(5142,plain,
! [SV864: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV864 )
| ( class_HOL_Otimes @ SV864 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(5143,plain,
! [SV865: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV865 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV865 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3778]) ).
thf(5144,plain,
! [SV866: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV866 )
| ( class_HOL_Ozero @ SV866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3779]) ).
thf(5145,plain,
! [SV867: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV867 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV867 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(5146,plain,
! [SV868: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV868 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV868 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(5147,plain,
! [SV869: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV869 )
| ( class_OrderedGroup_Osemigroup__add @ SV869 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(5148,plain,
! [SV870: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV870 )
| ( class_Ring__and__Field_Ocomm__ring @ SV870 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(5149,plain,
! [SV871: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV871 )
| ( class_Ring__and__Field_Oring @ SV871 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(5150,plain,
! [SV872: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV872 )
| ( class_Ring__and__Field_Osemiring @ SV872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(5151,plain,
! [SV873: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV873 )
| ( class_OrderedGroup_Osemigroup__mult @ SV873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(5152,plain,
! [SV874: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV874 )
| ( class_HOL_Otimes @ SV874 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3787]) ).
thf(5153,plain,
! [SV875: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV875 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(5154,plain,
! [SV876: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV876 )
| ( class_HOL_Ozero @ SV876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(5155,plain,
! [SV877: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV877 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(5156,plain,
! [SV878: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV878 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV878 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(5157,plain,
! [SV879: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV879 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV879 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(5158,plain,
! [SV880: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV880 )
| ( class_OrderedGroup_Osemigroup__add @ SV880 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3793]) ).
thf(5159,plain,
! [SV881: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV881 )
| ( class_HOL_Oplus @ SV881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(5160,plain,
! [SV882: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV882 )
| ( class_OrderedGroup_Oab__group__add @ SV882 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(5161,plain,
! [SV883: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV883 )
| ( class_Ring__and__Field_Opordered__comm__semiring @ SV883 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(5162,plain,
! [SV884: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV884 )
| ( class_Ring__and__Field_Opordered__semiring @ SV884 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(5163,plain,
! [SV885: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV885 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV885 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(5164,plain,
! [SV886: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV886 )
| ( class_Orderings_Oorder @ SV886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3799]) ).
thf(5165,plain,
! [SV887: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV887 )
| ( class_Orderings_Oord @ SV887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(5166,plain,
! [SV888: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV888 )
| ( class_HOL_Ominus @ SV888 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3801]) ).
thf(5167,plain,
! [SV889: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV889 )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV889 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(5168,plain,
! [SV890: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV890 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV890 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3803]) ).
thf(5169,plain,
! [SV891: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV891 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV891 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3804]) ).
thf(5170,plain,
! [SV892: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV892 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3805]) ).
thf(5171,plain,
! [SV893: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV893 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV893 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(5172,plain,
! [SV894: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV894 )
| ( class_Ring__and__Field_Osemiring__0 @ SV894 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(5173,plain,
! [SV895: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV895 )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ SV895 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(5174,plain,
! [SV896: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV896 )
| ( class_Ring__and__Field_Ocomm__semiring @ SV896 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3809]) ).
thf(5175,plain,
! [SV897: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV897 )
| ( class_HOL_Oplus @ SV897 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(5176,plain,
! [SV898: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV898 )
| ( class_HOL_Ozero @ SV898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3811]) ).
thf(5177,plain,
! [SV899: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV899 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3812]) ).
thf(5178,plain,
! [SV900: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV900 )
| ( class_Orderings_Oorder @ SV900 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3813]) ).
thf(5179,plain,
! [SV901: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV901 )
| ( class_Orderings_Oord @ SV901 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3814]) ).
thf(5180,plain,
! [SV902: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV902 )
| ( class_Ring__and__Field_Opordered__semiring @ SV902 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3815]) ).
thf(5181,plain,
! [SV903: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV903 )
| ( class_OrderedGroup_Oab__semigroup__mult @ SV903 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3816]) ).
thf(5182,plain,
! [SV904: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV904 )
| ( class_Ring__and__Field_Osemiring__0 @ SV904 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(5183,plain,
! [SV905: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV905 )
| ( class_Ring__and__Field_Osemiring @ SV905 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(5184,plain,
! [SV906: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV906 )
| ( class_OrderedGroup_Osemigroup__mult @ SV906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3819]) ).
thf(5185,plain,
! [SV907: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV907 )
| ( class_HOL_Otimes @ SV907 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3820]) ).
thf(5186,plain,
! [SV908: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV908 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3821]) ).
thf(5187,plain,
! [SV909: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV909 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV909 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3822]) ).
thf(5188,plain,
! [SV910: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV910 )
| ( class_OrderedGroup_Osemigroup__add @ SV910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3823]) ).
thf(5189,plain,
! [SV911: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV911 )
| ( class_Ring__and__Field_Oring @ SV911 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(5190,plain,
! [SV912: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV912 )
| ( class_OrderedGroup_Oab__group__add @ SV912 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3825]) ).
thf(5191,plain,
! [SV913: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV913 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(5192,plain,
! [SV914: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV914 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(5193,plain,
! [SV915: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV915 )
| ( class_OrderedGroup_Osemigroup__add @ SV915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(5194,plain,
! [SV916: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV916 )
| ( class_HOL_Oplus @ SV916 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(5195,plain,
! [SV917: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV917 )
| ( class_HOL_Ozero @ SV917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(5196,plain,
! [SV918: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV918 )
| ( class_Ring__and__Field_Opordered__semiring @ SV918 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(5197,plain,
! [SV919: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV919 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV919 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3832]) ).
thf(5198,plain,
! [SV920: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV920 )
| ( class_Orderings_Oorder @ SV920 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3833]) ).
thf(5199,plain,
! [SV921: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV921 )
| ( class_Orderings_Oord @ SV921 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3834]) ).
thf(5200,plain,
! [SV922: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV922 )
| ( class_OrderedGroup_Opordered__ab__group__add @ SV922 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(5201,plain,
! [SV923: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV923 )
| ( class_HOL_Ominus @ SV923 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(5202,plain,
! [SV924: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV924 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV924 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(5203,plain,
! [SV925: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV925 )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV925 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(5204,plain,
! [SV926: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV926 )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ SV926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(5205,plain,
! [SV927: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV927 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV927 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3840]) ).
thf(5206,plain,
! [SV928: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV928 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV928 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(5207,plain,
! [SV929: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV929 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV929 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(5208,plain,
! [SV930: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV930 )
| ( class_Ring__and__Field_Osemiring__0 @ SV930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3843]) ).
thf(5209,plain,
! [SV931: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV931 )
| ( class_Ring__and__Field_Osemiring @ SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(5210,plain,
! [SV932: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV932 )
| ( class_OrderedGroup_Osemigroup__mult @ SV932 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3845]) ).
thf(5211,plain,
! [SV933: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV933 )
| ( class_HOL_Otimes @ SV933 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3846]) ).
thf(5212,plain,
! [SV934: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV934 )
| ( class_Ring__and__Field_Osemiring__0 @ SV934 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(5213,plain,
! [SV935: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV935 )
| ( class_Ring__and__Field_Osemiring @ SV935 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3848]) ).
thf(5214,plain,
! [SV936: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV936 )
| ( class_Orderings_Oorder @ SV936 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(5215,plain,
! [SV937: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV937 )
| ( class_Orderings_Oord @ SV937 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(5216,plain,
! [SV938: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV938 )
| ( class_OrderedGroup_Osemigroup__mult @ SV938 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(5217,plain,
! [SV939: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV939 )
| ( class_HOL_Otimes @ SV939 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(5218,plain,
! [SV940: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV940 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV940 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(5219,plain,
! [SV941: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV941 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(5220,plain,
! [SV942: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV942 )
| ( class_OrderedGroup_Osemigroup__add @ SV942 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(5221,plain,
! [SV943: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV943 )
| ( class_HOL_Oplus @ SV943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3856]) ).
thf(5222,plain,
! [SV944: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV944 )
| ( class_HOL_Ozero @ SV944 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(5223,plain,
! [SV945: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV945 )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3858]) ).
thf(5224,plain,
! [SV946: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV946 )
| ( class_Ring__and__Field_Osemiring @ SV946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3859]) ).
thf(5225,plain,
! [SV947: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV947 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV947 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3860]) ).
thf(5226,plain,
! [SV948: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV948 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(5227,plain,
! [SV949: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV949 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV949 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3862]) ).
thf(5228,plain,
! [SV950: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV950 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV950 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(5229,plain,
! [SV951: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV951 )
| ( class_Ring__and__Field_Osemiring__0 @ SV951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(5230,plain,
! [SV952: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV952 )
| ( class_OrderedGroup_Osemigroup__add @ SV952 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(5231,plain,
! [SV953: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV953 )
| ( class_HOL_Oplus @ SV953 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(5232,plain,
! [SV954: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV954 )
| ( class_OrderedGroup_Osemigroup__mult @ SV954 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(5233,plain,
! [SV955: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV955 )
| ( class_HOL_Otimes @ SV955 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3868]) ).
thf(5234,plain,
! [SV956: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV956 )
| ( class_OrderedGroup_Oab__group__add @ SV956 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(5235,plain,
! [SV957: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV957 )
| ( class_HOL_Ominus @ SV957 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3870]) ).
thf(5236,plain,
! [SV958: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV958 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV958 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3871]) ).
thf(5237,plain,
! [SV959: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV959 )
| ( class_HOL_Ozero @ SV959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3872]) ).
thf(5238,plain,
! [SV960: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV960 )
| ( class_Ring__and__Field_Oring @ SV960 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(5239,plain,
! [SV961: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV961 )
| ( class_OrderedGroup_Oab__group__add @ SV961 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(5240,plain,
! [SV962: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV962 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV962 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(5241,plain,
! [SV963: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV963 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV963 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3876]) ).
thf(5242,plain,
! [SV964: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV964 )
| ( class_OrderedGroup_Osemigroup__add @ SV964 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3877]) ).
thf(5243,plain,
! [SV965: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV965 )
| ( class_HOL_Oplus @ SV965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(5244,plain,
! [SV966: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV966 )
| ( class_HOL_Ozero @ SV966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3879]) ).
thf(5245,plain,
! [SV967: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV967 )
| ( class_Ring__and__Field_Osemiring__1 @ SV967 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3880]) ).
thf(5246,plain,
! [SV968: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV968 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV968 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3881]) ).
thf(5247,plain,
! [SV969: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV969 )
| ( class_OrderedGroup_Omonoid__mult @ SV969 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(5248,plain,
! [SV970: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV970 )
| ( class_HOL_Oone @ SV970 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(5249,plain,
! [SV971: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV971 )
| ( class_Ring__and__Field_Osemiring__1__cancel @ SV971 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(5250,plain,
! [SV972: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV972 )
| ( class_HOL_Ominus @ SV972 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(5251,plain,
! [SV973: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV973 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(5252,plain,
! [SV974: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV974 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV974 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3887]) ).
thf(5253,plain,
! [SV975: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV975 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV975 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3888]) ).
thf(5254,plain,
! [SV976: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV976 )
| ( class_Ring__and__Field_Osemiring__0 @ SV976 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3889]) ).
thf(5255,plain,
! [SV977: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV977 )
| ( class_Ring__and__Field_Osemiring @ SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3890]) ).
thf(5256,plain,
! [SV978: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV978 )
| ( class_OrderedGroup_Osemigroup__mult @ SV978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3891]) ).
thf(5257,plain,
! [SV979: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV979 )
| ( class_HOL_Otimes @ SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3892]) ).
thf(5258,plain,
! [SV980: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV980 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3893]) ).
thf(5259,plain,
! [SV981: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV981 )
| ( class_OrderedGroup_Osemigroup__add @ SV981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(5260,plain,
! [SV982: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV982 )
| ( class_HOL_Oplus @ SV982 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(5261,plain,
! [SV983: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV983 )
| ( class_OrderedGroup_Osemigroup__mult @ SV983 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(5262,plain,
! [SV984: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV984 )
| ( class_HOL_Otimes @ SV984 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(5263,plain,
! [SV985: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV985 )
| ( class_Ring__and__Field_Osemiring @ SV985 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(5264,plain,
! [SV986: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV986 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV986 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(5265,plain,
! [SV987: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV987 )
| ( class_OrderedGroup_Osemigroup__add @ SV987 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(5266,plain,
! [SV988: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV988 )
| ( class_HOL_Oplus @ SV988 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(5267,plain,
! [SV989: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV989 )
| ( class_OrderedGroup_Osemigroup__mult @ SV989 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(5268,plain,
! [SV990: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV990 )
| ( class_HOL_Otimes @ SV990 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(5269,plain,
! [SV991: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV991 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV991 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3904]) ).
thf(5270,plain,
! [SV992: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV992 )
| ( class_HOL_Ozero @ SV992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3905]) ).
thf(5271,plain,
! [SV993: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV993 )
| ( class_Ring__and__Field_Osemiring__0 @ SV993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3906]) ).
thf(5272,plain,
! [SV994: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV994 )
| ( class_Ring__and__Field_Osemiring @ SV994 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3907]) ).
thf(5273,plain,
! [SV995: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV995 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV995 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3908]) ).
thf(5274,plain,
! [SV996: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV996 )
| ( class_OrderedGroup_Osemigroup__mult @ SV996 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3909]) ).
thf(5275,plain,
! [SV997: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV997 )
| ( class_HOL_Otimes @ SV997 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(5276,plain,
! [SV998: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV998 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV998 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(5277,plain,
! [SV999: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV999 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV999 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(5278,plain,
! [SV1000: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1000 )
| ( class_OrderedGroup_Osemigroup__add @ SV1000 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(5279,plain,
! [SV1001: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1001 )
| ( class_HOL_Oplus @ SV1001 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(5280,plain,
! [SV1002: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1002 )
| ( class_HOL_Ozero @ SV1002 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(5281,plain,
! [SV1003: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1003 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1003 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(5282,plain,
! [SV1004: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1004 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1004 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(5283,plain,
! [SV1005: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1005 )
| ( class_HOL_Ozero @ SV1005 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(5284,plain,
! [SV1006: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1006 )
| ( class_HOL_Oplus @ SV1006 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(5285,plain,
! [SV1007: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1007 )
| ( class_OrderedGroup_Omonoid__mult @ SV1007 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3920]) ).
thf(5286,plain,
! [SV1008: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1008 )
| ( class_HOL_Oone @ SV1008 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3921]) ).
thf(5287,plain,
! [SV1009: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1009 )
| ( class_Ring__and__Field_Osemiring__0 @ SV1009 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(5288,plain,
! [SV1010: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1010 )
| ( class_Ring__and__Field_Osemiring @ SV1010 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(5289,plain,
! [SV1011: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1011 )
| ( class_OrderedGroup_Osemigroup__mult @ SV1011 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(5290,plain,
! [SV1012: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1012 )
| ( class_HOL_Otimes @ SV1012 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3925]) ).
thf(5291,plain,
! [SV1013: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1013 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV1013 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3926]) ).
thf(5292,plain,
! [SV1014: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1014 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV1014 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(5293,plain,
! [SV1015: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1015 )
| ( class_OrderedGroup_Osemigroup__add @ SV1015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3928]) ).
thf(5294,plain,
! [SV1016: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1016 )
| ( class_Ring__and__Field_Osemiring__1 @ SV1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(5295,plain,
! [SV1017: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1017 )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1017 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3930]) ).
thf(5296,plain,
! [SV1018: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1018 )
| ( class_HOL_Oone @ SV1018 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3931]) ).
thf(5297,plain,
! [SV1019: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1019 )
| ( class_OrderedGroup_Osemigroup__mult @ SV1019 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(5298,plain,
! [SV1020: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1020 )
| ( class_HOL_Otimes @ SV1020 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(5299,plain,
! [SV1021: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1021 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1021 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3934]) ).
thf(5300,plain,
! [SV1022: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1022 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV1022 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(5301,plain,
! [SV1023: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1023 )
| ( class_Ring__and__Field_Osemiring__0__cancel @ SV1023 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(5302,plain,
! [SV1024: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1024 )
| ( class_Ring__and__Field_Osemiring__0 @ SV1024 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(5303,plain,
! [SV1025: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1025 )
| ( class_Ring__and__Field_Osemiring @ SV1025 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(5304,plain,
! [SV1026: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1026 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV1026 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(5305,plain,
! [SV1027: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1027 )
| ( class_HOL_Ozero @ SV1027 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(5306,plain,
! [SV1028: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1028 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV1028 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3941]) ).
thf(5307,plain,
! [SV1029: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1029 )
| ( class_OrderedGroup_Osemigroup__add @ SV1029 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(5308,plain,
! [SV1030: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1030 )
| ( class_HOL_Oplus @ SV1030 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(5309,plain,
! [SV1031: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1031 )
| ( class_OrderedGroup_Omonoid__mult @ SV1031 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(5310,plain,
! [SV1032: $i] :
( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1032 )
| ( class_Orderings_Oord @ SV1032 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(5311,plain,
! [SV1033: $i] :
( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1033 )
| ( class_Orderings_Oorder @ SV1033 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3946]) ).
thf(5312,plain,
! [SV1034: $i] :
( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1034 )
| ( class_LOrder_Omeet__semilorder @ SV1034 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(5313,plain,
! [SV1035: $i] :
( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1035 )
| ( class_LOrder_Ojoin__semilorder @ SV1035 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3948]) ).
thf(5314,plain,
! [SV1036: $i] :
( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1036 )
| ( class_LOrder_Olorder @ SV1036 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(5315,plain,
! [SV1037: $i] :
( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1037 )
| ( class_Orderings_Olinorder @ SV1037 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3950]) ).
thf(5316,plain,
! [SV1038: $i] :
( ( ! [SY2281: $i,SY2282: $i] :
( ~ ( c_in @ SV1038 @ ( c_Datatype_Oo2s @ SY2281 @ SY2282 ) @ SY2282 )
| ( SY2281
= ( c_Datatype_Ooption_OSome @ SV1038 @ SY2282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3951]) ).
thf(5317,plain,
! [SV1039: $i] :
( ( ! [SY2283: $i] : ( c_in @ SV1039 @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ SV1039 @ SY2283 ) @ SY2283 ) @ SY2283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(5318,plain,
! [SV1040: $i] :
( ( ! [SY2284: $i] :
( ( SV1040 = c_Datatype_Ooption_ONone )
| ( SV1040
= ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ SV1040 @ SY2284 ) @ SY2284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(5319,plain,
! [SV1041: $i] :
( ( ! [SY2285: $i] :
( ( SV1041 = c_Datatype_Ooption_ONone )
| ( SV1041
= ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ SV1041 @ SY2285 ) @ SY2285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(5320,plain,
! [SV1042: $i] :
( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1042 @ tc_nat )
| ( SV1042 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3973]) ).
thf(5321,plain,
! [SV1043: $i] :
( ( ! [SY2286: $i] :
( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1043 @ SY2286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(5322,plain,
! [SV1044: $i] :
( ( ! [SY2287: $i] :
( ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1044 @ SY2287 )
= c_emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(5323,plain,
! [SV1045: $i] :
( ( ! [SY2288: $i,SY2289: $i,SY2290: $i] :
( ~ ( c_in @ ( c_minus @ SV1045 @ ( c_insert @ SY2288 @ SY2289 @ SY2290 ) @ ( tc_set @ SY2290 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2290 ) )
| ( c_in @ ( c_minus @ SV1045 @ SY2289 @ ( tc_set @ SY2290 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3981]) ).
thf(5324,plain,
! [SV1046: $i] :
( ( ! [SY2291: $i,SY2292: $i,SY2293: $i] :
( ~ ( c_in @ ( c_minus @ SV1046 @ SY2291 @ ( tc_set @ SY2292 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2292 ) )
| ( c_in @ ( c_minus @ SV1046 @ ( c_insert @ SY2293 @ SY2291 @ SY2292 ) @ ( tc_set @ SY2292 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(5325,plain,
! [SV1047: $i] :
( ( ! [SY2294: $i] :
( ~ ( c_in @ ( c_Pow @ SV1047 @ SY2294 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2294 ) ) )
| ( c_in @ SV1047 @ c_Finite__Set_OFinites @ ( tc_set @ SY2294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3983]) ).
thf(5326,plain,
! [SV1048: $i] :
( ( ! [SY2295: $i] :
( ~ ( c_in @ SV1048 @ c_Finite__Set_OFinites @ ( tc_set @ SY2295 ) )
| ( c_in @ ( c_Pow @ SV1048 @ SY2295 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SY2295 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3984]) ).
thf(5327,plain,
! [SV1049: $i] :
( ( ! [SY2296: $i,SY2297: $i] :
( ~ ( c_in @ ( c_union @ SV1049 @ SY2296 @ SY2297 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2297 ) )
| ( c_in @ SV1049 @ c_Finite__Set_OFinites @ ( tc_set @ SY2297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3985]) ).
thf(5328,plain,
! [SV1050: $i] :
( ( ! [SY2298: $i,SY2299: $i] :
( ~ ( c_in @ ( c_union @ SV1050 @ SY2298 @ SY2299 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2299 ) )
| ( c_in @ SY2298 @ c_Finite__Set_OFinites @ ( tc_set @ SY2299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(5329,plain,
! [SV1051: $i] :
( ( ! [SY2300: $i,SY2301: $i] :
( ~ ( c_in @ SV1051 @ c_Finite__Set_OFinites @ ( tc_set @ SY2300 ) )
| ~ ( c_in @ SY2301 @ c_Finite__Set_OFinites @ ( tc_set @ SY2300 ) )
| ( c_in @ ( c_union @ SY2301 @ SV1051 @ SY2300 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(5330,plain,
! [SV1052: $i] :
( ( ! [SY2302: $i,SY2303: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ SV1052 @ SY2302 @ SY2303 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2303 @ SY2302 ) ) )
| ( c_in @ SV1052 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2302 @ SY2303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(5331,plain,
! [SV1053: $i] :
( ( ! [SY2304: $i,SY2305: $i] :
( ~ ( c_in @ SV1053 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2304 @ SY2305 ) ) )
| ( c_in @ ( c_Relation_Oconverse @ SV1053 @ SY2304 @ SY2305 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2305 @ SY2304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3989]) ).
thf(5332,plain,
! [SV1054: $i] :
( ( ! [SY2306: $i,SY2307: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1054 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2306 @ SY2307 @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1054 @ SY2306 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3990]) ).
thf(5333,plain,
! [SV1055: $i] :
( ( ! [SY2308: $i,SY2309: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1055 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2308 @ SY2309 @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1055 @ SY2309 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(5334,plain,
! [SV1056: $i] :
( ( ! [SY2310: $i,SY2311: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1056 @ SY2310 @ tc_nat )
| ~ ( c_Divides_Oop_Advd @ SV1056 @ SY2311 @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1056 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2311 @ SY2310 @ tc_nat @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3992]) ).
thf(5335,plain,
( ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(5336,plain,
! [SV1057: $i] :
( ( ! [SY2312: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1057 @ ( c_uminus @ SY2312 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ SV1057 @ SY2312 @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(5337,plain,
! [SV1058: $i] :
( ( ! [SY2313: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1058 @ SY2313 @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ SV1058 @ ( c_uminus @ SY2313 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3996]) ).
thf(5338,plain,
! [SV1059: $i] :
( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1059 @ tc_IntDef_Oint )
| ( SV1059 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(5339,plain,
! [SV1060: $i] :
( ( ! [SY2314: $i] :
( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ SV1060 @ tc_IntDef_Oint ) @ SY2314 @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ SV1060 @ SY2314 @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(5340,plain,
! [SV1061: $i] :
( ( ! [SY2315: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1061 @ SY2315 @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ ( c_uminus @ SV1061 @ tc_IntDef_Oint ) @ SY2315 @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(5341,plain,
! [SV1062: $i] :
( ( ! [SY2316: $i,SY2317: $i] :
~ ( c_in @ ( c_Pair @ SV1062 @ c_List_Olist_ONil @ ( tc_List_Olist @ SY2316 ) @ ( tc_List_Olist @ SY2316 ) ) @ ( c_List_Olex @ SY2317 @ SY2316 ) @ ( tc_prod @ ( tc_List_Olist @ SY2316 ) @ ( tc_List_Olist @ SY2316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4001]) ).
thf(5342,plain,
! [SV1063: $i] :
( ( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ SV1063 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(5343,plain,
! [SV1064: $i] :
( ( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ SV1064 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(5344,plain,
! [SV1065: $i] :
( ( ! [SY2318: $i,SY2319: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1065 @ ( tc_List_Olist @ SY2318 ) @ ( tc_List_Olist @ SY2318 ) ) @ ( c_List_Olex @ SY2319 @ SY2318 ) @ ( tc_prod @ ( tc_List_Olist @ SY2318 ) @ ( tc_List_Olist @ SY2318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(5345,plain,
! [SV1066: $i] :
( ( ! [SY2320: $i,SY2321: $i,SY2322: $i] :
( ~ ( c_in @ ( c_append @ SV1066 @ SY2320 @ SY2321 ) @ ( c_List_Olists @ SY2322 @ SY2321 ) @ ( tc_List_Olist @ SY2321 ) )
| ( c_in @ SV1066 @ ( c_List_Olists @ SY2322 @ SY2321 ) @ ( tc_List_Olist @ SY2321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4010]) ).
thf(5346,plain,
! [SV1067: $i] :
( ( ! [SY2323: $i,SY2324: $i,SY2325: $i] :
( ~ ( c_in @ ( c_append @ SV1067 @ SY2323 @ SY2324 ) @ ( c_List_Olists @ SY2325 @ SY2324 ) @ ( tc_List_Olist @ SY2324 ) )
| ( c_in @ SY2323 @ ( c_List_Olists @ SY2325 @ SY2324 ) @ ( tc_List_Olist @ SY2324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(5347,plain,
! [SV1068: $i] :
( ( ! [SY2326: $i,SY2327: $i,SY2328: $i] :
( ~ ( c_in @ SV1068 @ ( c_List_Olists @ SY2326 @ SY2327 ) @ ( tc_List_Olist @ SY2327 ) )
| ~ ( c_in @ SY2328 @ ( c_List_Olists @ SY2326 @ SY2327 ) @ ( tc_List_Olist @ SY2327 ) )
| ( c_in @ ( c_append @ SY2328 @ SV1068 @ SY2327 ) @ ( c_List_Olists @ SY2326 @ SY2327 ) @ ( tc_List_Olist @ SY2327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(5348,plain,
! [SV1069: $i] :
( ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ SV1069 )
= c_List_Olist_ONil )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(5349,plain,
! [SV1070: $i] :
( ( ! [SY2329: $i] :
( ( c_append @ c_List_Olist_ONil @ SV1070 @ SY2329 )
= SV1070 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(5350,plain,
! [SV1071: $i] :
( ( ! [SY2330: $i] :
( ( c_append @ SV1071 @ c_List_Olist_ONil @ SY2330 )
= SV1071 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(5351,plain,
! [SV1072: $i] :
( ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1072 ) )
= c_0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(5352,plain,
! [SV1073: $i] :
( ( ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1073 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(5353,plain,
! [SV1074: $i] :
( ( ! [SY2331: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ SV1074 @ ( tc_List_Olist @ SY2331 ) ) @ tc_nat )
| ( SV1074 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4026]) ).
thf(5354,plain,
! [SV1075: $i] :
( ( ! [SY2332: $i,SY2333: $i] :
( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ SV1075 @ SY2332 ) @ ( c_List_Olist_OCons @ SY2333 @ c_List_Olist_ONil @ SY2332 ) @ SY2332 ) @ SY2332 )
= ( c_List_Olist_OCons @ SY2333 @ SV1075 @ SY2332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4034]) ).
thf(5355,plain,
! [SV1076: $i] :
( ( ( c_List_Orev @ c_List_Olist_ONil @ SV1076 )
= c_List_Olist_ONil )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(5356,plain,
! [SV1077: $i] :
( ( ! [SY2334: $i] :
( SV1077
= ( c_append @ c_List_Olist_ONil @ SV1077 @ SY2334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(5357,plain,
! [SV1078: $i] :
( ( ! [SY2335: $i] :
( SV1078
= ( c_append @ SV1078 @ c_List_Olist_ONil @ SY2335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(5358,plain,
! [SV1079: $i] :
( ( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ SV1079 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4044]) ).
thf(5359,plain,
! [SV1080: $i] :
( ( ( c_List_Oset @ c_List_Olist_ONil @ SV1080 )
= c_emptyset )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4046]) ).
thf(5360,plain,
! [SV1081: $i] :
( ( ! [SY2336: $i] :
( ~ ( c_lessequals @ ( c_Suc @ SV1081 ) @ ( c_Suc @ SY2336 ) @ tc_nat )
| ( c_lessequals @ SV1081 @ SY2336 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4048]) ).
thf(5361,plain,
! [SV1082: $i] :
( ( ! [SY2337: $i] :
( ~ ( c_lessequals @ SV1082 @ SY2337 @ tc_nat )
| ( c_lessequals @ ( c_Suc @ SV1082 ) @ ( c_Suc @ SY2337 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4049]) ).
thf(5362,plain,
! [SV1083: $i] :
( ( ! [SY2338: $i] :
( ~ ( c_less @ ( c_Suc @ SV1083 ) @ ( c_Suc @ SY2338 ) @ tc_nat )
| ( c_less @ SV1083 @ SY2338 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4050]) ).
thf(5363,plain,
! [SV1084: $i] :
( ( ! [SY2339: $i] :
( ~ ( c_less @ SV1084 @ SY2339 @ tc_nat )
| ( c_less @ ( c_Suc @ SV1084 ) @ ( c_Suc @ SY2339 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4051]) ).
thf(5364,plain,
! [SV1085: $i] :
( ( ! [SY2340: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ SV1085 @ SY2340 @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ SY2340 @ tc_nat )
| ( c_less @ c_0 @ SV1085 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(5365,plain,
! [SV1086: $i] :
( ( ! [SY2341: $i] :
( ~ ( c_less @ c_0 @ SV1086 @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ SV1086 @ SY2341 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4055]) ).
thf(5366,plain,
! [SV1087: $i] :
( ( ! [SY2342: $i] :
( ~ ( c_less @ c_0 @ SV1087 @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ SY2342 @ SV1087 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4056]) ).
thf(5367,plain,
! [SV1088: $i] :
( ( ~ ( c_lessequals @ SV1088 @ c_0 @ tc_nat )
| ( SV1088 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(5368,plain,
! [SV1089: $i] :
( ( ~ ( c_less @ SV1089 @ ( c_Suc @ c_0 ) @ tc_nat )
| ( SV1089 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(5369,plain,
! [SV1090: $i] :
( ( ~ ( c_less @ SV1090 @ c_1 @ tc_nat )
| ( SV1090 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(5370,plain,
! [SV1091: $i] :
( ( ( c_less @ c_0 @ SV1091 @ tc_nat )
| ( SV1091 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4066]) ).
thf(5371,plain,
( ( c_less @ c_0 @ c_0 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4067]) ).
thf(5372,plain,
! [SV1092: $i] :
( ( ! [SY2343: $i] :
~ ( c_less @ ( c_plus @ SV1092 @ SY2343 @ tc_nat ) @ SV1092 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(5373,plain,
! [SV1093: $i] :
( ( ! [SY2344: $i] :
~ ( c_less @ ( c_plus @ SV1093 @ SY2344 @ tc_nat ) @ SY2344 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(5374,plain,
! [SV1094: $i] :
( ( ~ ( c_less @ SV1094 @ c_0 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4070]) ).
thf(5375,plain,
! [SV1095: $i] :
( ( ! [SY2345: $i] :
( ~ ( class_Orderings_Oorder @ SV1095 )
| ~ ( c_less @ SY2345 @ SY2345 @ SV1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4073]) ).
thf(5376,plain,
! [SV1096: $i] :
( ( ! [SY2346: $i] : ( c_in @ ( c_Pair @ SV1096 @ SV1096 @ SY2346 @ SY2346 ) @ c_Relation_OId @ ( tc_prod @ SY2346 @ SY2346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(5377,plain,
! [SV1097: $i] :
( ( ! [SY2347: $i,SY2348: $i,SY2349: $i,SY2350: $i] :
( ~ ( c_in @ SV1097 @ ( c_Relation_OImage @ SY2347 @ ( c_insert @ SY2348 @ c_emptyset @ SY2349 ) @ SY2349 @ SY2350 ) @ SY2350 )
| ( c_in @ ( c_Pair @ SY2348 @ SV1097 @ SY2349 @ SY2350 ) @ SY2347 @ ( tc_prod @ SY2349 @ SY2350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4077]) ).
thf(5378,plain,
! [SV1098: $i] :
( ( ! [SY2351: $i,SY2352: $i,SY2353: $i,SY2354: $i] :
( ~ ( c_in @ ( c_Pair @ SV1098 @ SY2351 @ SY2352 @ SY2353 ) @ SY2354 @ ( tc_prod @ SY2352 @ SY2353 ) )
| ( c_in @ SY2351 @ ( c_Relation_OImage @ SY2354 @ ( c_insert @ SV1098 @ c_emptyset @ SY2352 ) @ SY2352 @ SY2353 ) @ SY2353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(5379,plain,
! [SV1099: $i] :
( ( ! [SY2355: $i,SY2356: $i,SY2357: $i,SY2358: $i] :
( ~ ( c_in @ ( c_Pair @ SV1099 @ SY2355 @ SY2356 @ SY2357 ) @ ( c_Relation_Oconverse @ SY2358 @ SY2357 @ SY2356 ) @ ( tc_prod @ SY2356 @ SY2357 ) )
| ( c_in @ ( c_Pair @ SY2355 @ SV1099 @ SY2357 @ SY2356 ) @ SY2358 @ ( tc_prod @ SY2357 @ SY2356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4079]) ).
thf(5380,plain,
! [SV1100: $i] :
( ( ! [SY2359: $i,SY2360: $i,SY2361: $i,SY2362: $i] :
( ~ ( c_in @ ( c_Pair @ SV1100 @ SY2359 @ SY2360 @ SY2361 ) @ SY2362 @ ( tc_prod @ SY2360 @ SY2361 ) )
| ( c_in @ ( c_Pair @ SY2359 @ SV1100 @ SY2361 @ SY2360 ) @ ( c_Relation_Oconverse @ SY2362 @ SY2360 @ SY2361 ) @ ( tc_prod @ SY2361 @ SY2360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(5381,plain,
! [SV1101: $i] :
( ( ! [SY2363: $i,SY2364: $i] :
( ~ ( c_in @ ( c_Pair @ SV1101 @ SY2363 @ SY2364 @ SY2364 ) @ c_Relation_OId @ ( tc_prod @ SY2364 @ SY2364 ) )
| ( SV1101 = SY2363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4081]) ).
thf(5382,plain,
! [SV1102: $i] :
( ( ! [SY2365: $i,SY2366: $i] :
( ~ ( class_Orderings_Oord @ SV1102 )
| ~ ( c_in @ SY2365 @ ( c_SetInterval_OatLeast @ SY2366 @ SV1102 ) @ SV1102 )
| ( c_lessequals @ SY2366 @ SY2365 @ SV1102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4083]) ).
thf(5383,plain,
! [SV1103: $i] :
( ( ! [SY2367: $i,SY2368: $i] :
( ~ ( class_Orderings_Oord @ SV1103 )
| ~ ( c_lessequals @ SY2367 @ SY2368 @ SV1103 )
| ( c_in @ SY2368 @ ( c_SetInterval_OatLeast @ SY2367 @ SV1103 ) @ SV1103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4084]) ).
thf(5384,plain,
! [SV1104: $i] :
( ( ! [SY2369: $i,SY2370: $i] :
( ~ ( class_Orderings_Oorder @ SV1104 )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2369 @ SV1104 ) @ ( c_SetInterval_OatLeast @ SY2370 @ SV1104 ) @ ( tc_set @ SV1104 ) )
| ( c_lessequals @ SY2370 @ SY2369 @ SV1104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(5385,plain,
! [SV1105: $i] :
( ( ! [SY2371: $i,SY2372: $i] :
( ~ ( class_Orderings_Oorder @ SV1105 )
| ~ ( c_lessequals @ SY2371 @ SY2372 @ SV1105 )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2372 @ SV1105 ) @ ( c_SetInterval_OatLeast @ SY2371 @ SV1105 ) @ ( tc_set @ SV1105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4086]) ).
thf(5386,plain,
! [SV1106: $i] :
( ( ! [SY2373: $i,SY2374: $i] :
( ~ ( class_Orderings_Oord @ SV1106 )
| ~ ( c_in @ SY2373 @ ( c_SetInterval_OatMost @ SY2374 @ SV1106 ) @ SV1106 )
| ( c_lessequals @ SY2373 @ SY2374 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(5387,plain,
! [SV1107: $i] :
( ( ! [SY2375: $i,SY2376: $i] :
( ~ ( class_Orderings_Oord @ SV1107 )
| ~ ( c_lessequals @ SY2375 @ SY2376 @ SV1107 )
| ( c_in @ SY2375 @ ( c_SetInterval_OatMost @ SY2376 @ SV1107 ) @ SV1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4089]) ).
thf(5388,plain,
! [SV1108: $i] :
( ( ! [SY2377: $i,SY2378: $i] :
( ~ ( class_Orderings_Oorder @ SV1108 )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SY2377 @ SV1108 ) @ ( c_SetInterval_OatMost @ SY2378 @ SV1108 ) @ ( tc_set @ SV1108 ) )
| ( c_lessequals @ SY2377 @ SY2378 @ SV1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4090]) ).
thf(5389,plain,
! [SV1109: $i] :
( ( ! [SY2379: $i,SY2380: $i] :
( ~ ( class_Orderings_Oorder @ SV1109 )
| ~ ( c_lessequals @ SY2379 @ SY2380 @ SV1109 )
| ( c_lessequals @ ( c_SetInterval_OatMost @ SY2379 @ SV1109 ) @ ( c_SetInterval_OatMost @ SY2380 @ SV1109 ) @ ( tc_set @ SV1109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4091]) ).
thf(5390,plain,
! [SV1110: $i] :
( ( ! [SY2381: $i,SY2382: $i] :
( ~ ( class_Orderings_Oord @ SV1110 )
| ~ ( c_in @ SY2381 @ ( c_SetInterval_OgreaterThan @ SY2382 @ SV1110 ) @ SV1110 )
| ( c_less @ SY2382 @ SY2381 @ SV1110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(5391,plain,
! [SV1111: $i] :
( ( ! [SY2383: $i,SY2384: $i] :
( ~ ( class_Orderings_Oord @ SV1111 )
| ~ ( c_less @ SY2383 @ SY2384 @ SV1111 )
| ( c_in @ SY2384 @ ( c_SetInterval_OgreaterThan @ SY2383 @ SV1111 ) @ SV1111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4094]) ).
thf(5392,plain,
! [SV1112: $i] :
( ( ! [SY2385: $i,SY2386: $i] :
( ~ ( class_Orderings_Olinorder @ SV1112 )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2385 @ SV1112 ) @ ( c_SetInterval_OgreaterThan @ SY2386 @ SV1112 ) @ ( tc_set @ SV1112 ) )
| ( c_lessequals @ SY2386 @ SY2385 @ SV1112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(5393,plain,
! [SV1113: $i] :
( ( ! [SY2387: $i,SY2388: $i] :
( ~ ( class_Orderings_Olinorder @ SV1113 )
| ~ ( c_lessequals @ SY2387 @ SY2388 @ SV1113 )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2388 @ SV1113 ) @ ( c_SetInterval_OgreaterThan @ SY2387 @ SV1113 ) @ ( tc_set @ SV1113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(5394,plain,
! [SV1114: $i] :
( ( ! [SY2389: $i,SY2390: $i] :
( ~ ( class_Orderings_Oord @ SV1114 )
| ~ ( c_in @ SY2389 @ ( c_SetInterval_OlessThan @ SY2390 @ SV1114 ) @ SV1114 )
| ( c_less @ SY2389 @ SY2390 @ SV1114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(5395,plain,
! [SV1115: $i] :
( ( ! [SY2391: $i,SY2392: $i] :
( ~ ( class_Orderings_Oord @ SV1115 )
| ~ ( c_less @ SY2391 @ SY2392 @ SV1115 )
| ( c_in @ SY2391 @ ( c_SetInterval_OlessThan @ SY2392 @ SV1115 ) @ SV1115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(5396,plain,
! [SV1116: $i] :
( ( ! [SY2393: $i,SY2394: $i] :
( ~ ( class_Orderings_Olinorder @ SV1116 )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2393 @ SV1116 ) @ ( c_SetInterval_OlessThan @ SY2394 @ SV1116 ) @ ( tc_set @ SV1116 ) )
| ( c_lessequals @ SY2393 @ SY2394 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(5397,plain,
! [SV1117: $i] :
( ( ! [SY2395: $i,SY2396: $i] :
( ~ ( class_Orderings_Olinorder @ SV1117 )
| ~ ( c_lessequals @ SY2395 @ SY2396 @ SV1117 )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ SY2395 @ SV1117 ) @ ( c_SetInterval_OlessThan @ SY2396 @ SV1117 ) @ ( tc_set @ SV1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(5398,plain,
! [SV1118: $i] :
( ( ! [SY2397: $i,SY2398: $i] :
( ~ ( c_in @ SV1118 @ SY2397 @ SY2398 )
| ~ ( c_in @ SV1118 @ ( c_uminus @ SY2397 @ ( tc_set @ SY2398 ) ) @ SY2398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(5399,plain,
! [SV1119: $i] :
( ( ! [SY2399: $i,SY2400: $i] :
( ( c_in @ SV1119 @ SY2399 @ SY2400 )
| ( c_in @ SV1119 @ ( c_uminus @ SY2399 @ ( tc_set @ SY2400 ) ) @ SY2400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4103]) ).
thf(5400,plain,
! [SV1120: $i] :
( ( ! [SY2401: $i,SY2402: $i] :
( ~ ( c_lessequals @ ( c_uminus @ SV1120 @ ( tc_set @ SY2401 ) ) @ ( c_uminus @ SY2402 @ ( tc_set @ SY2401 ) ) @ ( tc_set @ SY2401 ) )
| ( c_lessequals @ SY2402 @ SV1120 @ ( tc_set @ SY2401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(5401,plain,
! [SV1121: $i] :
( ( ! [SY2403: $i,SY2404: $i] :
( ~ ( c_lessequals @ SV1121 @ SY2403 @ ( tc_set @ SY2404 ) )
| ( c_lessequals @ ( c_uminus @ SY2403 @ ( tc_set @ SY2404 ) ) @ ( c_uminus @ SV1121 @ ( tc_set @ SY2404 ) ) @ ( tc_set @ SY2404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(5402,plain,
! [SV1122: $i] :
( ( ! [SY2405: $i,SY2406: $i,SY2407: $i] :
( ~ ( c_in @ SV1122 @ SY2405 @ SY2406 )
| ~ ( c_in @ SV1122 @ ( c_minus @ SY2407 @ SY2405 @ ( tc_set @ SY2406 ) ) @ SY2406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4107]) ).
thf(5403,plain,
! [SV1123: $i] :
( ( ! [SY2408: $i,SY2409: $i,SY2410: $i] :
( ~ ( c_in @ SV1123 @ ( c_minus @ SY2408 @ SY2409 @ ( tc_set @ SY2410 ) ) @ SY2410 )
| ( c_in @ SV1123 @ SY2408 @ SY2410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4108]) ).
thf(5404,plain,
! [SV1124: $i] :
( ( ! [SY2411: $i,SY2412: $i,SY2413: $i] :
( ~ ( c_in @ SV1124 @ SY2411 @ SY2412 )
| ( c_in @ SV1124 @ SY2413 @ SY2412 )
| ( c_in @ SV1124 @ ( c_minus @ SY2411 @ SY2413 @ ( tc_set @ SY2412 ) ) @ SY2412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(5405,plain,
! [SV1125: $i] :
( ( ! [SY2414: $i,SY2415: $i,SY2416: $i] :
( ~ ( c_in @ SV1125 @ ( c_inter @ SY2414 @ SY2415 @ SY2416 ) @ SY2416 )
| ( c_in @ SV1125 @ SY2415 @ SY2416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(5406,plain,
! [SV1126: $i] :
( ( ! [SY2417: $i,SY2418: $i,SY2419: $i] :
( ~ ( c_in @ SV1126 @ ( c_inter @ SY2417 @ SY2418 @ SY2419 ) @ SY2419 )
| ( c_in @ SV1126 @ SY2417 @ SY2419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4111]) ).
thf(5407,plain,
! [SV1127: $i] :
( ( ! [SY2420: $i,SY2421: $i,SY2422: $i] :
( ~ ( c_in @ SV1127 @ SY2420 @ SY2421 )
| ~ ( c_in @ SV1127 @ SY2422 @ SY2421 )
| ( c_in @ SV1127 @ ( c_inter @ SY2422 @ SY2420 @ SY2421 ) @ SY2421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4112]) ).
thf(5408,plain,
! [SV1128: $i] :
( ( ! [SY2423: $i,SY2424: $i,SY2425: $i] :
( ~ ( c_in @ SV1128 @ SY2423 @ ( tc_set @ SY2424 ) )
| ~ ( c_in @ SY2425 @ ( c_Inter @ SY2423 @ SY2424 ) @ SY2424 )
| ( c_in @ SY2425 @ SV1128 @ SY2424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4113]) ).
thf(5409,plain,
! [SV1129: $i] :
( ( ! [SY2426: $i,SY2427: $i] :
( ~ ( c_in @ SV1129 @ ( c_Pow @ SY2426 @ SY2427 ) @ ( tc_set @ SY2427 ) )
| ( c_lessequals @ SV1129 @ SY2426 @ ( tc_set @ SY2427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4114]) ).
thf(5410,plain,
! [SV1130: $i] :
( ( ! [SY2428: $i,SY2429: $i] :
( ~ ( c_lessequals @ SV1130 @ SY2428 @ ( tc_set @ SY2429 ) )
| ( c_in @ SV1130 @ ( c_Pow @ SY2428 @ SY2429 ) @ ( tc_set @ SY2429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4115]) ).
thf(5411,plain,
! [SV1131: $i] :
( ( ! [SY2430: $i,SY2431: $i,SY2432: $i] :
( ~ ( c_in @ SV1131 @ SY2430 @ SY2431 )
| ( c_in @ SV1131 @ ( c_union @ SY2432 @ SY2430 @ SY2431 ) @ SY2431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(5412,plain,
! [SV1132: $i] :
( ( ! [SY2433: $i,SY2434: $i,SY2435: $i] :
( ~ ( c_in @ SV1132 @ SY2433 @ SY2434 )
| ( c_in @ SV1132 @ ( c_union @ SY2433 @ SY2435 @ SY2434 ) @ SY2434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(5413,plain,
! [SV1133: $i] :
( ( ! [SY2436: $i,SY2437: $i,SY2438: $i] :
( ~ ( c_in @ SV1133 @ ( c_union @ SY2436 @ SY2437 @ SY2438 ) @ SY2438 )
| ( c_in @ SV1133 @ SY2437 @ SY2438 )
| ( c_in @ SV1133 @ SY2436 @ SY2438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4119]) ).
thf(5414,plain,
! [SV1134: $i] :
( ( ( c_union @ c_emptyset @ c_emptyset @ SV1134 )
= c_emptyset )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4122]) ).
thf(5415,plain,
! [SV1135: $i] :
( ( ! [SY2439: $i,SY2440: $i,SY2441: $i] :
( ~ ( c_in @ SV1135 @ SY2439 @ SY2440 )
| ~ ( c_in @ SY2439 @ SY2441 @ ( tc_set @ SY2440 ) )
| ( c_in @ SV1135 @ ( c_Union @ SY2441 @ SY2440 ) @ SY2440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4123]) ).
thf(5416,plain,
! [SV1136: $i] :
( ( ! [SY2442: $i] :
~ ( c_in @ SV1136 @ c_emptyset @ SY2442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4124]) ).
thf(5417,plain,
! [SV1137: $i] :
( ( ! [SY2443: $i,SY2444: $i,SY2445: $i] :
( ~ ( c_in @ SV1137 @ SY2443 @ SY2444 )
| ( c_in @ SV1137 @ ( c_insert @ SY2445 @ SY2443 @ SY2444 ) @ SY2444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4125]) ).
thf(5418,plain,
! [SV1138: $i] :
( ( ! [SY2446: $i,SY2447: $i] : ( c_in @ SV1138 @ ( c_insert @ SV1138 @ SY2446 @ SY2447 ) @ SY2447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4126]) ).
thf(5419,plain,
! [SV1139: $i] :
( ( ! [SY2448: $i,SY2449: $i,SY2450: $i] :
( ~ ( c_in @ SV1139 @ ( c_insert @ SY2448 @ SY2449 @ SY2450 ) @ SY2450 )
| ( c_in @ SV1139 @ SY2449 @ SY2450 )
| ( SV1139 = SY2448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4127]) ).
thf(5420,plain,
! [SV1140: $i] :
( ( ! [SY2451: $i] :
~ ( c_less @ SV1140 @ c_emptyset @ ( tc_set @ SY2451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4128]) ).
thf(5421,plain,
! [SV1141: $i] :
( ( ! [SY2452: $i,SY2453: $i] :
( ~ ( c_lessequals @ SV1141 @ ( c_insert @ SY2452 @ c_emptyset @ SY2453 ) @ ( tc_set @ SY2453 ) )
| ( ( c_insert @ SY2452 @ SV1141 @ SY2453 )
= ( c_insert @ SY2452 @ c_emptyset @ SY2453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(5422,plain,
! [SV1142: $i] :
( ( ! [SY2454: $i,SY2455: $i] :
( ~ ( c_lessequals @ SV1142 @ ( c_insert @ SY2454 @ c_emptyset @ SY2455 ) @ ( tc_set @ SY2455 ) )
| ( ( c_insert @ SY2454 @ c_emptyset @ SY2455 )
= ( c_insert @ SY2454 @ SV1142 @ SY2455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(5423,plain,
! [SV1143: $i] :
( ( ! [SY2456: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1143 @ SY2456 @ SY2456 ) @ SY2456 )
| ( c_Wellfounded__Recursion_Oacyclic @ SV1143 @ SY2456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(5424,plain,
! [SV1144: $i] :
( ( ! [SY2457: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1144 @ SY2457 )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1144 @ SY2457 @ SY2457 ) @ SY2457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4140]) ).
thf(5425,plain,
! [SV1145: $i] :
( ( ! [SY2458: $i,SY2459: $i,SY2460: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1145 @ SY2458 @ SY2459 @ SY2459 ) @ SY2460 @ ( tc_prod @ SY2459 @ SY2459 ) ) @ SY2459 )
| ( c_Wellfounded__Recursion_Oacyclic @ SY2460 @ SY2459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(5426,plain,
! [SV1146: $i] :
( ( ! [SY2461: $i,SY2462: $i,SY2463: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1146 @ SY2461 @ SY2462 @ SY2462 ) @ SY2463 @ ( tc_prod @ SY2462 @ SY2462 ) ) @ SY2462 )
| ~ ( c_in @ ( c_Pair @ SY2461 @ SV1146 @ SY2462 @ SY2462 ) @ ( c_Transitive__Closure_Ortrancl @ SY2463 @ SY2462 ) @ ( tc_prod @ SY2462 @ SY2462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4142]) ).
thf(5427,plain,
! [SV1147: $i] :
( ( ! [SY2464: $i,SY2465: $i,SY2466: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1147 @ SY2464 )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SY2465 @ SY2466 @ SY2464 @ SY2464 ) @ SV1147 @ ( tc_prod @ SY2464 @ SY2464 ) ) @ SY2464 )
| ( c_in @ ( c_Pair @ SY2466 @ SY2465 @ SY2464 @ SY2464 ) @ ( c_Transitive__Closure_Ortrancl @ SV1147 @ SY2464 ) @ ( tc_prod @ SY2464 @ SY2464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4143]) ).
thf(5428,plain,
! [SV1148: $i] :
( ( ! [SY2467: $i,SY2468: $i,SY2469: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1148 @ SY2467 @ SY2468 @ SY2468 ) @ SY2469 @ ( tc_prod @ SY2468 @ SY2468 ) ) @ SY2468 )
| ( c_Wellfounded__Recursion_Owf @ SY2469 @ SY2468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4144]) ).
thf(5429,plain,
! [SV1149: $i] :
( ( ! [SY2470: $i,SY2471: $i,SY2472: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1149 @ SY2470 @ SY2471 @ SY2471 ) @ SY2472 @ ( tc_prod @ SY2471 @ SY2471 ) ) @ SY2471 )
| ~ ( c_in @ ( c_Pair @ SY2470 @ SV1149 @ SY2471 @ SY2471 ) @ ( c_Transitive__Closure_Ortrancl @ SY2472 @ SY2471 ) @ ( tc_prod @ SY2471 @ SY2471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4145]) ).
thf(5430,plain,
! [SV1150: $i] :
( ( ! [SY2473: $i,SY2474: $i,SY2475: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV1150 @ SY2473 )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SY2474 @ SY2475 @ SY2473 @ SY2473 ) @ SV1150 @ ( tc_prod @ SY2473 @ SY2473 ) ) @ SY2473 )
| ( c_in @ ( c_Pair @ SY2475 @ SY2474 @ SY2473 @ SY2473 ) @ ( c_Transitive__Closure_Ortrancl @ SV1150 @ SY2473 ) @ ( tc_prod @ SY2473 @ SY2473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4146]) ).
thf(5431,plain,
! [SV1151: $i] :
( ( ! [SY2476: $i] :
( ~ ( c_in @ ( c_Pair @ SV1151 @ SY2476 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ SV1151 @ SY2476 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4147]) ).
thf(5432,plain,
! [SV1152: $i] :
( ( ! [SY2477: $i] :
( ~ ( c_less @ SV1152 @ SY2477 @ tc_nat )
| ( c_in @ ( c_Pair @ SV1152 @ SY2477 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4148]) ).
thf(5433,plain,
! [SV1153: $i] :
( ( ! [SY2478: $i,SY2479: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1153 @ SY2478 ) @ ( c_Message_Oanalz @ SY2479 ) @ tc_Message_Omsg )
| ( c_in @ SY2478 @ ( c_Message_Oanalz @ SY2479 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4149]) ).
thf(5434,plain,
! [SV1154: $i] :
( ( ! [SY2480: $i,SY2481: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1154 @ SY2480 ) @ ( c_Message_Oanalz @ SY2481 ) @ tc_Message_Omsg )
| ( c_in @ SV1154 @ ( c_Message_Oanalz @ SY2481 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4150]) ).
thf(5435,plain,
! [SV1155: $i] :
( ( ! [SY2482: $i,SY2483: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1155 @ SY2482 ) @ ( c_Message_Oparts @ SY2483 ) @ tc_Message_Omsg )
| ( c_in @ SY2482 @ ( c_Message_Oparts @ SY2483 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4151]) ).
thf(5436,plain,
! [SV1156: $i] :
( ( ! [SY2484: $i,SY2485: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1156 @ SY2484 ) @ ( c_Message_Oparts @ SY2485 ) @ tc_Message_Omsg )
| ( c_in @ SV1156 @ ( c_Message_Oparts @ SY2485 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(5437,plain,
! [SV1157: $i] :
( ( ! [SY2486: $i,SY2487: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1157 @ SY2486 ) @ ( c_Message_Oanalz @ SY2487 ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1157 ) ) @ ( c_Message_Oanalz @ SY2487 ) @ tc_Message_Omsg )
| ( c_in @ SY2486 @ ( c_Message_Oanalz @ SY2487 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4160]) ).
thf(5438,plain,
! [SV1158: $i] :
( ( ! [SY2488: $i] :
( ~ ( c_in @ SV1158 @ SY2488 @ tc_Message_Omsg )
| ( c_in @ SV1158 @ ( c_Message_Oanalz @ SY2488 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4161]) ).
thf(5439,plain,
! [SV1159: $i] :
( ( ! [SY2489: $i] :
( ~ ( c_in @ SV1159 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SY2489 ) ) @ tc_Message_Omsg )
| ( c_in @ SV1159 @ ( c_Message_Oanalz @ SY2489 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4162]) ).
thf(5440,plain,
! [SV1160: $i] :
( ( ! [SY2490: $i] :
( ~ ( c_lessequals @ SV1160 @ SY2490 @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ SV1160 ) @ ( c_Message_Oanalz @ SY2490 ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4163]) ).
thf(5441,plain,
! [SV1161: $i] :
( ( ! [SY2491: $i,SY2492: $i] :
( ~ ( c_in @ SV1161 @ ( c_Message_Oparts @ ( c_union @ SY2491 @ SY2492 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SY2492 ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SY2491 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4164]) ).
thf(5442,plain,
! [SV1162: $i] :
( ( ! [SY2493: $i,SY2494: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1162 @ SY2493 ) @ ( c_Message_Oparts @ SY2494 ) @ tc_Message_Omsg )
| ( c_in @ SY2493 @ ( c_Message_Oparts @ SY2494 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4174]) ).
thf(5443,plain,
! [SV1163: $i] :
( ( ! [SY2495: $i] :
( ~ ( c_in @ SV1163 @ SY2495 @ tc_Message_Omsg )
| ( c_in @ SV1163 @ ( c_Message_Oparts @ SY2495 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(5444,plain,
! [SV1164: $i] :
( ( ~ ( c_in @ SV1164 @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4176]) ).
thf(5445,plain,
! [SV1165: $i] :
( ( ! [SY2496: $i] :
( ~ ( c_in @ SV1165 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SY2496 ) ) @ tc_Message_Omsg )
| ( c_in @ SV1165 @ ( c_Message_Oparts @ SY2496 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(5446,plain,
! [SV1166: $i] :
( ( ! [SY2497: $i,SY2498: $i] : ( c_lessequals @ SV1166 @ ( c_union @ SV1166 @ SY2497 @ SY2498 ) @ ( tc_set @ SY2498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(5447,plain,
! [SV1167: $i] :
( ( ! [SY2499: $i,SY2500: $i] : ( c_lessequals @ SV1167 @ ( c_union @ SY2499 @ SV1167 @ SY2500 ) @ ( tc_set @ SY2500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(5448,plain,
! [SV1168: $i] :
( ( ! [SY2501: $i,SY2502: $i,SY2503: $i] :
( ~ ( c_lessequals @ SV1168 @ SY2501 @ ( tc_set @ SY2502 ) )
| ~ ( c_lessequals @ SY2503 @ SV1168 @ ( tc_set @ SY2502 ) )
| ( c_lessequals @ SY2503 @ SY2501 @ ( tc_set @ SY2502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4180]) ).
thf(5449,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[4181]) ).
thf(5450,plain,
! [SV1169: $i] :
( ( ! [SY2504: $i,SY2505: $i,SY2506: $i] :
( ( c_Datatype__Universe_OIn0 @ SV1169 @ SY2504 @ SY2505 )
!= ( c_Datatype__Universe_OIn1 @ SY2506 @ SY2504 @ SY2505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4182]) ).
thf(5451,plain,
! [SV1170: $i] :
( ( ! [SY2507: $i,SY2508: $i,SY2509: $i] :
( ( ( c_Message_Omsg_OCrypt @ SV1170 @ SY2507 )
!= ( c_Message_Omsg_OCrypt @ SY2508 @ SY2509 ) )
| ( SV1170 = SY2508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4183]) ).
thf(5452,plain,
! [SV1171: $i] :
( ( ! [SY2510: $i] :
( ( ( c_List_Orev @ SV1171 @ SY2510 )
!= c_List_Olist_ONil )
| ( SV1171 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4184]) ).
thf(5453,plain,
! [SV1172: $i] :
( ( ! [SY2511: $i,SY2512: $i,SY2513: $i,SY2514: $i] :
( ( ( c_append @ SV1172 @ ( c_List_Olist_OCons @ SY2511 @ c_List_Olist_ONil @ SY2512 ) @ SY2512 )
!= ( c_append @ SY2513 @ ( c_List_Olist_OCons @ SY2514 @ c_List_Olist_ONil @ SY2512 ) @ SY2512 ) )
| ( SY2511 = SY2514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(5454,plain,
! [SV1173: $i] :
( ( ! [SY2515: $i,SY2516: $i,SY2517: $i,SY2518: $i] :
( ( c_Datatype__Universe_OScons @ SV1173 @ SY2515 @ SY2516 @ SY2517 )
!= ( c_Datatype__Universe_ONumb @ SY2518 @ SY2516 @ SY2517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4186]) ).
thf(5455,plain,
! [SV1174: $i] :
( ( ! [SY2519: $i] :
( ( ( c_List_Oset @ SV1174 @ SY2519 )
!= c_emptyset )
| ( SV1174 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(5456,plain,
! [SV1175: $i] :
( ( ! [SY2520: $i] :
( c_Datatype_Ooption_ONone
!= ( c_Datatype_Ooption_OSome @ SV1175 @ SY2520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4188]) ).
thf(5457,plain,
! [SV1176: $i] :
( ( ! [SY2521: $i,SY2522: $i,SY2523: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SV1176 @ SY2521 @ SY2522 )
!= ( c_Datatype__Universe_OLeaf @ SY2523 @ SY2521 @ SY2522 ) )
| ( SV1176 = SY2523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(5458,plain,
! [SV1177: $i] :
( ( ! [SY2524: $i,SY2525: $i,SY2526: $i] :
( ( c_Datatype__Universe_OIn1 @ SV1177 @ SY2524 @ SY2525 )
!= ( c_Datatype__Universe_OIn0 @ SY2526 @ SY2524 @ SY2525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(5459,plain,
! [SV1178: $i] :
( ( ! [SY2527: $i] :
( ( ( c_List_Oremdups @ SV1178 @ SY2527 )
!= SV1178 )
| ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1178 @ SY2527 ) @ ( tc_List_Olist @ SY2527 ) )
= ( c_Nat_Osize @ SV1178 @ ( tc_List_Olist @ SY2527 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4191]) ).
thf(5460,plain,
! [SV1179: $i] :
( ( ( c_Message_Oagent_OFriend @ SV1179 )
!= c_Message_Oagent_OSpy )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4192]) ).
thf(5461,plain,
( ( c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(5462,plain,
( ( c_UNIV = c_emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(5463,plain,
! [SV1180: $i] :
( ( ! [SY2528: $i,SY2529: $i,SY2530: $i] :
( ( ( c_Datatype__Universe_ONumb @ SV1180 @ SY2528 @ SY2529 )
!= ( c_Datatype__Universe_ONumb @ SY2530 @ SY2528 @ SY2529 ) )
| ( SV1180 = SY2530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(5464,plain,
! [SV1181: $i] :
( ( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ SV1181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(5465,plain,
! [SV1182: $i] :
( ( ! [SY2531: $i,SY2532: $i] :
( ( ( c_Equiv__Relations_Oquotient @ SV1182 @ SY2531 @ SY2532 )
!= c_emptyset )
| ( SV1182 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4197]) ).
thf(5466,plain,
! [SV1183: $i] :
( ( ! [SY2533: $i] :
( ( ( c_Nat_Osize @ SV1183 @ ( tc_List_Olist @ SY2533 ) )
!= c_0 )
| ( SV1183 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4198]) ).
thf(5467,plain,
! [SV1184: $i] :
( ( ! [SY2534: $i,SY2535: $i,SY2536: $i] :
( ( ( c_Message_Omsg_OMPair @ SV1184 @ SY2534 )
!= ( c_Message_Omsg_OMPair @ SY2535 @ SY2536 ) )
| ( SV1184 = SY2535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4199]) ).
thf(5468,plain,
! [SV1185: $i] :
( ( ! [SY2537: $i,SY2538: $i,SY2539: $i,SY2540: $i] :
( ( ( c_List_Olist_OCons @ SV1185 @ SY2537 @ SY2538 )
!= ( c_List_Olist_OCons @ SY2539 @ SY2540 @ SY2538 ) )
| ( SY2537 = SY2540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(5469,plain,
! [SV1186: $i] :
( ( ! [SY2541: $i,SY2542: $i,SY2543: $i] :
( ( c_Sum__Type_OInr @ SV1186 @ SY2541 @ SY2542 )
!= ( c_Sum__Type_OInl @ SY2543 @ SY2542 @ SY2541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4201]) ).
thf(5470,plain,
! [SV1187: $i] :
( ( ! [SY2544: $i] :
( ( ( c_Message_Omsg_OHash @ SV1187 )
!= ( c_Message_Omsg_OHash @ SY2544 ) )
| ( SV1187 = SY2544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4202]) ).
thf(5471,plain,
( ( c_Message_Oagent_OSpy = c_Message_Oagent_OServer )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4203]) ).
thf(5472,plain,
( ( c_Extraction_Osumbool_ORight = c_Extraction_Osumbool_OLeft )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4204]) ).
thf(5473,plain,
! [SV1188: $i] :
( ( ! [SY2545: $i,SY2546: $i,SY2547: $i,SY2548: $i] :
( ( ( c_append @ SV1188 @ ( c_List_Olist_OCons @ SY2545 @ c_List_Olist_ONil @ SY2546 ) @ SY2546 )
!= ( c_append @ SY2547 @ ( c_List_Olist_OCons @ SY2548 @ c_List_Olist_ONil @ SY2546 ) @ SY2546 ) )
| ( SV1188 = SY2547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4205]) ).
thf(5474,plain,
! [SV1189: $i] :
( ( ! [SY2549: $i,SY2550: $i,SY2551: $i] :
( ( ( c_Datatype__Universe_OAtom @ SV1189 @ SY2549 @ SY2550 )
!= ( c_Datatype__Universe_OAtom @ SY2551 @ SY2549 @ SY2550 ) )
| ( SV1189 = SY2551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4206]) ).
thf(5475,plain,
! [SV1190: $i] :
( ( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ SV1190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4207]) ).
thf(5476,plain,
! [SV1191: $i] :
( ( ! [SY2552: $i,SY2553: $i] :
( ( ( c_append @ SV1191 @ SY2552 @ SY2553 )
!= c_List_Olist_ONil )
| ( SY2552 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4208]) ).
thf(5477,plain,
! [SV1192: $i] :
( ( ! [SY2554: $i,SY2555: $i,SY2556: $i] :
( ( ( c_Datatype__Universe_OIn1 @ SV1192 @ SY2554 @ SY2555 )
!= ( c_Datatype__Universe_OIn1 @ SY2556 @ SY2554 @ SY2555 ) )
| ( SV1192 = SY2556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4209]) ).
thf(5478,plain,
! [SV1193: $i] :
( ( ! [SY2557: $i,SY2558: $i] :
( ( ( c_union @ SV1193 @ SY2557 @ SY2558 )
!= c_emptyset )
| ( SY2557 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4210]) ).
thf(5479,plain,
! [SV1194: $i] :
( ( ! [SY2559: $i,SY2560: $i] :
( ~ ( class_Orderings_Olinorder @ SV1194 )
| ( ( c_SetInterval_OlessThan @ SY2559 @ SV1194 )
!= ( c_SetInterval_OlessThan @ SY2560 @ SV1194 ) )
| ( SY2559 = SY2560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4211]) ).
thf(5480,plain,
! [SV1195: $i] :
( ( ! [SY2561: $i,SY2562: $i,SY2563: $i,SY2564: $i,SY2565: $i] :
( ( ( c_Pair @ SV1195 @ SY2561 @ SY2562 @ SY2563 )
!= ( c_Pair @ SY2564 @ SY2565 @ SY2562 @ SY2563 ) )
| ( SV1195 = SY2564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(5481,plain,
( ( c_Message_Oagent_OServer = c_Message_Oagent_OSpy )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(5482,plain,
! [SV1196: $i] :
( ( ! [SY2566: $i,SY2567: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SV1196 @ SY2566 @ SY2567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4214]) ).
thf(5483,plain,
! [SV1197: $i] :
( ( ! [SY2568: $i] :
( ( ( c_Message_Omsg_OKey @ SV1197 )
!= ( c_Message_Omsg_OKey @ SY2568 ) )
| ( SV1197 = SY2568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4215]) ).
thf(5484,plain,
! [SV1198: $i] :
( ( ! [SY2569: $i,SY2570: $i,SY2571: $i] :
( ( ( c_List_Ochar_OChar @ SV1198 @ SY2569 )
!= ( c_List_Ochar_OChar @ SY2570 @ SY2571 ) )
| ( SY2569 = SY2571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4216]) ).
thf(5485,plain,
! [SV1199: $i] :
( ( ! [SY2572: $i] :
( ( ( c_plus @ SV1199 @ SY2572 @ tc_nat )
!= c_0 )
| ( SY2572 = c_0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4217]) ).
thf(5486,plain,
! [SV1200: $i] :
( ( ! [SY2573: $i,SY2574: $i,SY2575: $i,SY2576: $i] :
( ( c_Datatype__Universe_OLeaf @ SV1200 @ SY2573 @ SY2574 )
!= ( c_Datatype__Universe_OScons @ SY2575 @ SY2576 @ SY2573 @ SY2574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(5487,plain,
! [SV1201: $i] :
( ( ! [SY2577: $i,SY2578: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ SV1201 @ SY2577 @ SY2578 ) )
| ( SY2577 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(5488,plain,
! [SV1202: $i] :
( ( ! [SY2579: $i,SY2580: $i,SY2581: $i] :
( ( ( c_append @ SV1202 @ SY2579 @ SY2580 )
!= ( c_append @ SV1202 @ SY2581 @ SY2580 ) )
| ( SY2579 = SY2581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4220]) ).
thf(5489,plain,
! [SV1203: $i] :
( ( ! [SY2582: $i,SY2583: $i] :
( ( ( c_union @ SV1203 @ SY2582 @ SY2583 )
!= c_emptyset )
| ( SV1203 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4221]) ).
thf(5490,plain,
! [SV1204: $i] :
( ( ( c_Suc @ SV1204 )
!= c_0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(5491,plain,
! [SV1205: $i] :
( ( ! [SY2584: $i,SY2585: $i,SY2586: $i] :
( ( ( c_Datatype__Universe_OIn0 @ SV1205 @ SY2584 @ SY2585 )
!= ( c_Datatype__Universe_OIn0 @ SY2586 @ SY2584 @ SY2585 ) )
| ( SV1205 = SY2586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4223]) ).
thf(5492,plain,
( ( c_Numeral_Obit_OB0 = c_Numeral_Obit_OB1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4224]) ).
thf(5493,plain,
! [SV1206: $i] :
( ( ! [SY2587: $i,SY2588: $i,SY2589: $i,SY2590: $i,SY2591: $i] :
( ( ( c_Pair @ SV1206 @ SY2587 @ SY2588 @ SY2589 )
!= ( c_Pair @ SY2590 @ SY2591 @ SY2588 @ SY2589 ) )
| ( SY2587 = SY2591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4225]) ).
thf(5494,plain,
! [SV1207: $i] :
( ( ! [SY2592: $i,SY2593: $i,SY2594: $i,SY2595: $i] :
( ( c_Datatype__Universe_OAtom @ SV1207 @ SY2592 @ SY2593 )
!= ( c_Datatype__Universe_OScons @ SY2594 @ SY2595 @ SY2592 @ SY2593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4226]) ).
thf(5495,plain,
! [SV1208: $i] :
( ( ( c_Message_Oagent_OFriend @ SV1208 )
!= c_Message_Oagent_OServer )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4227]) ).
thf(5496,plain,
! [SV1209: $i] :
( ( ! [SY2596: $i,SY2597: $i,SY2598: $i] :
( ( ( c_List_Orev @ SV1209 @ SY2596 )
!= ( c_List_Olist_OCons @ SY2597 @ SY2598 @ SY2596 ) )
| ( SV1209
= ( c_append @ ( c_List_Orev @ SY2598 @ SY2596 ) @ ( c_List_Olist_OCons @ SY2597 @ c_List_Olist_ONil @ SY2596 ) @ SY2596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(5497,plain,
! [SV1210: $i] :
( ( ! [SY2599: $i,SY2600: $i] :
( ~ ( class_Orderings_Olinorder @ SV1210 )
| ( ( c_SetInterval_OatLeast @ SY2599 @ SV1210 )
!= ( c_SetInterval_OatLeast @ SY2600 @ SV1210 ) )
| ( SY2599 = SY2600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4229]) ).
thf(5498,plain,
! [SV1211: $i] :
( ( ! [SY2601: $i,SY2602: $i] :
( ( ( c_uminus @ SV1211 @ ( tc_set @ SY2601 ) )
!= ( c_uminus @ SY2602 @ ( tc_set @ SY2601 ) ) )
| ( SV1211 = SY2602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4230]) ).
thf(5499,plain,
! [SV1212: $i] :
( ( ! [SY2603: $i,SY2604: $i,SY2605: $i,SY2606: $i] :
( ( c_Datatype__Universe_ONumb @ SV1212 @ SY2603 @ SY2604 )
!= ( c_Datatype__Universe_OScons @ SY2605 @ SY2606 @ SY2603 @ SY2604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4231]) ).
thf(5500,plain,
! [SV1213: $i] :
( ( ! [SY2607: $i,SY2608: $i,SY2609: $i] :
( ( ( c_insert @ SV1213 @ c_emptyset @ SY2607 )
!= ( c_insert @ SY2608 @ SY2609 @ SY2607 ) )
| ( SY2608 = SV1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(5501,plain,
! [SV1214: $i] :
( ( ! [SY2610: $i,SY2611: $i] :
( ( SV1214
!= ( c_append @ SY2610 @ SV1214 @ SY2611 ) )
| ( SY2610 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4233]) ).
thf(5502,plain,
! [SV1215: $i] :
( ( ! [SY2612: $i] :
( ( ( c_Message_Oagent_OFriend @ SV1215 )
!= ( c_Message_Oagent_OFriend @ SY2612 ) )
| ( SV1215 = SY2612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4234]) ).
thf(5503,plain,
! [SV1216: $i] :
( ( c_0
!= ( c_Suc @ SV1216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4235]) ).
thf(5504,plain,
! [SV1217: $i] :
( ( ! [SY2613: $i,SY2614: $i] :
( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ SV1217 @ SY2613 @ SY2614 ) )
| ( SV1217 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(5505,plain,
! [SV1218: $i] :
( ( ! [SY2615: $i,SY2616: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ SV1218 @ SY2615 @ SY2616 ) )
| ( SV1218 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(5506,plain,
! [SV1219: $i] :
( ( ! [SY2617: $i] :
( ( c_Datatype_Ooption_OSome @ SV1219 @ SY2617 )
!= c_Datatype_Ooption_ONone ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4238]) ).
thf(5507,plain,
! [SV1220: $i] :
( ( ! [SY2618: $i,SY2619: $i] :
( ( ( c_append @ SV1220 @ SY2618 @ SY2619 )
!= SV1220 )
| ( SY2618 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4239]) ).
thf(5508,plain,
! [SV1221: $i] :
( ( ! [SY2620: $i,SY2621: $i] :
( ~ ( class_Orderings_Olinorder @ SV1221 )
| ( ( c_SetInterval_OgreaterThan @ SY2620 @ SV1221 )
!= ( c_SetInterval_OgreaterThan @ SY2621 @ SV1221 ) )
| ( SY2620 = SY2621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(5509,plain,
( ( c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4241]) ).
thf(5510,plain,
! [SV1222: $i] :
( ( ! [SY2622: $i,SY2623: $i,SY2624: $i] :
( ( ( c_Message_Omsg_OCrypt @ SV1222 @ SY2622 )
!= ( c_Message_Omsg_OCrypt @ SY2623 @ SY2624 ) )
| ( SY2622 = SY2624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4242]) ).
thf(5511,plain,
! [SV1223: $i] :
( ( ! [SY2625: $i] :
( ( ( c_Message_Omsg_OAgent @ SV1223 )
!= ( c_Message_Omsg_OAgent @ SY2625 ) )
| ( SV1223 = SY2625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4243]) ).
thf(5512,plain,
! [SV1224: $i] :
( ( ! [SY2626: $i,SY2627: $i] :
( ( ( c_Datatype_Ooption_OSome @ SV1224 @ SY2626 )
!= ( c_Datatype_Ooption_OSome @ SY2627 @ SY2626 ) )
| ( SV1224 = SY2627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4244]) ).
thf(5513,plain,
! [SV1225: $i] :
( ( ! [SY2628: $i] :
( ( ( c_Message_Omsg_ONonce @ SV1225 )
!= ( c_Message_Omsg_ONonce @ SY2628 ) )
| ( SV1225 = SY2628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4245]) ).
thf(5514,plain,
! [SV1226: $i] :
( ( ! [SY2629: $i,SY2630: $i] :
( ( ( c_append @ SV1226 @ SY2629 @ SY2630 )
!= SY2629 )
| ( SV1226 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4246]) ).
thf(5515,plain,
! [SV1227: $i] :
( ( ! [SY2631: $i,SY2632: $i] :
( ( SV1227
!= ( c_append @ SV1227 @ SY2631 @ SY2632 ) )
| ( SY2631 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(5516,plain,
! [SV1228: $i] :
( ( ! [SY2633: $i] :
( ( ( c_Message_Omsg_ONumber @ SV1228 )
!= ( c_Message_Omsg_ONumber @ SY2633 ) )
| ( SV1228 = SY2633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(5517,plain,
! [SV1229: $i] :
( ( ! [SY2634: $i] :
( ( c_emptyset
!= ( c_List_Oset @ SV1229 @ SY2634 ) )
| ( SV1229 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4249]) ).
thf(5518,plain,
! [SV1230: $i] :
( ( ! [SY2635: $i,SY2636: $i] :
( ( ( c_insert @ SV1230 @ c_emptyset @ SY2635 )
!= ( c_insert @ SY2636 @ c_emptyset @ SY2635 ) )
| ( SV1230 = SY2636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4250]) ).
thf(5519,plain,
! [SV1231: $i] :
( ( ! [SY2637: $i] :
( ( ( c_Divides_Oop_Amod @ SV1231 @ SY2637 @ tc_nat )
!= c_0 )
| ( SV1231
= ( c_times @ SY2637 @ ( c_Main_Omod__eq__0D__dest__1 @ SY2637 @ SV1231 ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4251]) ).
thf(5520,plain,
! [SV1232: $i] :
( ( ! [SY2638: $i,SY2639: $i,SY2640: $i] :
( ( c_Sum__Type_OInl @ SV1232 @ SY2638 @ SY2639 )
!= ( c_Sum__Type_OInr @ SY2640 @ SY2639 @ SY2638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4252]) ).
thf(5521,plain,
! [SV1233: $i] :
( ( ! [SY2641: $i] :
( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1233 @ SY2641 ) @ ( tc_List_Olist @ SY2641 ) )
!= ( c_Nat_Osize @ SV1233 @ ( tc_List_Olist @ SY2641 ) ) )
| ( ( c_List_Oremdups @ SV1233 @ SY2641 )
= SV1233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4253]) ).
thf(5522,plain,
! [SV1234: $i] :
( ( ! [SY2642: $i,SY2643: $i,SY2644: $i,SY2645: $i] :
( ( c_Datatype__Universe_OScons @ SV1234 @ SY2642 @ SY2643 @ SY2644 )
!= ( c_Datatype__Universe_OLeaf @ SY2645 @ SY2643 @ SY2644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4254]) ).
thf(5523,plain,
! [SV1235: $i] :
( ( ! [SY2646: $i,SY2647: $i,SY2648: $i,SY2649: $i] :
( ( ( c_List_Olist_OCons @ SV1235 @ SY2646 @ SY2647 )
!= ( c_List_Olist_OCons @ SY2648 @ SY2649 @ SY2647 ) )
| ( SV1235 = SY2648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4255]) ).
thf(5524,plain,
! [SV1236: $i] :
( ( ! [SY2650: $i] :
( ( ( c_Suc @ SV1236 )
!= ( c_Suc @ SY2650 ) )
| ( SV1236 = SY2650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(5525,plain,
! [SV1237: $i] :
( ( ! [SY2651: $i,SY2652: $i,SY2653: $i] :
( ( c_Datatype__Universe_ONumb @ SV1237 @ SY2651 @ SY2652 )
!= ( c_Datatype__Universe_OLeaf @ SY2653 @ SY2651 @ SY2652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4257]) ).
thf(5526,plain,
! [SV1238: $i] :
( ( ! [SY2654: $i,SY2655: $i] :
( ( c_List_Olist_OCons @ SV1238 @ SY2654 @ SY2655 )
!= c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(5527,plain,
! [SV1239: $i] :
( ( ! [SY2656: $i] :
( ( ( c_plus @ SV1239 @ SY2656 @ tc_nat )
!= c_0 )
| ( SV1239 = c_0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4259]) ).
thf(5528,plain,
! [SV1240: $i] :
( ( ! [SY2657: $i,SY2658: $i,SY2659: $i] :
( ( ( c_Sum__Type_OInl @ SV1240 @ SY2657 @ SY2658 )
!= ( c_Sum__Type_OInl @ SY2659 @ SY2657 @ SY2658 ) )
| ( SV1240 = SY2659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4260]) ).
thf(5529,plain,
! [SV1241: $i] :
( ( ! [SY2660: $i,SY2661: $i,SY2662: $i,SY2663: $i,SY2664: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1241 @ SY2660 @ SY2661 @ SY2662 )
!= ( c_Datatype__Universe_OScons @ SY2663 @ SY2664 @ SY2661 @ SY2662 ) )
| ( SV1241 = SY2663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4261]) ).
thf(5530,plain,
! [SV1242: $i] :
( ( ! [SY2665: $i,SY2666: $i,SY2667: $i] :
( ( ( c_append @ SV1242 @ SY2665 @ SY2666 )
!= ( c_append @ SY2667 @ SY2665 @ SY2666 ) )
| ( SV1242 = SY2667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4262]) ).
thf(5531,plain,
! [SV1243: $i] :
( ( ! [SY2668: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Orev @ SV1243 @ SY2668 ) )
| ( SV1243 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(5532,plain,
! [SV1244: $i] :
( ( ! [SY2669: $i,SY2670: $i,SY2671: $i,SY2672: $i] :
( ( c_Datatype__Universe_OScons @ SV1244 @ SY2669 @ SY2670 @ SY2671 )
!= ( c_Datatype__Universe_OAtom @ SY2672 @ SY2670 @ SY2671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4264]) ).
thf(5533,plain,
! [SV1245: $i] :
( ( ! [SY2673: $i,SY2674: $i,SY2675: $i] :
( ( c_Datatype__Universe_OLeaf @ SV1245 @ SY2673 @ SY2674 )
!= ( c_Datatype__Universe_ONumb @ SY2675 @ SY2673 @ SY2674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4265]) ).
thf(5534,plain,
! [SV1246: $i] :
( ( ! [SY2676: $i,SY2677: $i,SY2678: $i] :
( ( ( c_List_Ochar_OChar @ SV1246 @ SY2676 )
!= ( c_List_Ochar_OChar @ SY2677 @ SY2678 ) )
| ( SV1246 = SY2677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4266]) ).
thf(5535,plain,
! [SV1247: $i] :
( ( ! [SY2679: $i,SY2680: $i] :
( ( ( c_append @ SV1247 @ SY2679 @ SY2680 )
!= c_List_Olist_ONil )
| ( SV1247 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4267]) ).
thf(5536,plain,
! [SV1248: $i] :
( ( ! [SY2681: $i,SY2682: $i,SY2683: $i,SY2684: $i,SY2685: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1248 @ SY2681 @ SY2682 @ SY2683 )
!= ( c_Datatype__Universe_OScons @ SY2684 @ SY2685 @ SY2682 @ SY2683 ) )
| ( SY2681 = SY2685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(5537,plain,
! [SV1249: $i] :
( ( ! [SY2686: $i,SY2687: $i] :
( ~ ( class_Orderings_Olinorder @ SV1249 )
| ( ( c_SetInterval_OatMost @ SY2686 @ SV1249 )
!= ( c_SetInterval_OatMost @ SY2687 @ SV1249 ) )
| ( SY2686 = SY2687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4269]) ).
thf(5538,plain,
! [SV1250: $i] :
( ( ! [SY2688: $i] :
( ( ( c_Divides_Oop_Amod @ SV1250 @ SY2688 @ tc_IntDef_Oint )
!= c_0 )
| ( SV1250
= ( c_times @ SY2688 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SY2688 @ SV1250 ) @ tc_IntDef_Oint ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4270]) ).
thf(5539,plain,
! [SV1251: $i] :
( ( ! [SY2689: $i,SY2690: $i] :
( ( ( c_List_Orev @ SV1251 @ SY2689 )
!= ( c_List_Orev @ SY2690 @ SY2689 ) )
| ( SV1251 = SY2690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4271]) ).
thf(5540,plain,
! [SV1252: $i] :
( ( ! [SY2691: $i,SY2692: $i,SY2693: $i] :
( ( ( c_Message_Omsg_OMPair @ SV1252 @ SY2691 )
!= ( c_Message_Omsg_OMPair @ SY2692 @ SY2693 ) )
| ( SY2691 = SY2693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4272]) ).
thf(5541,plain,
! [SV1253: $i] :
( ( ! [SY2694: $i,SY2695: $i,SY2696: $i] :
( ( ( c_insert @ SV1253 @ c_emptyset @ SY2694 )
!= ( c_insert @ SY2695 @ SY2696 @ SY2694 ) )
| ( c_lessequals @ SY2696 @ ( c_insert @ SV1253 @ c_emptyset @ SY2694 ) @ ( tc_set @ SY2694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4273]) ).
thf(5542,plain,
! [SV1254: $i] :
( ( ! [SY2697: $i] :
( ( ( c_IntDef_Oint @ SV1254 )
!= ( c_IntDef_Oint @ SY2697 ) )
| ( SV1254 = SY2697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4274]) ).
thf(5543,plain,
! [SV1255: $i] :
( ( ! [SY2698: $i,SY2699: $i,SY2700: $i] :
( ( ( c_Sum__Type_OInr @ SV1255 @ SY2698 @ SY2699 )
!= ( c_Sum__Type_OInr @ SY2700 @ SY2698 @ SY2699 ) )
| ( SV1255 = SY2700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4275]) ).
thf(5544,plain,
! [SV1256: $i] :
( ( ! [SY2701: $i,SY2702: $i,SY2703: $i] :
( ( ( c_insert @ SV1256 @ SY2701 @ SY2702 )
!= ( c_insert @ SY2703 @ c_emptyset @ SY2702 ) )
| ( c_lessequals @ SY2701 @ ( c_insert @ SY2703 @ c_emptyset @ SY2702 ) @ ( tc_set @ SY2702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4276]) ).
thf(5545,plain,
! [SV1257: $i] :
( ( ! [SY2704: $i,SY2705: $i,SY2706: $i] :
( ( ( c_insert @ SV1257 @ SY2704 @ SY2705 )
!= ( c_insert @ SY2706 @ c_emptyset @ SY2705 ) )
| ( SV1257 = SY2706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4277]) ).
thf(5546,plain,
( ( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( ~ ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4278]) ).
thf(5547,plain,
! [SV1258: $i,SV1: $i] :
( ( ! [SY2707: $i,SY2708: $i,SY2709: $i] :
( ~ ( c_in @ SV1 @ ( c_Datatype__Universe_Odprod @ SV1258 @ SY2707 @ SY2708 @ SY2709 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2708 @ SY2709 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2708 @ SY2709 ) ) ) )
| ( SV1
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV1 @ SV1258 @ SY2707 @ SY2708 @ SY2709 ) @ ( c_Main_OdprodE__2 @ SV1 @ SV1258 @ SY2707 @ SY2708 @ SY2709 ) @ SY2708 @ SY2709 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV1 @ SV1258 @ SY2707 @ SY2708 @ SY2709 ) @ ( c_Main_OdprodE__4 @ SV1 @ SV1258 @ SY2707 @ SY2708 @ SY2709 ) @ SY2708 @ SY2709 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2708 @ SY2709 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2708 @ SY2709 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4279]) ).
thf(5548,plain,
! [SV1259: $i,SV2: $i] :
( ( ! [SY2710: $i,SY2711: $i,SY2712: $i] :
( ~ ( c_in @ SV2 @ ( c_Datatype__Universe_Odprod @ SV1259 @ SY2710 @ SY2711 @ SY2712 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2711 @ SY2712 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2711 @ SY2712 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV2 @ SV1259 @ SY2710 @ SY2711 @ SY2712 ) @ ( c_Main_OdprodE__4 @ SV2 @ SV1259 @ SY2710 @ SY2711 @ SY2712 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2711 @ SY2712 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2711 @ SY2712 ) ) ) @ SY2710 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2711 @ SY2712 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2711 @ SY2712 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(5549,plain,
! [SV1260: $i,SV3: $i] :
( ( ! [SY2713: $i,SY2714: $i,SY2715: $i] :
( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1260 @ SY2713 @ SY2714 @ SY2715 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2714 @ SY2715 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2714 @ SY2715 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV3 @ SV1260 @ SY2713 @ SY2714 @ SY2715 ) @ ( c_Main_OdprodE__3 @ SV3 @ SV1260 @ SY2713 @ SY2714 @ SY2715 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2714 @ SY2715 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2714 @ SY2715 ) ) ) @ SV1260 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2714 @ SY2715 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2714 @ SY2715 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4281]) ).
thf(5550,plain,
! [SV1261: $i,SV4: $i] :
( ( ! [SY2716: $i,SY2717: $i,SY2718: $i,SY2719: $i,SY2720: $i,SY2721: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) ) @ SY2718 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SY2719 @ SY2720 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) ) @ SY2721 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY2719 @ SV4 @ SY2716 @ SY2717 ) @ ( c_Datatype__Universe_OScons @ SY2720 @ SV1261 @ SY2716 @ SY2717 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY2721 @ SY2718 @ SY2716 @ SY2717 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2716 @ SY2717 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4282]) ).
thf(5551,plain,
! [SV1262: $i,SV5: $i] :
( ( ! [SY2722: $i,SY2723: $i,SY2724: $i] :
( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SV1262 @ SY2722 @ SY2723 @ SY2724 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2723 @ SY2724 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2723 @ SY2724 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1262 @ SV5 @ SY2723 @ SY2724 ) @ SY2723 @ SY2724 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1262 @ SV5 @ SY2723 @ SY2724 ) @ SY2723 @ SY2724 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2723 @ SY2724 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2723 @ SY2724 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2722 @ SV5 @ SY2723 @ SY2724 ) @ SY2723 @ SY2724 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2722 @ SV5 @ SY2723 @ SY2724 ) @ SY2723 @ SY2724 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2723 @ SY2724 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2723 @ SY2724 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4283]) ).
thf(5552,plain,
! [SV1263: $i,SV6: $i] :
( ( ! [SY2725: $i,SY2726: $i,SY2727: $i] :
( ~ ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SV1263 @ SY2725 @ SY2726 @ SY2727 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2725 @ SV6 @ SY2726 @ SY2727 ) @ ( c_Main_OdsumE__4 @ SY2725 @ SV6 @ SY2726 @ SY2727 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) ) @ SY2725 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) ) )
| ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1263 @ SV6 @ SY2726 @ SY2727 ) @ SY2726 @ SY2727 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1263 @ SV6 @ SY2726 @ SY2727 ) @ SY2726 @ SY2727 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2726 @ SY2727 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4284]) ).
thf(5553,plain,
! [SV1264: $i,SV7: $i] :
( ( ! [SY2728: $i,SY2729: $i,SY2730: $i] :
( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1264 @ SY2728 @ SY2729 @ SY2730 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1264 @ SV7 @ SY2729 @ SY2730 ) @ ( c_Main_OdsumE__2 @ SV1264 @ SV7 @ SY2729 @ SY2730 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) ) @ SV1264 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) ) )
| ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SY2728 @ SV7 @ SY2729 @ SY2730 ) @ SY2729 @ SY2730 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SY2728 @ SV7 @ SY2729 @ SY2730 ) @ SY2729 @ SY2730 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2729 @ SY2730 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4285]) ).
thf(5554,plain,
! [SV1265: $i,SV8: $i] :
( ( ! [SY2731: $i,SY2732: $i,SY2733: $i] :
( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1265 @ SY2731 @ SY2732 @ SY2733 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1265 @ SV8 @ SY2732 @ SY2733 ) @ ( c_Main_OdsumE__2 @ SV1265 @ SV8 @ SY2732 @ SY2733 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) ) @ SV1265 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SY2731 @ SV8 @ SY2732 @ SY2733 ) @ ( c_Main_OdsumE__4 @ SY2731 @ SV8 @ SY2732 @ SY2733 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) ) @ SY2731 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2732 @ SY2733 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4286]) ).
thf(5555,plain,
! [SV1266: $i,SV9: $i] :
( ( ! [SY2734: $i,SY2735: $i,SY2736: $i,SY2737: $i] :
( ~ ( c_in @ ( c_Pair @ SV9 @ SV1266 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) ) @ SY2736 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SY2734 @ SY2735 ) @ ( c_Datatype__Universe_OIn0 @ SV1266 @ SY2734 @ SY2735 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2736 @ SY2737 @ SY2734 @ SY2735 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2734 @ SY2735 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(5556,plain,
! [SV1267: $i,SV10: $i] :
( ( ! [SY2738: $i,SY2739: $i,SY2740: $i,SY2741: $i] :
( ~ ( c_in @ ( c_Pair @ SV10 @ SV1267 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) ) @ SY2740 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SY2738 @ SY2739 ) @ ( c_Datatype__Universe_OIn1 @ SV1267 @ SY2738 @ SY2739 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY2741 @ SY2740 @ SY2738 @ SY2739 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2738 @ SY2739 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(5557,plain,
! [SV1268: $i,SV11: $i] :
( ( ! [SY2742: $i,SY2743: $i,SY2744: $i] :
( ~ ( c_in @ SV11 @ ( c_Datatype__Universe_Ouprod @ SV1268 @ SY2742 @ SY2743 @ SY2744 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2743 @ SY2744 ) ) )
| ( SV11
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1268 @ SY2742 @ SV11 @ SY2743 @ SY2744 ) @ ( c_Main_OuprodE__2 @ SV1268 @ SY2742 @ SV11 @ SY2743 @ SY2744 ) @ SY2743 @ SY2744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4289]) ).
thf(5558,plain,
! [SV1269: $i,SV12: $i] :
( ( ! [SY2745: $i,SY2746: $i,SY2747: $i] :
( ~ ( c_in @ SV12 @ ( c_Datatype__Universe_Ouprod @ SV1269 @ SY2745 @ SY2746 @ SY2747 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2746 @ SY2747 ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ SV1269 @ SY2745 @ SV12 @ SY2746 @ SY2747 ) @ SY2745 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2746 @ SY2747 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(5559,plain,
! [SV1270: $i,SV13: $i] :
( ( ! [SY2748: $i,SY2749: $i,SY2750: $i] :
( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1270 @ SY2748 @ SY2749 @ SY2750 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2749 @ SY2750 ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ SV1270 @ SY2748 @ SV13 @ SY2749 @ SY2750 ) @ SV1270 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2749 @ SY2750 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4291]) ).
thf(5560,plain,
! [SV1271: $i,SV14: $i] :
( ( ! [SY2751: $i,SY2752: $i,SY2753: $i,SY2754: $i] :
( ~ ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) )
| ~ ( c_in @ SY2753 @ SY2754 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SY2753 @ SV14 @ SY2751 @ SY2752 ) @ ( c_Datatype__Universe_Ouprod @ SY2754 @ SV1271 @ SY2751 @ SY2752 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2751 @ SY2752 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4292]) ).
thf(5561,plain,
! [SV1272: $i,SV15: $i] :
( ( ! [SY2755: $i,SY2756: $i,SY2757: $i] :
( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SV1272 @ SY2755 @ SY2756 @ SY2757 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2756 @ SY2757 ) ) )
| ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1272 @ SV15 @ SY2756 @ SY2757 ) @ SY2756 @ SY2757 ) )
| ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2755 @ SV15 @ SY2756 @ SY2757 ) @ SY2756 @ SY2757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4293]) ).
thf(5562,plain,
! [SV1273: $i,SV16: $i] :
( ( ! [SY2758: $i,SY2759: $i,SY2760: $i] :
( ~ ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SV1273 @ SY2758 @ SY2759 @ SY2760 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2759 @ SY2760 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SY2758 @ SV16 @ SY2759 @ SY2760 ) @ SY2758 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2759 @ SY2760 ) ) )
| ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1273 @ SV16 @ SY2759 @ SY2760 ) @ SY2759 @ SY2760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4294]) ).
thf(5563,plain,
! [SV1274: $i,SV17: $i] :
( ( ! [SY2761: $i,SY2762: $i,SY2763: $i] :
( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1274 @ SY2761 @ SY2762 @ SY2763 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2762 @ SY2763 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1274 @ SV17 @ SY2762 @ SY2763 ) @ SV1274 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2762 @ SY2763 ) ) )
| ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SY2761 @ SV17 @ SY2762 @ SY2763 ) @ SY2762 @ SY2763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4295]) ).
thf(5564,plain,
! [SV1275: $i,SV18: $i] :
( ( ! [SY2764: $i,SY2765: $i,SY2766: $i] :
( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1275 @ SY2764 @ SY2765 @ SY2766 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2765 @ SY2766 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1275 @ SV18 @ SY2765 @ SY2766 ) @ SV1275 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2765 @ SY2766 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SY2764 @ SV18 @ SY2765 @ SY2766 ) @ SY2764 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2765 @ SY2766 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4296]) ).
thf(5565,plain,
! [SV1276: $i,SV19: $i] :
( ( ! [SY2767: $i,SY2768: $i,SY2769: $i] :
( ~ ( c_in @ SV19 @ SV1276 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2767 @ SY2768 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn0 @ SV19 @ SY2767 @ SY2768 ) @ ( c_Datatype__Universe_Ousum @ SV1276 @ SY2769 @ SY2767 @ SY2768 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2767 @ SY2768 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4297]) ).
thf(5566,plain,
! [SV1277: $i,SV20: $i] :
( ( ! [SY2770: $i,SY2771: $i,SY2772: $i] :
( ~ ( c_in @ SV20 @ SV1277 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2770 @ SY2771 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn1 @ SV20 @ SY2770 @ SY2771 ) @ ( c_Datatype__Universe_Ousum @ SY2772 @ SV1277 @ SY2770 @ SY2771 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY2770 @ SY2771 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4298]) ).
thf(5567,plain,
! [SV1278: $i,SV23: $i] :
( ( c_Divides_Oop_Advd @ SV23 @ ( c_times @ SV23 @ SV1278 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4301]) ).
thf(5568,plain,
! [SV1279: $i,SV24: $i] :
( ( c_Divides_Oop_Advd @ SV24 @ ( c_times @ SV1279 @ SV24 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4302]) ).
thf(5569,plain,
! [SV1280: $i,SV26: $i] :
( ( ! [SY2773: $i] :
( ~ ( c_in @ SV26 @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) )
| ( c_in @ ( c_insert @ SY2773 @ SV26 @ SV1280 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4304]) ).
thf(5570,plain,
! [SV1281: $i,SV27: $i] :
( ( ! [SY2774: $i] :
( ~ ( c_in @ SV27 @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) )
| ( c_in @ ( c_inter @ SV27 @ SY2774 @ SV1281 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4305]) ).
thf(5571,plain,
! [SV1282: $i,SV28: $i] :
( ( ! [SY2775: $i] :
( ~ ( c_in @ SV28 @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) )
| ( c_in @ ( c_inter @ SY2775 @ SV28 @ SV1282 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4306]) ).
thf(5572,plain,
! [SV1283: $i,SV29: $i] :
( ( ~ ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1283 ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ SV29 @ SV1283 ) @ SV29 @ ( tc_set @ SV1283 ) )
| ( c_in @ ( c_Union @ SV29 @ SV1283 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4307]) ).
thf(5573,plain,
! [SV1284: $i,SV30: $i] :
( ( ~ ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1284 ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) )
| ( c_in @ ( c_Union @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4308]) ).
thf(5574,plain,
! [SV1285: $i,SV31: $i] :
( ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV31 @ SV1285 @ tc_nat @ tc_nat ) ) @ SV31 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4309]) ).
thf(5575,plain,
! [SV1286: $i,SV32: $i] :
( ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ SV32 @ SV1286 @ tc_nat @ tc_nat ) ) @ SV1286 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4310]) ).
thf(5576,plain,
! [SV1287: $i,SV33: $i] :
( ( ! [SY2776: $i,SY2777: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
| ~ ( c_in @ SY2776 @ SV33 @ SV1287 )
| ~ ( c_in @ SY2777 @ SV33 @ SV1287 )
| ( SY2776 = SY2777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4311]) ).
thf(5577,plain,
! [SV1288: $i,SV34: $i] :
( ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ SV34 ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SV1288 ) @ tc_IntDef_Oint )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4312]) ).
thf(5578,plain,
! [SV1289: $i,SV35: $i] :
( ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ SV35 ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ SV1289 ) @ tc_IntDef_Oint )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(5579,plain,
! [SV1290: $i,SV38: $i] :
( ( c_Divides_Oop_Advd @ SV38 @ ( c_times @ SV38 @ SV1290 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4316]) ).
thf(5580,plain,
! [SV1291: $i,SV39: $i] :
( ( c_Divides_Oop_Advd @ SV39 @ ( c_times @ SV1291 @ SV39 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4317]) ).
thf(5581,plain,
! [SV1292: $i,SV40: $i] :
( ( c_List_Odistinct @ ( c_List_Oremdups @ SV40 @ SV1292 ) @ SV1292 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(5582,plain,
! [SV1293: $i,SV41: $i] :
( ( c_in @ ( c_List_Oset @ SV41 @ SV1293 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4319]) ).
thf(5583,plain,
! [SV1294: $i,SV42: $i] :
( ( ! [SY2778: $i,SY2779: $i] :
( ~ ( c_in @ SV42 @ ( c_List_Olists @ SV1294 @ SY2778 ) @ ( tc_List_Olist @ SY2778 ) )
| ~ ( c_in @ SY2779 @ ( c_List_Oset @ SV42 @ SY2778 ) @ SY2778 )
| ( c_in @ SY2779 @ SV1294 @ SY2778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4320]) ).
thf(5584,plain,
! [SV1295: $i,SV43: $i] :
( ( ! [SY2780: $i] :
( ( c_in @ SV43 @ ( c_List_Olists @ SV1295 @ SY2780 ) @ ( tc_List_Olist @ SY2780 ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ SV1295 @ SV43 @ SY2780 ) @ ( c_List_Oset @ SV43 @ SY2780 ) @ SY2780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4321]) ).
thf(5585,plain,
! [SV1296: $i,SV44: $i] :
( ( ! [SY2781: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV44 @ SV1296 @ SY2781 ) @ SV44 @ SY2781 )
| ( c_in @ SV1296 @ ( c_List_Olists @ SV44 @ SY2781 ) @ ( tc_List_Olist @ SY2781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4322]) ).
thf(5586,plain,
! [SV1297: $i,SV45: $i] :
( ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ SV45 @ SV1297 ) @ ( tc_List_Olist @ SV1297 ) ) @ ( c_Nat_Osize @ SV45 @ ( tc_List_Olist @ SV1297 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4323]) ).
thf(5587,plain,
! [SV1298: $i,SV46: $i] :
( ( ! [SY2782: $i,SY2783: $i,SY2784: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV46 @ SV1298 @ SY2782 ) @ SY2783 @ ( tc_List_Olist @ SY2782 ) @ ( tc_List_Olist @ SY2782 ) ) @ ( c_List_Olistrel @ SY2784 @ SY2782 ) @ ( tc_prod @ ( tc_List_Olist @ SY2782 ) @ ( tc_List_Olist @ SY2782 ) ) )
| ( SY2783
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY2784 @ SY2783 @ SV46 @ SV1298 @ SY2782 ) @ ( c_Main_Olistrel__Cons1__2 @ SY2784 @ SY2783 @ SV46 @ SV1298 @ SY2782 ) @ SY2782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4324]) ).
thf(5588,plain,
! [SV1299: $i,SV47: $i] :
( ( ! [SY2785: $i,SY2786: $i,SY2787: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV47 @ SV1299 @ SY2785 ) @ SY2786 @ ( tc_List_Olist @ SY2785 ) @ ( tc_List_Olist @ SY2785 ) ) @ ( c_List_Olistrel @ SY2787 @ SY2785 ) @ ( tc_prod @ ( tc_List_Olist @ SY2785 ) @ ( tc_List_Olist @ SY2785 ) ) )
| ( c_in @ ( c_Pair @ SV1299 @ ( c_Main_Olistrel__Cons1__2 @ SY2787 @ SY2786 @ SV47 @ SV1299 @ SY2785 ) @ ( tc_List_Olist @ SY2785 ) @ ( tc_List_Olist @ SY2785 ) ) @ ( c_List_Olistrel @ SY2787 @ SY2785 ) @ ( tc_prod @ ( tc_List_Olist @ SY2785 ) @ ( tc_List_Olist @ SY2785 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(5589,plain,
! [SV1300: $i,SV48: $i] :
( ( ! [SY2788: $i,SY2789: $i,SY2790: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV48 @ SV1300 @ SY2788 ) @ SY2789 @ ( tc_List_Olist @ SY2788 ) @ ( tc_List_Olist @ SY2788 ) ) @ ( c_List_Olistrel @ SY2790 @ SY2788 ) @ ( tc_prod @ ( tc_List_Olist @ SY2788 ) @ ( tc_List_Olist @ SY2788 ) ) )
| ( c_in @ ( c_Pair @ SV48 @ ( c_Main_Olistrel__Cons1__1 @ SY2790 @ SY2789 @ SV48 @ SV1300 @ SY2788 ) @ SY2788 @ SY2788 ) @ SY2790 @ ( tc_prod @ SY2788 @ SY2788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(5590,plain,
! [SV1301: $i,SV49: $i] :
( ( ! [SY2791: $i,SY2792: $i,SY2793: $i] :
( ~ ( c_in @ ( c_Pair @ SV49 @ ( c_List_Olist_OCons @ SV1301 @ SY2791 @ SY2792 ) @ ( tc_List_Olist @ SY2792 ) @ ( tc_List_Olist @ SY2792 ) ) @ ( c_List_Olistrel @ SY2793 @ SY2792 ) @ ( tc_prod @ ( tc_List_Olist @ SY2792 ) @ ( tc_List_Olist @ SY2792 ) ) )
| ( SV49
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY2793 @ SV49 @ SV1301 @ SY2791 @ SY2792 ) @ ( c_Main_Olistrel__Cons2__2 @ SY2793 @ SV49 @ SV1301 @ SY2791 @ SY2792 ) @ SY2792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4327]) ).
thf(5591,plain,
! [SV1302: $i,SV50: $i] :
( ( ! [SY2794: $i,SY2795: $i,SY2796: $i] :
( ~ ( c_in @ ( c_Pair @ SV50 @ ( c_List_Olist_OCons @ SV1302 @ SY2794 @ SY2795 ) @ ( tc_List_Olist @ SY2795 ) @ ( tc_List_Olist @ SY2795 ) ) @ ( c_List_Olistrel @ SY2796 @ SY2795 ) @ ( tc_prod @ ( tc_List_Olist @ SY2795 ) @ ( tc_List_Olist @ SY2795 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY2796 @ SV50 @ SV1302 @ SY2794 @ SY2795 ) @ SY2794 @ ( tc_List_Olist @ SY2795 ) @ ( tc_List_Olist @ SY2795 ) ) @ ( c_List_Olistrel @ SY2796 @ SY2795 ) @ ( tc_prod @ ( tc_List_Olist @ SY2795 ) @ ( tc_List_Olist @ SY2795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4328]) ).
thf(5592,plain,
! [SV1303: $i,SV51: $i] :
( ( ! [SY2797: $i,SY2798: $i,SY2799: $i] :
( ~ ( c_in @ ( c_Pair @ SV51 @ ( c_List_Olist_OCons @ SV1303 @ SY2797 @ SY2798 ) @ ( tc_List_Olist @ SY2798 ) @ ( tc_List_Olist @ SY2798 ) ) @ ( c_List_Olistrel @ SY2799 @ SY2798 ) @ ( tc_prod @ ( tc_List_Olist @ SY2798 ) @ ( tc_List_Olist @ SY2798 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY2799 @ SV51 @ SV1303 @ SY2797 @ SY2798 ) @ SV1303 @ SY2798 @ SY2798 ) @ SY2799 @ ( tc_prod @ SY2798 @ SY2798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4329]) ).
thf(5593,plain,
! [SV1304: $i,SV52: $i] :
( ( ! [SY2800: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV52 @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) @ ( c_List_Olistrel @ SY2800 @ SV1304 ) @ ( tc_prod @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) )
| ( SV52 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4330]) ).
thf(5594,plain,
! [SV1305: $i,SV53: $i] :
( ( ! [SY2801: $i] :
( ~ ( c_in @ ( c_Pair @ SV53 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) @ ( c_List_Olistrel @ SY2801 @ SV1305 ) @ ( tc_prod @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) )
| ( SV53 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4331]) ).
thf(5595,plain,
! [SV1306: $i,SV54: $i] :
( ( ! [SY2802: $i,SY2803: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ SV54 @ SV1306 @ SY2802 ) @ ( c_List_Olists @ SY2803 @ SY2802 ) @ ( tc_List_Olist @ SY2802 ) )
| ( c_in @ SV1306 @ ( c_List_Olists @ SY2803 @ SY2802 ) @ ( tc_List_Olist @ SY2802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4332]) ).
thf(5596,plain,
! [SV1307: $i,SV55: $i] :
( ( ! [SY2804: $i,SY2805: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ SV55 @ SV1307 @ SY2804 ) @ ( c_List_Olists @ SY2805 @ SY2804 ) @ ( tc_List_Olist @ SY2804 ) )
| ( c_in @ SV55 @ SY2805 @ SY2804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4333]) ).
thf(5597,plain,
! [SV1308: $i,SV56: $i] :
( ( ! [SY2806: $i,SY2807: $i] :
( ~ ( c_in @ SV56 @ SV1308 @ SY2806 )
| ~ ( c_in @ SY2807 @ ( c_List_Olists @ SV1308 @ SY2806 ) @ ( tc_List_Olist @ SY2806 ) )
| ( c_in @ ( c_List_Olist_OCons @ SV56 @ SY2807 @ SY2806 ) @ ( c_List_Olists @ SV1308 @ SY2806 ) @ ( tc_List_Olist @ SY2806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(5598,plain,
! [SV1309: $i,SV57: $i] :
( ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ SV57 @ SV1309 ) @ ( tc_List_Olist @ SV1309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4335]) ).
thf(5599,plain,
! [SV1310: $i,SV58: $i] :
( ( ~ ( c_Wellfounded__Recursion_Owf @ SV58 @ SV1310 )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV58 @ SV1310 ) @ ( tc_List_Olist @ SV1310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(5600,plain,
! [SV1311: $i,SV59: $i] :
( ( ~ ( c_Wellfounded__Recursion_Owf @ SV59 @ SV1311 )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV59 @ SV1311 ) @ ( tc_List_Olist @ SV1311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4337]) ).
thf(5601,plain,
! [SV62: $i] :
( ( c_less @ SV62 @ SV62 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(5602,plain,
! [SV1312: $i,SV64: $i] :
( ( ~ ( class_Orderings_Oorder @ SV64 )
| ( c_lessequals @ SV1312 @ SV1312 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(5603,plain,
! [SV1313: $i,SV65: $i] :
( ( ! [SY2808: $i,SY2809: $i] :
( ~ ( c_in @ SV65 @ ( c_Relation_ODomain @ SV1313 @ SY2808 @ SY2809 ) @ SY2808 )
| ( c_in @ ( c_Pair @ SV65 @ ( c_Main_ODomainE__1 @ SV65 @ SV1313 @ SY2808 @ SY2809 ) @ SY2808 @ SY2809 ) @ SV1313 @ ( tc_prod @ SY2808 @ SY2809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(5604,plain,
! [SV1314: $i,SV66: $i] :
( ( ! [SY2810: $i,SY2811: $i,SY2812: $i] :
( ~ ( c_in @ ( c_Pair @ SV66 @ SV1314 @ SY2810 @ SY2811 ) @ SY2812 @ ( tc_prod @ SY2810 @ SY2811 ) )
| ( c_in @ SV66 @ ( c_Relation_ODomain @ SY2812 @ SY2810 @ SY2811 ) @ SY2810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(5605,plain,
! [SV1315: $i,SV67: $i] :
( ( ~ ( c_in @ SV67 @ c_Relation_OId @ ( tc_prod @ SV1315 @ SV1315 ) )
| ( SV67
= ( c_Pair @ ( c_Main_OIdE__1 @ SV67 @ SV1315 ) @ ( c_Main_OIdE__1 @ SV67 @ SV1315 ) @ SV1315 @ SV1315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4345]) ).
thf(5606,plain,
! [SV1316: $i,SV68: $i] :
( ( ! [SY2813: $i,SY2814: $i,SY2815: $i] :
( ~ ( c_in @ SV68 @ ( c_Relation_OImage @ SV1316 @ SY2813 @ SY2814 @ SY2815 ) @ SY2815 )
| ( c_in @ ( c_Main_OImageE__1 @ SY2813 @ SV68 @ SV1316 @ SY2814 @ SY2815 ) @ SY2813 @ SY2814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4346]) ).
thf(5607,plain,
! [SV1317: $i,SV69: $i] :
( ( ! [SY2816: $i,SY2817: $i,SY2818: $i] :
( ~ ( c_in @ SV69 @ ( c_Relation_OImage @ SV1317 @ SY2816 @ SY2817 @ SY2818 ) @ SY2818 )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SY2816 @ SV69 @ SV1317 @ SY2817 @ SY2818 ) @ SV69 @ SY2817 @ SY2818 ) @ SV1317 @ ( tc_prod @ SY2817 @ SY2818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(5608,plain,
! [SV1318: $i,SV70: $i] :
( ( ! [SY2819: $i,SY2820: $i,SY2821: $i,SY2822: $i] :
( ~ ( c_in @ SV70 @ SV1318 @ SY2819 )
| ~ ( c_in @ ( c_Pair @ SV70 @ SY2820 @ SY2819 @ SY2821 ) @ SY2822 @ ( tc_prod @ SY2819 @ SY2821 ) )
| ( c_in @ SY2820 @ ( c_Relation_OImage @ SY2822 @ SV1318 @ SY2819 @ SY2821 ) @ SY2821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4348]) ).
thf(5609,plain,
! [SV1319: $i,SV71: $i] :
( ( ! [SY2823: $i,SY2824: $i] :
( ~ ( c_in @ SV71 @ ( c_Relation_ORange @ SV1319 @ SY2823 @ SY2824 ) @ SY2824 )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV71 @ SV1319 @ SY2824 @ SY2823 ) @ SV71 @ SY2823 @ SY2824 ) @ SV1319 @ ( tc_prod @ SY2823 @ SY2824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4349]) ).
thf(5610,plain,
! [SV1320: $i,SV72: $i] :
( ( ! [SY2825: $i,SY2826: $i,SY2827: $i] :
( ~ ( c_in @ ( c_Pair @ SV72 @ SV1320 @ SY2825 @ SY2826 ) @ SY2827 @ ( tc_prod @ SY2825 @ SY2826 ) )
| ( c_in @ SV1320 @ ( c_Relation_ORange @ SY2827 @ SY2825 @ SY2826 ) @ SY2826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4350]) ).
thf(5611,plain,
! [SV1321: $i,SV73: $i] :
( ( ! [SY2828: $i,SY2829: $i] :
( ~ ( c_in @ SV73 @ ( c_Relation_Oconverse @ SV1321 @ SY2828 @ SY2829 ) @ ( tc_prod @ SY2829 @ SY2828 ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1321 @ SV73 @ SY2828 @ SY2829 ) @ ( c_Main_OconverseE__2 @ SV1321 @ SV73 @ SY2828 @ SY2829 ) @ SY2828 @ SY2829 ) @ SV1321 @ ( tc_prod @ SY2828 @ SY2829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4351]) ).
thf(5612,plain,
! [SV1322: $i,SV74: $i] :
( ( ! [SY2830: $i,SY2831: $i] :
( ~ ( c_in @ SV74 @ ( c_Relation_Oconverse @ SV1322 @ SY2830 @ SY2831 ) @ ( tc_prod @ SY2831 @ SY2830 ) )
| ( SV74
= ( c_Pair @ ( c_Main_OconverseE__2 @ SV1322 @ SV74 @ SY2830 @ SY2831 ) @ ( c_Main_OconverseE__1 @ SV1322 @ SV74 @ SY2830 @ SY2831 ) @ SY2831 @ SY2830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4352]) ).
thf(5613,plain,
! [SV1323: $i,SV75: $i] :
( ( ! [SY2832: $i] :
( ~ ( c_in @ SV75 @ ( c_Relation_Odiag @ SV1323 @ SY2832 ) @ ( tc_prod @ SY2832 @ SY2832 ) )
| ( SV75
= ( c_Pair @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SY2832 ) @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SY2832 ) @ SY2832 @ SY2832 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4353]) ).
thf(5614,plain,
! [SV1324: $i,SV76: $i] :
( ( ! [SY2833: $i] :
( ~ ( c_in @ SV76 @ ( c_Relation_Odiag @ SV1324 @ SY2833 ) @ ( tc_prod @ SY2833 @ SY2833 ) )
| ( c_in @ ( c_Main_OdiagE__1 @ SV1324 @ SV76 @ SY2833 ) @ SV1324 @ SY2833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4354]) ).
thf(5615,plain,
! [SV1325: $i,SV77: $i] :
( ( ! [SY2834: $i] :
( ~ ( c_in @ SV77 @ SV1325 @ SY2834 )
| ( c_in @ ( c_Pair @ SV77 @ SV77 @ SY2834 @ SY2834 ) @ ( c_Relation_Odiag @ SV1325 @ SY2834 ) @ ( tc_prod @ SY2834 @ SY2834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4355]) ).
thf(5616,plain,
! [SV1326: $i,SV78: $i] :
( ( ! [SY2835: $i,SY2836: $i,SY2837: $i,SY2838: $i] :
( ~ ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SV1326 @ SY2835 @ SY2836 @ SY2837 @ SY2838 ) @ ( tc_prod @ SY2838 @ SY2837 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1326 @ SY2835 @ SV78 @ SY2836 @ SY2837 @ SY2838 ) @ ( c_Main_Orel__compE__3 @ SV1326 @ SY2835 @ SV78 @ SY2836 @ SY2837 @ SY2838 ) @ SY2836 @ SY2837 ) @ SV1326 @ ( tc_prod @ SY2836 @ SY2837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4356]) ).
thf(5617,plain,
! [SV1327: $i,SV79: $i] :
( ( ! [SY2839: $i,SY2840: $i,SY2841: $i,SY2842: $i] :
( ~ ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SV1327 @ SY2839 @ SY2840 @ SY2841 @ SY2842 ) @ ( tc_prod @ SY2842 @ SY2841 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1327 @ SY2839 @ SV79 @ SY2840 @ SY2841 @ SY2842 ) @ ( c_Main_Orel__compE__2 @ SV1327 @ SY2839 @ SV79 @ SY2840 @ SY2841 @ SY2842 ) @ SY2842 @ SY2840 ) @ SY2839 @ ( tc_prod @ SY2842 @ SY2840 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(5618,plain,
! [SV1328: $i,SV80: $i] :
( ( ! [SY2843: $i,SY2844: $i,SY2845: $i,SY2846: $i] :
( ~ ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SV1328 @ SY2843 @ SY2844 @ SY2845 @ SY2846 ) @ ( tc_prod @ SY2846 @ SY2845 ) )
| ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1328 @ SY2843 @ SV80 @ SY2844 @ SY2845 @ SY2846 ) @ ( c_Main_Orel__compE__3 @ SV1328 @ SY2843 @ SV80 @ SY2844 @ SY2845 @ SY2846 ) @ SY2846 @ SY2845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(5619,plain,
! [SV1329: $i,SV81: $i] :
( ( ! [SY2847: $i,SY2848: $i,SY2849: $i,SY2850: $i,SY2851: $i,SY2852: $i] :
( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SY2847 @ SY2848 ) @ SY2849 @ ( tc_prod @ SY2847 @ SY2848 ) )
| ~ ( c_in @ ( c_Pair @ SY2850 @ SV81 @ SY2851 @ SY2847 ) @ SY2852 @ ( tc_prod @ SY2851 @ SY2847 ) )
| ( c_in @ ( c_Pair @ SY2850 @ SV1329 @ SY2851 @ SY2848 ) @ ( c_Relation_Orel__comp @ SY2849 @ SY2852 @ SY2847 @ SY2848 @ SY2851 ) @ ( tc_prod @ SY2851 @ SY2848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(5620,plain,
! [SV1330: $i,SV82: $i] :
( ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV82 @ SV1330 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(5621,plain,
! [SV1331: $i,SV83: $i] :
( ( c_in @ ( c_SetInterval_OatLeastAtMost @ SV83 @ SV1331 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(5622,plain,
! [SV1332: $i,SV84: $i] :
( ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV84 @ SV1332 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(5623,plain,
! [SV1333: $i,SV85: $i] :
( ( c_in @ ( c_SetInterval_OatLeastLessThan @ SV85 @ SV1333 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(5624,plain,
! [SV1334: $i,SV87: $i] :
( ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV87 @ SV1334 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(5625,plain,
! [SV1335: $i,SV88: $i] :
( ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ SV88 @ SV1335 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4366]) ).
thf(5626,plain,
! [SV1336: $i,SV89: $i] :
( ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV89 @ SV1336 @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(5627,plain,
! [SV1337: $i,SV90: $i] :
( ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ SV90 @ SV1337 @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4368]) ).
thf(5628,plain,
! [SV1338: $i,SV92: $i] :
( ( ! [SY2853: $i] :
( ( c_in @ SV92 @ ( c_Inter @ SV1338 @ SY2853 ) @ SY2853 )
| ( c_in @ ( c_Main_OInterI__1 @ SV92 @ SV1338 @ SY2853 ) @ SV1338 @ ( tc_set @ SY2853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4370]) ).
thf(5629,plain,
! [SV1339: $i,SV93: $i] :
( ( ! [SY2854: $i] :
( ~ ( c_in @ SV93 @ ( c_Main_OInterI__1 @ SV93 @ SV1339 @ SY2854 ) @ SY2854 )
| ( c_in @ SV93 @ ( c_Inter @ SV1339 @ SY2854 ) @ SY2854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4371]) ).
thf(5630,plain,
! [SV1340: $i,SV94: $i] :
( ( c_in @ SV94 @ c_UNIV @ SV1340 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4372]) ).
thf(5631,plain,
! [SV1341: $i,SV95: $i] :
( ( ! [SY2855: $i] :
( ~ ( c_in @ SV95 @ ( c_Union @ SV1341 @ SY2855 ) @ SY2855 )
| ( c_in @ ( c_Main_OUnionE__1 @ SV95 @ SV1341 @ SY2855 ) @ SV1341 @ ( tc_set @ SY2855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(5632,plain,
! [SV1342: $i,SV96: $i] :
( ( ! [SY2856: $i] :
( ~ ( c_in @ SV96 @ ( c_Union @ SV1342 @ SY2856 ) @ SY2856 )
| ( c_in @ SV96 @ ( c_Main_OUnionE__1 @ SV96 @ SV1342 @ SY2856 ) @ SY2856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(5633,plain,
! [SV1343: $i,SV97: $i] :
( ( c_lessequals @ c_emptyset @ SV97 @ ( tc_set @ SV1343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4375]) ).
thf(5634,plain,
! [SV1344: $i,SV98: $i] :
( ( ! [SY2857: $i] :
( ~ ( c_less @ SV98 @ SV1344 @ ( tc_set @ SY2857 ) )
| ~ ( c_lessequals @ SV1344 @ SV98 @ ( tc_set @ SY2857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4376]) ).
thf(5635,plain,
! [SV1345: $i,SV99: $i] :
( ( ! [SY2858: $i] :
( ~ ( c_less @ SV99 @ SV1345 @ ( tc_set @ SY2858 ) )
| ( c_lessequals @ SV99 @ SV1345 @ ( tc_set @ SY2858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(5636,plain,
! [SV1346: $i,SV100: $i] :
( ( ! [SY2859: $i] :
( ~ ( c_lessequals @ SV100 @ SV1346 @ ( tc_set @ SY2859 ) )
| ( c_less @ SV100 @ SV1346 @ ( tc_set @ SY2859 ) )
| ( SV100 = SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4378]) ).
thf(5637,plain,
! [SV1347: $i,SV101: $i] :
( ( ! [SY2860: $i] :
( ~ ( c_in @ SV101 @ ( c_insert @ SV1347 @ c_emptyset @ SY2860 ) @ SY2860 )
| ( SV101 = SV1347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4379]) ).
thf(5638,plain,
! [SV1348: $i,SV102: $i] :
( ( c_in @ SV102 @ ( c_insert @ SV102 @ c_emptyset @ SV1348 ) @ SV1348 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4380]) ).
thf(5639,plain,
! [SV1349: $i,SV103: $i] :
( ( ! [SY2861: $i,SY2862: $i] :
( ~ ( c_in @ SV103 @ SV1349 @ SY2861 )
| ~ ( c_lessequals @ SV1349 @ SY2862 @ ( tc_set @ SY2861 ) )
| ( c_in @ SV103 @ SY2862 @ SY2861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(5640,plain,
! [SV1350: $i,SV104: $i] :
( ( ! [SY2863: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV104 @ SV1350 @ SY2863 ) @ SV104 @ SY2863 )
| ( c_lessequals @ SV104 @ SV1350 @ ( tc_set @ SY2863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4382]) ).
thf(5641,plain,
! [SV1351: $i,SV105: $i] :
( ( ! [SY2864: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV105 @ SV1351 @ SY2864 ) @ SV1351 @ SY2864 )
| ( c_lessequals @ SV105 @ SV1351 @ ( tc_set @ SY2864 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4383]) ).
thf(5642,plain,
! [SV1352: $i,SV106: $i] :
( ( ! [SY2865: $i] :
( ~ ( c_lessequals @ SV106 @ SV1352 @ ( tc_set @ SY2865 ) )
| ~ ( c_lessequals @ SV1352 @ SV106 @ ( tc_set @ SY2865 ) )
| ( SV1352 = SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4384]) ).
thf(5643,plain,
! [SV1353: $i,SV107: $i] :
( ( c_lessequals @ SV107 @ SV107 @ ( tc_set @ SV1353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(5644,plain,
! [SV1354: $i,SV108: $i] :
( ( ! [SY2866: $i,SY2867: $i,SY2868: $i] :
( ~ ( c_in @ SV108 @ SV1354 @ SY2866 )
| ( c_in @ ( c_Sum__Type_OInl @ SV108 @ SY2866 @ SY2867 ) @ ( c_Sum__Type_OPlus @ SV1354 @ SY2868 @ SY2866 @ SY2867 ) @ ( tc_sum @ SY2866 @ SY2867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(5645,plain,
! [SV1355: $i,SV109: $i] :
( ( ! [SY2869: $i,SY2870: $i,SY2871: $i] :
( ~ ( c_in @ SV109 @ SV1355 @ SY2869 )
| ( c_in @ ( c_Sum__Type_OInr @ SV109 @ SY2869 @ SY2870 ) @ ( c_Sum__Type_OPlus @ SY2871 @ SV1355 @ SY2870 @ SY2869 ) @ ( tc_sum @ SY2870 @ SY2869 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4387]) ).
thf(5646,plain,
! [SV1356: $i,SV110: $i] :
( ( ! [SY2872: $i,SY2873: $i,SY2874: $i] :
( ~ ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SV1356 @ SY2872 @ SY2873 @ SY2874 ) @ ( tc_sum @ SY2873 @ SY2874 ) )
| ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1356 @ SV110 @ SY2873 @ SY2874 ) @ SY2873 @ SY2874 ) )
| ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2872 @ SV110 @ SY2874 @ SY2873 ) @ SY2874 @ SY2873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4388]) ).
thf(5647,plain,
! [SV1357: $i,SV111: $i] :
( ( ! [SY2875: $i,SY2876: $i,SY2877: $i] :
( ~ ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SV1357 @ SY2875 @ SY2876 @ SY2877 ) @ ( tc_sum @ SY2876 @ SY2877 ) )
| ( c_in @ ( c_Main_OPlusE__2 @ SY2875 @ SV111 @ SY2877 @ SY2876 ) @ SY2875 @ SY2877 )
| ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1357 @ SV111 @ SY2876 @ SY2877 ) @ SY2876 @ SY2877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4389]) ).
thf(5648,plain,
! [SV1358: $i,SV112: $i] :
( ( ! [SY2878: $i,SY2879: $i,SY2880: $i] :
( ~ ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SV1358 @ SY2878 @ SY2879 @ SY2880 ) @ ( tc_sum @ SY2879 @ SY2880 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1358 @ SV112 @ SY2879 @ SY2880 ) @ SV1358 @ SY2879 )
| ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SY2878 @ SV112 @ SY2880 @ SY2879 ) @ SY2880 @ SY2879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4390]) ).
thf(5649,plain,
! [SV1359: $i,SV113: $i] :
( ( ! [SY2881: $i,SY2882: $i,SY2883: $i] :
( ~ ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SV1359 @ SY2881 @ SY2882 @ SY2883 ) @ ( tc_sum @ SY2882 @ SY2883 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1359 @ SV113 @ SY2882 @ SY2883 ) @ SV1359 @ SY2882 )
| ( c_in @ ( c_Main_OPlusE__2 @ SY2881 @ SV113 @ SY2883 @ SY2882 ) @ SY2881 @ SY2883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4391]) ).
thf(5650,plain,
! [SV1360: $i,SV114: $i] :
( ( ! [SY2884: $i] :
( ~ ( c_in @ SV114 @ SV1360 @ ( tc_prod @ SY2884 @ SY2884 ) )
| ( c_in @ SV114 @ ( c_Transitive__Closure_Ortrancl @ SV1360 @ SY2884 ) @ ( tc_prod @ SY2884 @ SY2884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4392]) ).
thf(5651,plain,
! [SV1361: $i,SV115: $i] :
( ( ! [SY2885: $i] : ( c_in @ ( c_Pair @ SV115 @ SV115 @ SV1361 @ SV1361 ) @ ( c_Transitive__Closure_Ortrancl @ SY2885 @ SV1361 ) @ ( tc_prod @ SV1361 @ SV1361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(5652,plain,
! [SV1362: $i,SV116: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ~ ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SY2886 @ SY2886 ) @ SY2887 @ ( tc_prod @ SY2886 @ SY2886 ) )
| ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SY2886 @ SY2886 ) @ ( c_Transitive__Closure_Otrancl @ SY2887 @ SY2886 ) @ ( tc_prod @ SY2886 @ SY2886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(5653,plain,
! [SV1363: $i,SV117: $i] :
( ( ! [SY2888: $i,SY2889: $i] :
( ~ ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SY2888 @ SY2888 ) @ ( c_Transitive__Closure_Otrancl @ SY2889 @ SY2888 ) @ ( tc_prod @ SY2888 @ SY2888 ) )
| ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SY2888 @ SY2888 ) @ ( c_Transitive__Closure_Ortrancl @ SY2889 @ SY2888 ) @ ( tc_prod @ SY2888 @ SY2888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4395]) ).
thf(5654,plain,
! [SV1364: $i,SV119: $i] :
( ( ! [SY2890: $i,SY2891: $i] :
( ~ ( c_Relation_Otrans @ SV119 @ SV1364 )
| ~ ( c_Relation_Otrans @ SY2890 @ SY2891 )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SY2890 @ SV119 @ SY2891 @ SV1364 ) @ ( tc_prod @ SY2891 @ SV1364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(5655,plain,
! [SV1365: $i,SV120: $i] :
( ( ! [SY2892: $i,SY2893: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV120 @ SV1365 )
| ~ ( c_Wellfounded__Recursion_Owf @ SY2892 @ SY2893 )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SY2892 @ SV120 @ SY2893 @ SV1365 ) @ ( tc_prod @ SY2893 @ SV1365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4398]) ).
thf(5656,plain,
! [SV121: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ SV121 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4399]) ).
thf(5657,plain,
! [SV1366: $i,SV122: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV122 @ SV1366 ) )
| ~ ( class_Finite__Set_Ofinite @ SV1366 )
| ~ ( class_Finite__Set_Ofinite @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4400]) ).
thf(5658,plain,
! [SV1367: $i,SV123: $i] :
( ( class_Nat_Opower @ ( tc_fun @ SV123 @ SV1367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4401]) ).
thf(5659,plain,
! [SV1368: $i,SV124: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV124 @ SV1368 ) )
| ~ ( class_Finite__Set_Ofinite @ SV1368 )
| ~ ( class_Finite__Set_Ofinite @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4402]) ).
thf(5660,plain,
! [SV128: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_set @ SV128 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(5661,plain,
! [SV1369: $i,SV130: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV130 @ SV1369 ) )
| ~ ( class_Finite__Set_Ofinite @ SV1369 )
| ~ ( class_Finite__Set_Ofinite @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4408]) ).
thf(5662,plain,
! [SV131: $i] :
( ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV131 ) )
= $true )
| ( ( class_Orderings_Oord @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4409]) ).
thf(5663,plain,
! [SV132: $i] :
( ( ( ~ ( class_LOrder_Ojoin__semilorder @ SV132 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4410]) ).
thf(5664,plain,
! [SV133: $i] :
( ( ( ~ ( class_LOrder_Olorder @ SV133 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4411]) ).
thf(5665,plain,
! [SV134: $i] :
( ( ( ~ ( class_LOrder_Olorder @ SV134 ) )
= $true )
| ( ( class_Orderings_Oord @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4412]) ).
thf(5666,plain,
! [SV135: $i] :
( ( ( ~ ( class_LOrder_Olorder @ SV135 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4413]) ).
thf(5667,plain,
! [SV136: $i] :
( ( ( ~ ( class_LOrder_Olorder @ SV136 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4414]) ).
thf(5668,plain,
! [SV137: $i] :
( ( ( ~ ( class_LOrder_Omeet__semilorder @ SV137 ) )
= $true )
| ( ( class_Orderings_Oord @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4415]) ).
thf(5669,plain,
! [SV138: $i] :
( ( ( ~ ( class_LOrder_Omeet__semilorder @ SV138 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(5670,plain,
! [SV139: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV139 ) )
= $true )
| ( ( class_HOL_Oplus @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4417]) ).
thf(5671,plain,
! [SV140: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV140 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4418]) ).
thf(5672,plain,
! [SV141: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV141 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(5673,plain,
! [SV142: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV142 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(5674,plain,
! [SV143: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV143 ) )
= $true )
| ( ( class_HOL_Ominus @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(5675,plain,
! [SV144: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV144 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4422]) ).
thf(5676,plain,
! [SV145: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV145 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4423]) ).
thf(5677,plain,
! [SV146: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV146 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4424]) ).
thf(5678,plain,
! [SV147: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV147 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4425]) ).
thf(5679,plain,
! [SV148: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV148 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4426]) ).
thf(5680,plain,
! [SV149: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV149 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4427]) ).
thf(5681,plain,
! [SV150: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV150 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4428]) ).
thf(5682,plain,
! [SV151: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV151 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4429]) ).
thf(5683,plain,
! [SV152: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV152 ) )
= $true )
| ( ( class_HOL_Oone @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(5684,plain,
! [SV153: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV153 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4431]) ).
thf(5685,plain,
! [SV154: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV154 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4432]) ).
thf(5686,plain,
! [SV155: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV155 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(5687,plain,
! [SV156: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV156 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4434]) ).
thf(5688,plain,
! [SV157: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV157 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(5689,plain,
! [SV158: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV158 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4436]) ).
thf(5690,plain,
! [SV159: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV159 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(5691,plain,
! [SV160: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV160 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4438]) ).
thf(5692,plain,
! [SV161: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV161 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4439]) ).
thf(5693,plain,
! [SV162: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV162 ) )
= $true )
| ( ( class_HOL_Otimes @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(5694,plain,
! [SV163: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV163 ) )
= $true )
| ( ( class_Numeral_Onumber @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4441]) ).
thf(5695,plain,
! [SV164: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV164 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4442]) ).
thf(5696,plain,
! [SV165: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV165 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(5697,plain,
! [SV166: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV166 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4444]) ).
thf(5698,plain,
! [SV167: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV167 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4445]) ).
thf(5699,plain,
! [SV168: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV168 ) )
= $true )
| ( ( class_HOL_Ozero @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4446]) ).
thf(5700,plain,
! [SV169: $i] :
( ( ( ~ ( class_Numeral_Onumber__ring @ SV169 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(5701,plain,
! [SV170: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV170 ) )
= $true )
| ( ( class_HOL_Ominus @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4448]) ).
thf(5702,plain,
! [SV171: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV171 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(5703,plain,
! [SV172: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV172 ) )
= $true )
| ( ( class_HOL_Ozero @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4450]) ).
thf(5704,plain,
! [SV173: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV173 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4451]) ).
thf(5705,plain,
! [SV174: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV174 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4452]) ).
thf(5706,plain,
! [SV175: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV175 ) )
= $true )
| ( ( class_HOL_Oplus @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4453]) ).
thf(5707,plain,
! [SV176: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV176 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(5708,plain,
! [SV177: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV177 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(5709,plain,
! [SV178: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV178 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4456]) ).
thf(5710,plain,
! [SV179: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV179 ) )
= $true )
| ( ( class_HOL_Oplus @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4457]) ).
thf(5711,plain,
! [SV180: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV180 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(5712,plain,
! [SV181: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV181 ) )
= $true )
| ( ( class_HOL_Otimes @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4459]) ).
thf(5713,plain,
! [SV182: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV182 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(5714,plain,
! [SV183: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV183 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4461]) ).
thf(5715,plain,
! [SV184: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV184 ) )
= $true )
| ( ( class_HOL_Oplus @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4462]) ).
thf(5716,plain,
! [SV185: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV185 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4463]) ).
thf(5717,plain,
! [SV186: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV186 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4464]) ).
thf(5718,plain,
! [SV187: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV187 ) )
= $true )
| ( ( class_HOL_Oplus @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(5719,plain,
! [SV188: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV188 ) )
= $true )
| ( ( class_HOL_Ozero @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(5720,plain,
! [SV189: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV189 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(5721,plain,
! [SV190: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV190 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4468]) ).
thf(5722,plain,
! [SV191: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV191 ) )
= $true )
| ( ( class_HOL_Oplus @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4469]) ).
thf(5723,plain,
! [SV192: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV192 ) )
= $true )
| ( ( class_HOL_Oone @ SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4470]) ).
thf(5724,plain,
! [SV193: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV193 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4471]) ).
thf(5725,plain,
! [SV194: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV194 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4472]) ).
thf(5726,plain,
! [SV195: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV195 ) )
= $true )
| ( ( class_HOL_Otimes @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4473]) ).
thf(5727,plain,
! [SV196: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV196 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4474]) ).
thf(5728,plain,
! [SV197: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV197 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(5729,plain,
! [SV198: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV198 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4476]) ).
thf(5730,plain,
! [SV199: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV199 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(5731,plain,
! [SV200: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV200 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4478]) ).
thf(5732,plain,
! [SV201: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV201 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4479]) ).
thf(5733,plain,
! [SV202: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV202 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4480]) ).
thf(5734,plain,
! [SV203: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV203 ) )
= $true )
| ( ( class_HOL_Oplus @ SV203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4481]) ).
thf(5735,plain,
! [SV204: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV204 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4482]) ).
thf(5736,plain,
! [SV205: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV205 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(5737,plain,
! [SV206: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV206 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4484]) ).
thf(5738,plain,
! [SV207: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV207 ) )
= $true )
| ( ( class_HOL_Ominus @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4485]) ).
thf(5739,plain,
! [SV208: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV208 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV208 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4486]) ).
thf(5740,plain,
! [SV209: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV209 ) )
= $true )
| ( ( class_HOL_Ozero @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(5741,plain,
! [SV210: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV210 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4488]) ).
thf(5742,plain,
! [SV211: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV211 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4489]) ).
thf(5743,plain,
! [SV212: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV212 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4490]) ).
thf(5744,plain,
! [SV213: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV213 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4491]) ).
thf(5745,plain,
! [SV214: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group @ SV214 ) )
= $true )
| ( ( class_Orderings_Oord @ SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4492]) ).
thf(5746,plain,
! [SV215: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV215 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4493]) ).
thf(5747,plain,
! [SV216: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV216 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(5748,plain,
! [SV217: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV217 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4495]) ).
thf(5749,plain,
! [SV218: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV218 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(5750,plain,
! [SV219: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV219 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4497]) ).
thf(5751,plain,
! [SV220: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV220 ) )
= $true )
| ( ( class_HOL_Oplus @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4498]) ).
thf(5752,plain,
! [SV221: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV221 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(5753,plain,
! [SV222: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV222 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4500]) ).
thf(5754,plain,
! [SV223: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV223 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(5755,plain,
! [SV224: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV224 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4502]) ).
thf(5756,plain,
! [SV225: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV225 ) )
= $true )
| ( ( class_Orderings_Oord @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4503]) ).
thf(5757,plain,
! [SV226: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV226 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(5758,plain,
! [SV227: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV227 ) )
= $true )
| ( ( class_HOL_Ominus @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(5759,plain,
! [SV228: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV228 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4506]) ).
thf(5760,plain,
! [SV229: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV229 ) )
= $true )
| ( ( class_HOL_Ozero @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4507]) ).
thf(5761,plain,
! [SV230: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV230 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4508]) ).
thf(5762,plain,
! [SV231: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV231 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(5763,plain,
! [SV232: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV232 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4510]) ).
thf(5764,plain,
! [SV233: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV233 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4511]) ).
thf(5765,plain,
! [SV234: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV234 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4512]) ).
thf(5766,plain,
! [SV235: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV235 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4513]) ).
thf(5767,plain,
! [SV236: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV236 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV236 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4514]) ).
thf(5768,plain,
! [SV237: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV237 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4515]) ).
thf(5769,plain,
! [SV238: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV238 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4516]) ).
thf(5770,plain,
! [SV239: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV239 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4517]) ).
thf(5771,plain,
! [SV240: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV240 ) )
= $true )
| ( ( class_HOL_Oplus @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(5772,plain,
! [SV241: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV241 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(5773,plain,
! [SV242: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV242 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4520]) ).
thf(5774,plain,
! [SV243: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV243 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4521]) ).
thf(5775,plain,
! [SV244: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV244 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4522]) ).
thf(5776,plain,
! [SV245: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV245 ) )
= $true )
| ( ( class_HOL_Ominus @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4523]) ).
thf(5777,plain,
! [SV246: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV246 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(5778,plain,
! [SV247: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV247 ) )
= $true )
| ( ( class_HOL_Ozero @ SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(5779,plain,
! [SV248: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV248 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4526]) ).
thf(5780,plain,
! [SV249: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV249 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4527]) ).
thf(5781,plain,
! [SV250: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV250 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4528]) ).
thf(5782,plain,
! [SV251: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV251 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(5783,plain,
! [SV252: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__join @ SV252 ) )
= $true )
| ( ( class_Orderings_Oord @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(5784,plain,
! [SV253: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV253 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4531]) ).
thf(5785,plain,
! [SV254: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV254 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4532]) ).
thf(5786,plain,
! [SV255: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV255 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(5787,plain,
! [SV256: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV256 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4534]) ).
thf(5788,plain,
! [SV257: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV257 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4535]) ).
thf(5789,plain,
! [SV258: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV258 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(5790,plain,
! [SV259: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV259 ) )
= $true )
| ( ( class_HOL_Oplus @ SV259 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4537]) ).
thf(5791,plain,
! [SV260: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV260 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4538]) ).
thf(5792,plain,
! [SV261: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV261 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4539]) ).
thf(5793,plain,
! [SV262: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV262 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4540]) ).
thf(5794,plain,
! [SV263: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV263 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4541]) ).
thf(5795,plain,
! [SV264: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV264 ) )
= $true )
| ( ( class_HOL_Ominus @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(5796,plain,
! [SV265: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV265 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV265 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(5797,plain,
! [SV266: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV266 ) )
= $true )
| ( ( class_HOL_Ozero @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(5798,plain,
! [SV267: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV267 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4545]) ).
thf(5799,plain,
! [SV268: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV268 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV268 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(5800,plain,
! [SV269: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV269 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4547]) ).
thf(5801,plain,
! [SV270: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV270 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(5802,plain,
! [SV271: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ SV271 ) )
= $true )
| ( ( class_Orderings_Oord @ SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4549]) ).
thf(5803,plain,
! [SV272: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV272 ) )
= $true )
| ( ( class_HOL_Oone @ SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4550]) ).
thf(5804,plain,
! [SV273: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV273 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4551]) ).
thf(5805,plain,
! [SV274: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV274 ) )
= $true )
| ( ( class_HOL_Otimes @ SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4552]) ).
thf(5806,plain,
! [SV275: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV275 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4553]) ).
thf(5807,plain,
! [SV276: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV276 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4554]) ).
thf(5808,plain,
! [SV277: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV277 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4555]) ).
thf(5809,plain,
! [SV278: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV278 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4556]) ).
thf(5810,plain,
! [SV279: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV279 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4557]) ).
thf(5811,plain,
! [SV280: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV280 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4558]) ).
thf(5812,plain,
! [SV281: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV281 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(5813,plain,
! [SV282: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV282 ) )
= $true )
| ( ( class_Orderings_Oord @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(5814,plain,
! [SV283: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV283 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4561]) ).
thf(5815,plain,
! [SV284: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV284 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4562]) ).
thf(5816,plain,
! [SV285: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV285 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV285 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(5817,plain,
! [SV286: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV286 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV286 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4564]) ).
thf(5818,plain,
! [SV287: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV287 ) )
= $true )
| ( ( class_HOL_Oplus @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(5819,plain,
! [SV288: $i] :
( ( ( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV288 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4566]) ).
thf(5820,plain,
! [SV289: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV289 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4567]) ).
thf(5821,plain,
! [SV290: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV290 ) )
= $true )
| ( ( class_HOL_Ominus @ SV290 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4568]) ).
thf(5822,plain,
! [SV291: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV291 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV291 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(5823,plain,
! [SV292: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV292 ) )
= $true )
| ( ( class_Orderings_Oord @ SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4570]) ).
thf(5824,plain,
! [SV293: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV293 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV293 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(5825,plain,
! [SV294: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV294 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4572]) ).
thf(5826,plain,
! [SV295: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV295 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4573]) ).
thf(5827,plain,
! [SV296: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV296 ) )
= $true )
| ( ( class_HOL_Ozero @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4574]) ).
thf(5828,plain,
! [SV297: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV297 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4575]) ).
thf(5829,plain,
! [SV298: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV298 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4576]) ).
thf(5830,plain,
! [SV299: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV299 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4577]) ).
thf(5831,plain,
! [SV300: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV300 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4578]) ).
thf(5832,plain,
! [SV301: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV301 ) )
= $true )
| ( ( class_HOL_Oplus @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(5833,plain,
! [SV302: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV302 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4580]) ).
thf(5834,plain,
! [SV303: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV303 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV303 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(5835,plain,
! [SV304: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV304 ) )
= $true )
| ( ( class_Orderings_Oord @ SV304 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(5836,plain,
! [SV305: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV305 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV305 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(5837,plain,
! [SV306: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV306 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4584]) ).
thf(5838,plain,
! [SV307: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV307 ) )
= $true )
| ( ( class_HOL_Oplus @ SV307 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4585]) ).
thf(5839,plain,
! [SV308: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV308 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV308 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4586]) ).
thf(5840,plain,
! [SV309: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV309 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV309 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4587]) ).
thf(5841,plain,
! [SV310: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV310 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV310 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4588]) ).
thf(5842,plain,
! [SV311: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV311 ) )
= $true )
| ( ( class_Orderings_Oord @ SV311 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4589]) ).
thf(5843,plain,
! [SV312: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV312 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV312 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4590]) ).
thf(5844,plain,
! [SV313: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV313 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4591]) ).
thf(5845,plain,
! [SV314: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV314 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV314 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4592]) ).
thf(5846,plain,
! [SV315: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV315 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV315 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4593]) ).
thf(5847,plain,
! [SV316: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV316 ) )
= $true )
| ( ( class_HOL_Oplus @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4594]) ).
thf(5848,plain,
! [SV317: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV317 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV317 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4595]) ).
thf(5849,plain,
! [SV318: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV318 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4596]) ).
thf(5850,plain,
! [SV319: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV319 ) )
= $true )
| ( ( class_Orderings_Oord @ SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4597]) ).
thf(5851,plain,
! [SV320: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4598]) ).
thf(5852,plain,
! [SV321: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV321 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4599]) ).
thf(5853,plain,
! [SV322: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV322 ) )
= $true )
| ( ( class_HOL_Oplus @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4600]) ).
thf(5854,plain,
! [SV323: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV323 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV323 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4601]) ).
thf(5855,plain,
! [SV324: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV324 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV324 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(5856,plain,
! [SV325: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV325 ) )
= $true )
| ( ( class_HOL_Oplus @ SV325 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(5857,plain,
! [SV326: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__mult @ SV326 ) )
= $true )
| ( ( class_HOL_Otimes @ SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4604]) ).
thf(5858,plain,
! [SV327: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV327 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4605]) ).
thf(5859,plain,
! [SV328: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV328 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4606]) ).
thf(5860,plain,
! [SV329: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV329 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(5861,plain,
! [SV330: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV330 ) )
= $true )
| ( ( class_Orderings_Oord @ SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4608]) ).
thf(5862,plain,
! [SV331: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV331 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4609]) ).
thf(5863,plain,
! [SV332: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV332 ) )
= $true )
| ( ( class_Orderings_Oord @ SV332 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4610]) ).
thf(5864,plain,
! [SV333: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV333 ) )
= $true )
| ( ( class_Nat_Opower @ SV333 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4611]) ).
thf(5865,plain,
! [SV334: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV334 ) )
= $true )
| ( ( class_HOL_Ozero @ SV334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4612]) ).
thf(5866,plain,
! [SV335: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV335 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4613]) ).
thf(5867,plain,
! [SV336: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV336 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV336 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(5868,plain,
! [SV337: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV337 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4615]) ).
thf(5869,plain,
! [SV338: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV338 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV338 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4616]) ).
thf(5870,plain,
! [SV339: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV339 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4617]) ).
thf(5871,plain,
! [SV340: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV340 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4618]) ).
thf(5872,plain,
! [SV341: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV341 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4619]) ).
thf(5873,plain,
! [SV342: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV342 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4620]) ).
thf(5874,plain,
! [SV343: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV343 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4621]) ).
thf(5875,plain,
! [SV344: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV344 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(5876,plain,
! [SV345: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV345 ) )
= $true )
| ( ( class_HOL_Oone @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4623]) ).
thf(5877,plain,
! [SV346: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV346 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4624]) ).
thf(5878,plain,
! [SV347: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV347 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV347 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4625]) ).
thf(5879,plain,
! [SV348: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV348 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV348 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4626]) ).
thf(5880,plain,
! [SV349: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV349 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV349 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4627]) ).
thf(5881,plain,
! [SV350: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV350 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV350 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4628]) ).
thf(5882,plain,
! [SV351: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV351 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV351 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4629]) ).
thf(5883,plain,
! [SV352: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV352 ) )
= $true )
| ( ( class_HOL_Oplus @ SV352 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4630]) ).
thf(5884,plain,
! [SV353: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV353 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV353 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(5885,plain,
! [SV354: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV354 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV354 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(5886,plain,
! [SV355: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV355 ) )
= $true )
| ( ( class_HOL_Otimes @ SV355 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4633]) ).
thf(5887,plain,
! [SV356: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV356 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV356 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4634]) ).
thf(5888,plain,
! [SV357: $i] :
( ( ( ~ ( class_Power_Orecpower @ SV357 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(5889,plain,
! [SV358: $i] :
( ( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV358 ) )
= $true )
| ( ( class_HOL_Ozero @ SV358 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4636]) ).
thf(5890,plain,
! [SV359: $i] :
( ( ( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV359 ) )
= $true )
| ( ( class_HOL_Oone @ SV359 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4637]) ).
thf(5891,plain,
! [SV360: $i] :
( ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV360 ) )
= $true )
| ( ( class_HOL_Ominus @ SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(5892,plain,
! [SV361: $i] :
( ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV361 ) )
= $true )
| ( ( class_Orderings_Oord @ SV361 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4639]) ).
thf(5893,plain,
! [SV362: $i] :
( ( ( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ SV362 ) )
= $true )
| ( ( class_HOL_Ozero @ SV362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(5894,plain,
! [SV363: $i] :
( ( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV363 ) )
= $true )
| ( ( class_HOL_Ozero @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(5895,plain,
! [SV364: $i] :
( ( ( ~ ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV364 ) )
= $true )
| ( ( class_HOL_Otimes @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(5896,plain,
! [SV365: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV365 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(5897,plain,
! [SV366: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV366 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4644]) ).
thf(5898,plain,
! [SV367: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV367 ) )
= $true )
| ( ( class_HOL_Oplus @ SV367 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4645]) ).
thf(5899,plain,
! [SV368: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV368 ) )
= $true )
| ( ( class_HOL_Ozero @ SV368 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4646]) ).
thf(5900,plain,
! [SV369: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV369 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV369 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(5901,plain,
! [SV370: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV370 ) )
= $true )
| ( ( class_HOL_Ominus @ SV370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(5902,plain,
! [SV371: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV371 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(5903,plain,
! [SV372: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV372 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV372 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4650]) ).
thf(5904,plain,
! [SV373: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV373 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV373 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4651]) ).
thf(5905,plain,
! [SV374: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV374 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4652]) ).
thf(5906,plain,
! [SV375: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV375 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV375 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4653]) ).
thf(5907,plain,
! [SV376: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV376 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV376 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4654]) ).
thf(5908,plain,
! [SV377: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV377 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4655]) ).
thf(5909,plain,
! [SV378: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV378 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(5910,plain,
! [SV379: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV379 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV379 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(5911,plain,
! [SV380: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV380 ) )
= $true )
| ( ( class_HOL_Otimes @ SV380 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4658]) ).
thf(5912,plain,
! [SV381: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV381 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4659]) ).
thf(5913,plain,
! [SV382: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV382 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(5914,plain,
! [SV383: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV383 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4661]) ).
thf(5915,plain,
! [SV384: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV384 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV384 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4662]) ).
thf(5916,plain,
! [SV385: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV385 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(5917,plain,
! [SV386: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV386 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4664]) ).
thf(5918,plain,
! [SV387: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV387 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV387 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4665]) ).
thf(5919,plain,
! [SV388: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV388 ) )
= $true )
| ( ( class_HOL_Otimes @ SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4666]) ).
thf(5920,plain,
! [SV389: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV389 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV389 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4667]) ).
thf(5921,plain,
! [SV390: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV390 ) )
= $true )
| ( ( class_HOL_Ozero @ SV390 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4668]) ).
thf(5922,plain,
! [SV391: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV391 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV391 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4669]) ).
thf(5923,plain,
! [SV392: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV392 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV392 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(5924,plain,
! [SV393: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV393 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4671]) ).
thf(5925,plain,
! [SV394: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV394 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4672]) ).
thf(5926,plain,
! [SV395: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV395 ) )
= $true )
| ( ( class_HOL_Oplus @ SV395 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4673]) ).
thf(5927,plain,
! [SV396: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV396 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV396 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(5928,plain,
! [SV397: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV397 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV397 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(5929,plain,
! [SV398: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV398 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV398 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(5930,plain,
! [SV399: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV399 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV399 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(5931,plain,
! [SV400: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV400 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4678]) ).
thf(5932,plain,
! [SV401: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV401 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV401 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4679]) ).
thf(5933,plain,
! [SV402: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV402 ) )
= $true )
| ( ( class_HOL_Oone @ SV402 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4680]) ).
thf(5934,plain,
! [SV403: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV403 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV403 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4681]) ).
thf(5935,plain,
! [SV404: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV404 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV404 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4682]) ).
thf(5936,plain,
! [SV405: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV405 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV405 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4683]) ).
thf(5937,plain,
! [SV406: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV406 ) )
= $true )
| ( ( class_HOL_Ominus @ SV406 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4684]) ).
thf(5938,plain,
! [SV407: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV407 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV407 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4685]) ).
thf(5939,plain,
! [SV408: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV408 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV408 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4686]) ).
thf(5940,plain,
! [SV409: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV409 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV409 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4687]) ).
thf(5941,plain,
! [SV410: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV410 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4688]) ).
thf(5942,plain,
! [SV411: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV411 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4689]) ).
thf(5943,plain,
! [SV412: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV412 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV412 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4690]) ).
thf(5944,plain,
! [SV413: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV413 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV413 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4691]) ).
thf(5945,plain,
! [SV414: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV414 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4692]) ).
thf(5946,plain,
! [SV415: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV415 ) )
= $true )
| ( ( class_HOL_Oplus @ SV415 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4693]) ).
thf(5947,plain,
! [SV416: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV416 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV416 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4694]) ).
thf(5948,plain,
! [SV417: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV417 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4695]) ).
thf(5949,plain,
! [SV418: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV418 ) )
= $true )
| ( ( class_HOL_Otimes @ SV418 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(5950,plain,
! [SV419: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV419 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4697]) ).
thf(5951,plain,
! [SV420: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV420 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV420 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4698]) ).
thf(5952,plain,
! [SV421: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV421 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV421 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(5953,plain,
! [SV422: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV422 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV422 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4700]) ).
thf(5954,plain,
! [SV423: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV423 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV423 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(5955,plain,
! [SV424: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV424 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV424 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(5956,plain,
! [SV425: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV425 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV425 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4703]) ).
thf(5957,plain,
! [SV426: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV426 ) )
= $true )
| ( ( class_HOL_Oplus @ SV426 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4704]) ).
thf(5958,plain,
! [SV427: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV427 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV427 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4705]) ).
thf(5959,plain,
! [SV428: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV428 ) )
= $true )
| ( ( class_HOL_Otimes @ SV428 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4706]) ).
thf(5960,plain,
! [SV429: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV429 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4707]) ).
thf(5961,plain,
! [SV430: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ SV430 ) )
= $true )
| ( ( class_HOL_Ozero @ SV430 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4708]) ).
thf(5962,plain,
! [SV431: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV431 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4709]) ).
thf(5963,plain,
! [SV432: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV432 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV432 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4710]) ).
thf(5964,plain,
! [SV433: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV433 ) )
= $true )
| ( ( class_HOL_Oplus @ SV433 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4711]) ).
thf(5965,plain,
! [SV434: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV434 ) )
= $true )
| ( ( class_HOL_Ozero @ SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4712]) ).
thf(5966,plain,
! [SV435: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV435 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4713]) ).
thf(5967,plain,
! [SV436: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV436 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4714]) ).
thf(5968,plain,
! [SV437: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV437 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV437 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(5969,plain,
! [SV438: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV438 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV438 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4716]) ).
thf(5970,plain,
! [SV439: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV439 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4717]) ).
thf(5971,plain,
! [SV440: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV440 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV440 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(5972,plain,
! [SV441: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV441 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV441 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4719]) ).
thf(5973,plain,
! [SV442: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV442 ) )
= $true )
| ( ( class_HOL_Otimes @ SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4720]) ).
thf(5974,plain,
! [SV443: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV443 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV443 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4721]) ).
thf(5975,plain,
! [SV444: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV444 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV444 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4722]) ).
thf(5976,plain,
! [SV445: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV445 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV445 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4723]) ).
thf(5977,plain,
! [SV446: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV446 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV446 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(5978,plain,
! [SV447: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV447 ) )
= $true )
| ( ( class_HOL_Ozero @ SV447 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4725]) ).
thf(5979,plain,
! [SV448: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV448 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4726]) ).
thf(5980,plain,
! [SV449: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV449 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4727]) ).
thf(5981,plain,
! [SV450: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV450 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4728]) ).
thf(5982,plain,
! [SV451: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV451 ) )
= $true )
| ( ( class_HOL_Oplus @ SV451 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4729]) ).
thf(5983,plain,
! [SV452: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV452 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV452 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(5984,plain,
! [SV453: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV453 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4731]) ).
thf(5985,plain,
! [SV454: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV454 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4732]) ).
thf(5986,plain,
! [SV455: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV455 ) )
= $true )
| ( ( class_HOL_Oone @ SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4733]) ).
thf(5987,plain,
! [SV456: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV456 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4734]) ).
thf(5988,plain,
! [SV457: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV457 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV457 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4735]) ).
thf(5989,plain,
! [SV458: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV458 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV458 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(5990,plain,
! [SV459: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV459 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV459 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(5991,plain,
! [SV460: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV460 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(5992,plain,
! [SV461: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV461 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV461 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4739]) ).
thf(5993,plain,
! [SV462: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV462 ) )
= $true )
| ( ( class_HOL_Otimes @ SV462 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4740]) ).
thf(5994,plain,
! [SV463: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV463 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV463 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4741]) ).
thf(5995,plain,
! [SV464: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV464 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV464 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(5996,plain,
! [SV465: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV465 ) )
= $true )
| ( ( class_HOL_Ozero @ SV465 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4743]) ).
thf(5997,plain,
! [SV466: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV466 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV466 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(5998,plain,
! [SV467: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV467 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV467 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4745]) ).
thf(5999,plain,
! [SV468: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV468 ) )
= $true )
| ( ( class_HOL_Oplus @ SV468 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4746]) ).
thf(6000,plain,
! [SV469: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV469 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV469 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4747]) ).
thf(6001,plain,
! [SV470: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV470 ) )
= $true )
| ( ( class_HOL_Oone @ SV470 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(6002,plain,
! [SV471: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV471 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4749]) ).
thf(6003,plain,
! [SV472: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV472 ) )
= $true )
| ( ( class_HOL_Otimes @ SV472 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(6004,plain,
! [SV473: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV473 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(6005,plain,
! [SV474: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV474 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV474 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(6006,plain,
! [SV475: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV475 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV475 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(6007,plain,
! [SV476: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV476 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV476 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4754]) ).
thf(6008,plain,
! [SV477: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV477 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV477 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(6009,plain,
! [SV478: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV478 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV478 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(6010,plain,
! [SV479: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV479 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(6011,plain,
! [SV480: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV480 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV480 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4758]) ).
thf(6012,plain,
! [SV481: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV481 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV481 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4759]) ).
thf(6013,plain,
! [SV482: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV482 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4760]) ).
thf(6014,plain,
! [SV483: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV483 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV483 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(6015,plain,
! [SV484: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV484 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV484 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(6016,plain,
! [SV485: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV485 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV485 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4763]) ).
thf(6017,plain,
! [SV486: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV486 ) )
= $true )
| ( ( class_HOL_Ozero @ SV486 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(6018,plain,
! [SV487: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV487 ) )
= $true )
| ( ( class_HOL_Oinverse @ SV487 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(6019,plain,
! [SV488: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV488 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV488 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4766]) ).
thf(6020,plain,
! [SV489: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV489 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4767]) ).
thf(6021,plain,
! [SV490: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV490 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV490 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4768]) ).
thf(6022,plain,
! [SV491: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV491 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4769]) ).
thf(6023,plain,
! [SV492: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV492 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV492 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4770]) ).
thf(6024,plain,
! [SV493: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV493 ) )
= $true )
| ( ( class_HOL_Oone @ SV493 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4771]) ).
thf(6025,plain,
! [SV494: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV494 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4772]) ).
thf(6026,plain,
! [SV495: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV495 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV495 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4773]) ).
thf(6027,plain,
! [SV496: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV496 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV496 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(6028,plain,
! [SV497: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV497 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV497 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4775]) ).
thf(6029,plain,
! [SV498: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV498 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV498 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4776]) ).
thf(6030,plain,
! [SV499: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV499 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4777]) ).
thf(6031,plain,
! [SV500: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV500 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV500 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(6032,plain,
! [SV501: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV501 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV501 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(6033,plain,
! [SV502: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV502 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV502 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(6034,plain,
! [SV503: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV503 ) )
= $true )
| ( ( class_HOL_Otimes @ SV503 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4781]) ).
thf(6035,plain,
! [SV504: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV504 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV504 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4782]) ).
thf(6036,plain,
! [SV505: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV505 ) )
= $true )
| ( ( class_HOL_Ozero @ SV505 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(6037,plain,
! [SV506: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV506 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV506 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(6038,plain,
! [SV507: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV507 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4785]) ).
thf(6039,plain,
! [SV508: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV508 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(6040,plain,
! [SV509: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV509 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV509 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(6041,plain,
! [SV510: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV510 ) )
= $true )
| ( ( class_HOL_Oplus @ SV510 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4788]) ).
thf(6042,plain,
! [SV511: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV511 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV511 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4789]) ).
thf(6043,plain,
! [SV512: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV512 ) )
= $true )
| ( ( class_HOL_Oinverse @ SV512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4790]) ).
thf(6044,plain,
! [SV513: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV513 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV513 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(6045,plain,
! [SV514: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV514 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(6046,plain,
! [SV515: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV515 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV515 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4793]) ).
thf(6047,plain,
! [SV516: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV516 ) )
= $true )
| ( ( class_HOL_Ominus @ SV516 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4794]) ).
thf(6048,plain,
! [SV517: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV517 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV517 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4795]) ).
thf(6049,plain,
! [SV518: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV518 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV518 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4796]) ).
thf(6050,plain,
! [SV519: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV519 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV519 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4797]) ).
thf(6051,plain,
! [SV520: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV520 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4798]) ).
thf(6052,plain,
! [SV521: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV521 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV521 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4799]) ).
thf(6053,plain,
! [SV522: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV522 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV522 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4800]) ).
thf(6054,plain,
! [SV523: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV523 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV523 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4801]) ).
thf(6055,plain,
! [SV524: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV524 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV524 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4802]) ).
thf(6056,plain,
! [SV525: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV525 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV525 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4803]) ).
thf(6057,plain,
! [SV526: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV526 ) )
= $true )
| ( ( class_HOL_Oone @ SV526 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4804]) ).
thf(6058,plain,
! [SV527: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV527 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV527 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4805]) ).
thf(6059,plain,
! [SV528: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV528 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV528 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4806]) ).
thf(6060,plain,
! [SV529: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV529 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV529 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4807]) ).
thf(6061,plain,
! [SV530: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV530 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV530 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(6062,plain,
! [SV531: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV531 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV531 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4809]) ).
thf(6063,plain,
! [SV532: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV532 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV532 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(6064,plain,
! [SV533: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV533 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV533 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(6065,plain,
! [SV534: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV534 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV534 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4812]) ).
thf(6066,plain,
! [SV535: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV535 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4813]) ).
thf(6067,plain,
! [SV536: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV536 ) )
= $true )
| ( ( class_HOL_Otimes @ SV536 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4814]) ).
thf(6068,plain,
! [SV537: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV537 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV537 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4815]) ).
thf(6069,plain,
! [SV538: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV538 ) )
= $true )
| ( ( class_HOL_Ozero @ SV538 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4816]) ).
thf(6070,plain,
! [SV539: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV539 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4817]) ).
thf(6071,plain,
! [SV540: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV540 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV540 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4818]) ).
thf(6072,plain,
! [SV541: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV541 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV541 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4819]) ).
thf(6073,plain,
! [SV542: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV542 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV542 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(6074,plain,
! [SV543: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV543 ) )
= $true )
| ( ( class_HOL_Oplus @ SV543 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(6075,plain,
! [SV544: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV544 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV544 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4822]) ).
thf(6076,plain,
! [SV545: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV545 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV545 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4823]) ).
thf(6077,plain,
! [SV546: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV546 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4824]) ).
thf(6078,plain,
! [SV547: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV547 ) )
= $true )
| ( ( class_HOL_Ominus @ SV547 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4825]) ).
thf(6079,plain,
! [SV548: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV548 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV548 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4826]) ).
thf(6080,plain,
! [SV549: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV549 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4827]) ).
thf(6081,plain,
! [SV550: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV550 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV550 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4828]) ).
thf(6082,plain,
! [SV551: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV551 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV551 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4829]) ).
thf(6083,plain,
! [SV552: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV552 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV552 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4830]) ).
thf(6084,plain,
! [SV553: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV553 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV553 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4831]) ).
thf(6085,plain,
! [SV554: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV554 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV554 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(6086,plain,
! [SV555: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV555 ) )
= $true )
| ( ( class_Orderings_Oord @ SV555 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4833]) ).
thf(6087,plain,
! [SV556: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV556 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4834]) ).
thf(6088,plain,
! [SV557: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV557 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV557 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4835]) ).
thf(6089,plain,
! [SV558: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV558 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV558 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4836]) ).
thf(6090,plain,
! [SV559: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV559 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV559 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4837]) ).
thf(6091,plain,
! [SV560: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV560 ) )
= $true )
| ( ( class_HOL_Otimes @ SV560 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4838]) ).
thf(6092,plain,
! [SV561: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV561 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV561 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4839]) ).
thf(6093,plain,
! [SV562: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV562 ) )
= $true )
| ( ( class_HOL_Ozero @ SV562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(6094,plain,
! [SV563: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV563 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(6095,plain,
! [SV564: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV564 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(6096,plain,
! [SV565: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV565 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV565 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(6097,plain,
! [SV566: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV566 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(6098,plain,
! [SV567: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV567 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV567 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(6099,plain,
! [SV568: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV568 ) )
= $true )
| ( ( class_HOL_Oplus @ SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4846]) ).
thf(6100,plain,
! [SV569: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV569 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4847]) ).
thf(6101,plain,
! [SV570: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV570 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV570 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4848]) ).
thf(6102,plain,
! [SV571: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV571 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV571 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4849]) ).
thf(6103,plain,
! [SV572: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV572 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4850]) ).
thf(6104,plain,
! [SV573: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV573 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV573 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4851]) ).
thf(6105,plain,
! [SV574: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV574 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4852]) ).
thf(6106,plain,
! [SV575: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV575 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV575 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4853]) ).
thf(6107,plain,
! [SV576: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV576 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV576 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(6108,plain,
! [SV577: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV577 ) )
= $true )
| ( ( class_HOL_Ominus @ SV577 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(6109,plain,
! [SV578: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV578 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV578 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4856]) ).
thf(6110,plain,
! [SV579: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV579 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV579 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4857]) ).
thf(6111,plain,
! [SV580: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV580 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV580 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4858]) ).
thf(6112,plain,
! [SV581: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV581 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV581 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4859]) ).
thf(6113,plain,
! [SV582: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV582 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV582 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4860]) ).
thf(6114,plain,
! [SV583: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV583 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV583 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(6115,plain,
! [SV584: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV584 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV584 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(6116,plain,
! [SV585: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV585 ) )
= $true )
| ( ( class_HOL_Oplus @ SV585 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4863]) ).
thf(6117,plain,
! [SV586: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV586 ) )
= $true )
| ( ( class_HOL_Ozero @ SV586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4864]) ).
thf(6118,plain,
! [SV587: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV587 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV587 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4865]) ).
thf(6119,plain,
! [SV588: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV588 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV588 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(6120,plain,
! [SV589: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV589 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV589 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(6121,plain,
! [SV590: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV590 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV590 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(6122,plain,
! [SV591: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV591 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV591 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4869]) ).
thf(6123,plain,
! [SV592: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV592 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV592 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4870]) ).
thf(6124,plain,
! [SV593: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV593 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV593 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4871]) ).
thf(6125,plain,
! [SV594: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV594 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV594 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4872]) ).
thf(6126,plain,
! [SV595: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV595 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV595 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(6127,plain,
! [SV596: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV596 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV596 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(6128,plain,
! [SV597: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV597 ) )
= $true )
| ( ( class_Orderings_Oord @ SV597 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(6129,plain,
! [SV598: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV598 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV598 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4876]) ).
thf(6130,plain,
! [SV599: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV599 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV599 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4877]) ).
thf(6131,plain,
! [SV600: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV600 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV600 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4878]) ).
thf(6132,plain,
! [SV601: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV601 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV601 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4879]) ).
thf(6133,plain,
! [SV602: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV602 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV602 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4880]) ).
thf(6134,plain,
! [SV603: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV603 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV603 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4881]) ).
thf(6135,plain,
! [SV604: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV604 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV604 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4882]) ).
thf(6136,plain,
! [SV605: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV605 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV605 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4883]) ).
thf(6137,plain,
! [SV606: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV606 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4884]) ).
thf(6138,plain,
! [SV607: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV607 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV607 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4885]) ).
thf(6139,plain,
! [SV608: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV608 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV608 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4886]) ).
thf(6140,plain,
! [SV609: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV609 ) )
= $true )
| ( ( class_HOL_Otimes @ SV609 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(6141,plain,
! [SV610: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV610 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV610 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4888]) ).
thf(6142,plain,
! [SV611: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV611 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV611 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4889]) ).
thf(6143,plain,
! [SV612: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV612 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4890]) ).
thf(6144,plain,
! [SV613: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV613 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV613 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4891]) ).
thf(6145,plain,
! [SV614: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV614 ) )
= $true )
| ( ( class_HOL_Oinverse @ SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4892]) ).
thf(6146,plain,
! [SV615: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV615 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV615 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4893]) ).
thf(6147,plain,
! [SV616: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV616 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV616 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4894]) ).
thf(6148,plain,
! [SV617: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV617 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV617 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4895]) ).
thf(6149,plain,
! [SV618: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV618 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV618 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4896]) ).
thf(6150,plain,
! [SV619: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV619 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV619 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4897]) ).
thf(6151,plain,
! [SV620: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV620 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV620 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4898]) ).
thf(6152,plain,
! [SV621: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV621 ) )
= $true )
| ( ( class_HOL_Oone @ SV621 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4899]) ).
thf(6153,plain,
! [SV622: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV622 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV622 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4900]) ).
thf(6154,plain,
! [SV623: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV623 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4901]) ).
thf(6155,plain,
! [SV624: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV624 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV624 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4902]) ).
thf(6156,plain,
! [SV625: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV625 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV625 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(6157,plain,
! [SV626: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV626 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV626 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4904]) ).
thf(6158,plain,
! [SV627: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV627 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV627 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(6159,plain,
! [SV628: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV628 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(6160,plain,
! [SV629: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV629 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV629 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4907]) ).
thf(6161,plain,
! [SV630: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV630 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV630 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4908]) ).
thf(6162,plain,
! [SV631: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV631 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV631 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4909]) ).
thf(6163,plain,
! [SV632: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV632 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV632 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4910]) ).
thf(6164,plain,
! [SV633: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV633 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV633 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4911]) ).
thf(6165,plain,
! [SV634: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV634 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV634 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4912]) ).
thf(6166,plain,
! [SV635: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV635 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV635 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4913]) ).
thf(6167,plain,
! [SV636: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV636 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV636 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(6168,plain,
! [SV637: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV637 ) )
= $true )
| ( ( class_HOL_Oplus @ SV637 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4915]) ).
thf(6169,plain,
! [SV638: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV638 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV638 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4916]) ).
thf(6170,plain,
! [SV639: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV639 ) )
= $true )
| ( ( class_HOL_Ozero @ SV639 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4917]) ).
thf(6171,plain,
! [SV640: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV640 ) )
= $true )
| ( ( class_HOL_Otimes @ SV640 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4918]) ).
thf(6172,plain,
! [SV641: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV641 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV641 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4919]) ).
thf(6173,plain,
! [SV642: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV642 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV642 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(6174,plain,
! [SV643: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV643 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV643 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(6175,plain,
! [SV644: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV644 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV644 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(6176,plain,
! [SV645: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV645 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV645 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(6177,plain,
! [SV646: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV646 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV646 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4924]) ).
thf(6178,plain,
! [SV647: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV647 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV647 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4925]) ).
thf(6179,plain,
! [SV648: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV648 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV648 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(6180,plain,
! [SV649: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV649 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV649 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4927]) ).
thf(6181,plain,
! [SV650: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV650 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV650 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4928]) ).
thf(6182,plain,
! [SV651: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV651 ) )
= $true )
| ( ( class_Ring__and__Field_Olordered__ring @ SV651 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4929]) ).
thf(6183,plain,
! [SV652: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV652 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV652 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4930]) ).
thf(6184,plain,
! [SV653: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV653 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV653 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(6185,plain,
! [SV654: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV654 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV654 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4932]) ).
thf(6186,plain,
! [SV655: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV655 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV655 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4933]) ).
thf(6187,plain,
! [SV656: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV656 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV656 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4934]) ).
thf(6188,plain,
! [SV657: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV657 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV657 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(6189,plain,
! [SV658: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV658 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV658 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4936]) ).
thf(6190,plain,
! [SV659: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV659 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV659 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4937]) ).
thf(6191,plain,
! [SV660: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV660 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV660 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4938]) ).
thf(6192,plain,
! [SV661: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV661 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV661 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4939]) ).
thf(6193,plain,
! [SV662: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV662 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV662 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4940]) ).
thf(6194,plain,
! [SV663: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV663 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV663 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4941]) ).
thf(6195,plain,
! [SV664: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV664 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV664 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4942]) ).
thf(6196,plain,
! [SV665: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV665 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV665 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4943]) ).
thf(6197,plain,
! [SV666: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV666 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV666 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4944]) ).
thf(6198,plain,
! [SV667: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV667 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV667 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4945]) ).
thf(6199,plain,
! [SV668: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV668 ) )
= $true )
| ( ( class_Orderings_Oord @ SV668 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4946]) ).
thf(6200,plain,
! [SV669: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV669 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV669 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4947]) ).
thf(6201,plain,
! [SV670: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV670 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV670 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4948]) ).
thf(6202,plain,
! [SV671: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV671 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV671 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4949]) ).
thf(6203,plain,
! [SV672: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV672 ) )
= $true )
| ( ( class_HOL_Ominus @ SV672 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4950]) ).
thf(6204,plain,
! [SV673: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV673 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV673 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4951]) ).
thf(6205,plain,
! [SV674: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV674 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV674 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4952]) ).
thf(6206,plain,
! [SV675: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV675 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV675 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4953]) ).
thf(6207,plain,
! [SV676: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV676 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV676 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(6208,plain,
! [SV677: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV677 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV677 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(6209,plain,
! [SV678: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV678 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV678 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4956]) ).
thf(6210,plain,
! [SV679: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV679 ) )
= $true )
| ( ( class_HOL_Oone @ SV679 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4957]) ).
thf(6211,plain,
! [SV680: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV680 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV680 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4958]) ).
thf(6212,plain,
! [SV681: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV681 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV681 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4959]) ).
thf(6213,plain,
! [SV682: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV682 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV682 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4960]) ).
thf(6214,plain,
! [SV683: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV683 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV683 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(6215,plain,
! [SV684: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV684 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4962]) ).
thf(6216,plain,
! [SV685: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV685 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV685 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4963]) ).
thf(6217,plain,
! [SV686: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV686 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV686 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4964]) ).
thf(6218,plain,
! [SV687: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV687 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV687 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4965]) ).
thf(6219,plain,
! [SV688: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV688 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV688 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4966]) ).
thf(6220,plain,
! [SV689: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV689 ) )
= $true )
| ( ( class_HOL_Otimes @ SV689 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4967]) ).
thf(6221,plain,
! [SV690: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV690 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV690 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4968]) ).
thf(6222,plain,
! [SV691: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV691 ) )
= $true )
| ( ( class_HOL_Ozero @ SV691 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4969]) ).
thf(6223,plain,
! [SV692: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV692 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV692 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4970]) ).
thf(6224,plain,
! [SV693: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV693 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV693 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4971]) ).
thf(6225,plain,
! [SV694: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV694 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV694 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4972]) ).
thf(6226,plain,
! [SV695: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV695 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV695 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4973]) ).
thf(6227,plain,
! [SV696: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV696 ) )
= $true )
| ( ( class_HOL_Oplus @ SV696 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4974]) ).
thf(6228,plain,
! [SV697: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV697 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV697 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(6229,plain,
! [SV698: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV698 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV698 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4976]) ).
thf(6230,plain,
! [SV699: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV699 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV699 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4977]) ).
thf(6231,plain,
! [SV700: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV700 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV700 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4978]) ).
thf(6232,plain,
! [SV701: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV701 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV701 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(6233,plain,
! [SV702: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV702 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV702 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4980]) ).
thf(6234,plain,
! [SV703: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV703 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV703 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4981]) ).
thf(6235,plain,
! [SV704: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV704 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV704 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4982]) ).
thf(6236,plain,
! [SV705: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV705 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV705 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4983]) ).
thf(6237,plain,
! [SV706: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV706 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV706 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4984]) ).
thf(6238,plain,
! [SV707: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV707 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV707 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(6239,plain,
! [SV708: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV708 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV708 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(6240,plain,
! [SV709: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV709 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV709 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4987]) ).
thf(6241,plain,
! [SV710: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV710 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV710 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4988]) ).
thf(6242,plain,
! [SV711: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV711 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV711 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4989]) ).
thf(6243,plain,
! [SV712: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV712 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV712 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4990]) ).
thf(6244,plain,
! [SV713: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV713 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV713 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4991]) ).
thf(6245,plain,
! [SV714: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV714 ) )
= $true )
| ( ( class_Orderings_Oord @ SV714 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4992]) ).
thf(6246,plain,
! [SV715: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV715 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV715 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4993]) ).
thf(6247,plain,
! [SV716: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV716 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV716 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4994]) ).
thf(6248,plain,
! [SV717: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV717 ) )
= $true )
| ( ( class_Ring__and__Field_Olordered__ring @ SV717 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4995]) ).
thf(6249,plain,
! [SV718: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV718 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV718 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4996]) ).
thf(6250,plain,
! [SV719: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV719 ) )
= $true )
| ( ( class_HOL_Ominus @ SV719 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(6251,plain,
! [SV720: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV720 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV720 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4998]) ).
thf(6252,plain,
! [SV721: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV721 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV721 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4999]) ).
thf(6253,plain,
! [SV722: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV722 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV722 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5000]) ).
thf(6254,plain,
! [SV723: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV723 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV723 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5001]) ).
thf(6255,plain,
! [SV724: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV724 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV724 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5002]) ).
thf(6256,plain,
! [SV725: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV725 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV725 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5003]) ).
thf(6257,plain,
! [SV726: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV726 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV726 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(6258,plain,
! [SV727: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV727 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV727 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5005]) ).
thf(6259,plain,
! [SV728: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV728 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5006]) ).
thf(6260,plain,
! [SV729: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV729 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV729 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5007]) ).
thf(6261,plain,
! [SV730: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV730 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV730 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(6262,plain,
! [SV731: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV731 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV731 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5009]) ).
thf(6263,plain,
! [SV732: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV732 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV732 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5010]) ).
thf(6264,plain,
! [SV733: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV733 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV733 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(6265,plain,
! [SV734: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV734 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV734 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5012]) ).
thf(6266,plain,
! [SV735: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV735 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV735 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5013]) ).
thf(6267,plain,
! [SV736: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV736 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV736 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(6268,plain,
! [SV737: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV737 ) )
= $true )
| ( ( class_HOL_Oplus @ SV737 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(6269,plain,
! [SV738: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV738 ) )
= $true )
| ( ( class_HOL_Ozero @ SV738 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5016]) ).
thf(6270,plain,
! [SV739: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV739 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV739 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5017]) ).
thf(6271,plain,
! [SV740: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV740 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV740 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5018]) ).
thf(6272,plain,
! [SV741: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV741 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV741 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5019]) ).
thf(6273,plain,
! [SV742: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV742 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV742 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5020]) ).
thf(6274,plain,
! [SV743: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV743 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV743 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5021]) ).
thf(6275,plain,
! [SV744: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV744 ) )
= $true )
| ( ( class_HOL_Ominus @ SV744 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5022]) ).
thf(6276,plain,
! [SV745: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV745 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5023]) ).
thf(6277,plain,
! [SV746: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV746 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV746 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5024]) ).
thf(6278,plain,
! [SV747: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV747 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(6279,plain,
! [SV748: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV748 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV748 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(6280,plain,
! [SV749: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV749 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV749 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5027]) ).
thf(6281,plain,
! [SV750: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV750 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV750 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5028]) ).
thf(6282,plain,
! [SV751: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV751 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV751 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5029]) ).
thf(6283,plain,
! [SV752: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV752 ) )
= $true )
| ( ( class_Orderings_Oord @ SV752 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5030]) ).
thf(6284,plain,
! [SV753: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV753 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV753 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5031]) ).
thf(6285,plain,
! [SV754: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV754 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV754 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5032]) ).
thf(6286,plain,
! [SV755: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV755 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV755 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5033]) ).
thf(6287,plain,
! [SV756: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV756 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV756 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5034]) ).
thf(6288,plain,
! [SV757: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV757 ) )
= $true )
| ( ( class_Ring__and__Field_Olordered__ring @ SV757 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5035]) ).
thf(6289,plain,
! [SV758: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV758 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV758 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5036]) ).
thf(6290,plain,
! [SV759: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV759 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV759 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5037]) ).
thf(6291,plain,
! [SV760: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV760 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV760 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5038]) ).
thf(6292,plain,
! [SV761: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV761 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV761 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5039]) ).
thf(6293,plain,
! [SV762: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV762 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV762 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5040]) ).
thf(6294,plain,
! [SV763: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV763 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV763 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5041]) ).
thf(6295,plain,
! [SV764: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV764 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV764 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5042]) ).
thf(6296,plain,
! [SV765: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV765 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV765 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5043]) ).
thf(6297,plain,
! [SV766: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV766 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV766 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5044]) ).
thf(6298,plain,
! [SV767: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV767 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV767 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(6299,plain,
! [SV768: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV768 ) )
= $true )
| ( ( class_HOL_Otimes @ SV768 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5046]) ).
thf(6300,plain,
! [SV769: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV769 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV769 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(6301,plain,
! [SV770: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV770 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV770 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5048]) ).
thf(6302,plain,
! [SV771: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV771 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV771 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5049]) ).
thf(6303,plain,
! [SV772: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV772 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV772 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5050]) ).
thf(6304,plain,
! [SV773: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV773 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV773 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5051]) ).
thf(6305,plain,
! [SV774: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV774 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV774 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5052]) ).
thf(6306,plain,
! [SV775: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV775 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV775 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5053]) ).
thf(6307,plain,
! [SV776: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV776 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV776 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5054]) ).
thf(6308,plain,
! [SV777: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV777 ) )
= $true )
| ( ( class_HOL_Otimes @ SV777 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5055]) ).
thf(6309,plain,
! [SV778: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV778 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV778 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5056]) ).
thf(6310,plain,
! [SV779: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV779 ) )
= $true )
| ( ( class_HOL_Ozero @ SV779 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5057]) ).
thf(6311,plain,
! [SV780: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV780 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV780 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(6312,plain,
! [SV781: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV781 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV781 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5059]) ).
thf(6313,plain,
! [SV782: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV782 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV782 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5060]) ).
thf(6314,plain,
! [SV783: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV783 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV783 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5061]) ).
thf(6315,plain,
! [SV784: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV784 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV784 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5062]) ).
thf(6316,plain,
! [SV785: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV785 ) )
= $true )
| ( ( class_HOL_Oplus @ SV785 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5063]) ).
thf(6317,plain,
! [SV786: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV786 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV786 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5064]) ).
thf(6318,plain,
! [SV787: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV787 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV787 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5065]) ).
thf(6319,plain,
! [SV788: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV788 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV788 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5066]) ).
thf(6320,plain,
! [SV789: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV789 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV789 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5067]) ).
thf(6321,plain,
! [SV790: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV790 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV790 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5068]) ).
thf(6322,plain,
! [SV791: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV791 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV791 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5069]) ).
thf(6323,plain,
! [SV792: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV792 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV792 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5070]) ).
thf(6324,plain,
! [SV793: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV793 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV793 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5071]) ).
thf(6325,plain,
! [SV794: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV794 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV794 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5072]) ).
thf(6326,plain,
! [SV795: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV795 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV795 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5073]) ).
thf(6327,plain,
! [SV796: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV796 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV796 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5074]) ).
thf(6328,plain,
! [SV797: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV797 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV797 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5075]) ).
thf(6329,plain,
! [SV798: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV798 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV798 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5076]) ).
thf(6330,plain,
! [SV799: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV799 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV799 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(6331,plain,
! [SV800: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV800 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV800 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5078]) ).
thf(6332,plain,
! [SV801: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV801 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV801 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5079]) ).
thf(6333,plain,
! [SV802: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV802 ) )
= $true )
| ( ( class_Orderings_Oord @ SV802 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5080]) ).
thf(6334,plain,
! [SV803: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV803 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV803 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5081]) ).
thf(6335,plain,
! [SV804: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV804 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV804 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5082]) ).
thf(6336,plain,
! [SV805: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV805 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV805 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5083]) ).
thf(6337,plain,
! [SV806: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV806 ) )
= $true )
| ( ( class_HOL_Oone @ SV806 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5084]) ).
thf(6338,plain,
! [SV807: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV807 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV807 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5085]) ).
thf(6339,plain,
! [SV808: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV808 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV808 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(6340,plain,
! [SV809: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV809 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV809 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5087]) ).
thf(6341,plain,
! [SV810: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV810 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV810 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(6342,plain,
! [SV811: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV811 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV811 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5089]) ).
thf(6343,plain,
! [SV812: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV812 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV812 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5090]) ).
thf(6344,plain,
! [SV813: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV813 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV813 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5091]) ).
thf(6345,plain,
! [SV814: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV814 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV814 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5092]) ).
thf(6346,plain,
! [SV815: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV815 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV815 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5093]) ).
thf(6347,plain,
! [SV816: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV816 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV816 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5094]) ).
thf(6348,plain,
! [SV817: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV817 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV817 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5095]) ).
thf(6349,plain,
! [SV818: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV818 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV818 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5096]) ).
thf(6350,plain,
! [SV819: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV819 ) )
= $true )
| ( ( class_Orderings_Oord @ SV819 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5097]) ).
thf(6351,plain,
! [SV820: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV820 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV820 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5098]) ).
thf(6352,plain,
! [SV821: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV821 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV821 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5099]) ).
thf(6353,plain,
! [SV822: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV822 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV822 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5100]) ).
thf(6354,plain,
! [SV823: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV823 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV823 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5101]) ).
thf(6355,plain,
! [SV824: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV824 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV824 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5102]) ).
thf(6356,plain,
! [SV825: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV825 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV825 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5103]) ).
thf(6357,plain,
! [SV826: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV826 ) )
= $true )
| ( ( class_HOL_Otimes @ SV826 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5104]) ).
thf(6358,plain,
! [SV827: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV827 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV827 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5105]) ).
thf(6359,plain,
! [SV828: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV828 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV828 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5106]) ).
thf(6360,plain,
! [SV829: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV829 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV829 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5107]) ).
thf(6361,plain,
! [SV830: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV830 ) )
= $true )
| ( ( class_HOL_Oplus @ SV830 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5108]) ).
thf(6362,plain,
! [SV831: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV831 ) )
= $true )
| ( ( class_HOL_Ozero @ SV831 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5109]) ).
thf(6363,plain,
! [SV832: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV832 ) )
= $true )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV832 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5110]) ).
thf(6364,plain,
! [SV833: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV833 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV833 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5111]) ).
thf(6365,plain,
! [SV834: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV834 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV834 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5112]) ).
thf(6366,plain,
! [SV835: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV835 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV835 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5113]) ).
thf(6367,plain,
! [SV836: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV836 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV836 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5114]) ).
thf(6368,plain,
! [SV837: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV837 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV837 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5115]) ).
thf(6369,plain,
! [SV838: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV838 ) )
= $true )
| ( ( class_HOL_Oplus @ SV838 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5116]) ).
thf(6370,plain,
! [SV839: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV839 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV839 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(6371,plain,
! [SV840: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV840 ) )
= $true )
| ( ( class_Orderings_Oord @ SV840 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5118]) ).
thf(6372,plain,
! [SV841: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV841 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV841 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5119]) ).
thf(6373,plain,
! [SV842: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV842 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV842 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5120]) ).
thf(6374,plain,
! [SV843: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV843 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV843 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5121]) ).
thf(6375,plain,
! [SV844: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV844 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV844 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(6376,plain,
! [SV845: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV845 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV845 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(6377,plain,
! [SV846: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV846 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV846 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(6378,plain,
! [SV847: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV847 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV847 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(6379,plain,
! [SV848: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV848 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV848 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(6380,plain,
! [SV849: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV849 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV849 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(6381,plain,
! [SV850: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV850 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV850 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(6382,plain,
! [SV851: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV851 ) )
= $true )
| ( ( class_HOL_Otimes @ SV851 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(6383,plain,
! [SV852: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV852 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV852 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5130]) ).
thf(6384,plain,
! [SV853: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV853 ) )
= $true )
| ( ( class_HOL_Ozero @ SV853 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5131]) ).
thf(6385,plain,
! [SV854: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV854 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV854 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5132]) ).
thf(6386,plain,
! [SV855: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV855 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV855 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5133]) ).
thf(6387,plain,
! [SV856: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV856 ) )
= $true )
| ( ( class_HOL_Oplus @ SV856 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5134]) ).
thf(6388,plain,
! [SV857: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV857 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV857 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(6389,plain,
! [SV858: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV858 ) )
= $true )
| ( ( class_Orderings_Oord @ SV858 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(6390,plain,
! [SV859: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV859 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV859 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(6391,plain,
! [SV860: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV860 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV860 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5138]) ).
thf(6392,plain,
! [SV861: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV861 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV861 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5139]) ).
thf(6393,plain,
! [SV862: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV862 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV862 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(6394,plain,
! [SV863: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV863 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV863 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5141]) ).
thf(6395,plain,
! [SV864: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV864 ) )
= $true )
| ( ( class_HOL_Otimes @ SV864 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5142]) ).
thf(6396,plain,
! [SV865: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV865 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV865 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(6397,plain,
! [SV866: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV866 ) )
= $true )
| ( ( class_HOL_Ozero @ SV866 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5144]) ).
thf(6398,plain,
! [SV867: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV867 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV867 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5145]) ).
thf(6399,plain,
! [SV868: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV868 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV868 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5146]) ).
thf(6400,plain,
! [SV869: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV869 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV869 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5147]) ).
thf(6401,plain,
! [SV870: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV870 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV870 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5148]) ).
thf(6402,plain,
! [SV871: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV871 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV871 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5149]) ).
thf(6403,plain,
! [SV872: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV872 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV872 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(6404,plain,
! [SV873: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV873 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV873 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5151]) ).
thf(6405,plain,
! [SV874: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV874 ) )
= $true )
| ( ( class_HOL_Otimes @ SV874 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5152]) ).
thf(6406,plain,
! [SV875: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV875 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV875 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5153]) ).
thf(6407,plain,
! [SV876: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV876 ) )
= $true )
| ( ( class_HOL_Ozero @ SV876 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5154]) ).
thf(6408,plain,
! [SV877: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV877 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV877 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5155]) ).
thf(6409,plain,
! [SV878: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV878 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV878 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5156]) ).
thf(6410,plain,
! [SV879: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV879 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV879 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5157]) ).
thf(6411,plain,
! [SV880: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV880 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV880 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5158]) ).
thf(6412,plain,
! [SV881: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV881 ) )
= $true )
| ( ( class_HOL_Oplus @ SV881 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5159]) ).
thf(6413,plain,
! [SV882: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV882 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV882 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5160]) ).
thf(6414,plain,
! [SV883: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV883 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV883 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5161]) ).
thf(6415,plain,
! [SV884: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV884 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV884 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5162]) ).
thf(6416,plain,
! [SV885: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV885 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV885 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5163]) ).
thf(6417,plain,
! [SV886: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV886 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV886 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5164]) ).
thf(6418,plain,
! [SV887: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV887 ) )
= $true )
| ( ( class_Orderings_Oord @ SV887 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5165]) ).
thf(6419,plain,
! [SV888: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV888 ) )
= $true )
| ( ( class_HOL_Ominus @ SV888 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5166]) ).
thf(6420,plain,
! [SV889: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV889 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV889 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5167]) ).
thf(6421,plain,
! [SV890: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV890 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV890 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5168]) ).
thf(6422,plain,
! [SV891: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV891 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV891 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5169]) ).
thf(6423,plain,
! [SV892: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV892 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV892 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5170]) ).
thf(6424,plain,
! [SV893: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV893 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV893 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5171]) ).
thf(6425,plain,
! [SV894: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__ring @ SV894 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV894 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5172]) ).
thf(6426,plain,
! [SV895: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV895 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV895 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(6427,plain,
! [SV896: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV896 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV896 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5174]) ).
thf(6428,plain,
! [SV897: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV897 ) )
= $true )
| ( ( class_HOL_Oplus @ SV897 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5175]) ).
thf(6429,plain,
! [SV898: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV898 ) )
= $true )
| ( ( class_HOL_Ozero @ SV898 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5176]) ).
thf(6430,plain,
! [SV899: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV899 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV899 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5177]) ).
thf(6431,plain,
! [SV900: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV900 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV900 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(6432,plain,
! [SV901: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV901 ) )
= $true )
| ( ( class_Orderings_Oord @ SV901 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5179]) ).
thf(6433,plain,
! [SV902: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV902 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV902 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5180]) ).
thf(6434,plain,
! [SV903: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV903 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV903 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5181]) ).
thf(6435,plain,
! [SV904: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV904 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV904 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(6436,plain,
! [SV905: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV905 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV905 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(6437,plain,
! [SV906: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV906 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV906 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5184]) ).
thf(6438,plain,
! [SV907: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV907 ) )
= $true )
| ( ( class_HOL_Otimes @ SV907 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5185]) ).
thf(6439,plain,
! [SV908: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV908 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV908 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5186]) ).
thf(6440,plain,
! [SV909: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV909 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV909 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5187]) ).
thf(6441,plain,
! [SV910: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ SV910 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV910 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5188]) ).
thf(6442,plain,
! [SV911: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV911 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV911 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(6443,plain,
! [SV912: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV912 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV912 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(6444,plain,
! [SV913: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV913 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV913 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(6445,plain,
! [SV914: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV914 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV914 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5192]) ).
thf(6446,plain,
! [SV915: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV915 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV915 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5193]) ).
thf(6447,plain,
! [SV916: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV916 ) )
= $true )
| ( ( class_HOL_Oplus @ SV916 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5194]) ).
thf(6448,plain,
! [SV917: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV917 ) )
= $true )
| ( ( class_HOL_Ozero @ SV917 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(6449,plain,
! [SV918: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV918 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV918 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5196]) ).
thf(6450,plain,
! [SV919: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV919 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV919 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5197]) ).
thf(6451,plain,
! [SV920: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV920 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV920 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(6452,plain,
! [SV921: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV921 ) )
= $true )
| ( ( class_Orderings_Oord @ SV921 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5199]) ).
thf(6453,plain,
! [SV922: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV922 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV922 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5200]) ).
thf(6454,plain,
! [SV923: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV923 ) )
= $true )
| ( ( class_HOL_Ominus @ SV923 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5201]) ).
thf(6455,plain,
! [SV924: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV924 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV924 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5202]) ).
thf(6456,plain,
! [SV925: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV925 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV925 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5203]) ).
thf(6457,plain,
! [SV926: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV926 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV926 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5204]) ).
thf(6458,plain,
! [SV927: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV927 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV927 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5205]) ).
thf(6459,plain,
! [SV928: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV928 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV928 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5206]) ).
thf(6460,plain,
! [SV929: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV929 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV929 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5207]) ).
thf(6461,plain,
! [SV930: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV930 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV930 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5208]) ).
thf(6462,plain,
! [SV931: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV931 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV931 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5209]) ).
thf(6463,plain,
! [SV932: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV932 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV932 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5210]) ).
thf(6464,plain,
! [SV933: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV933 ) )
= $true )
| ( ( class_HOL_Otimes @ SV933 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5211]) ).
thf(6465,plain,
! [SV934: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV934 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV934 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5212]) ).
thf(6466,plain,
! [SV935: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV935 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV935 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5213]) ).
thf(6467,plain,
! [SV936: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV936 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV936 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5214]) ).
thf(6468,plain,
! [SV937: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV937 ) )
= $true )
| ( ( class_Orderings_Oord @ SV937 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(6469,plain,
! [SV938: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV938 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV938 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5216]) ).
thf(6470,plain,
! [SV939: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV939 ) )
= $true )
| ( ( class_HOL_Otimes @ SV939 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5217]) ).
thf(6471,plain,
! [SV940: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV940 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV940 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5218]) ).
thf(6472,plain,
! [SV941: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV941 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV941 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5219]) ).
thf(6473,plain,
! [SV942: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV942 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV942 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5220]) ).
thf(6474,plain,
! [SV943: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV943 ) )
= $true )
| ( ( class_HOL_Oplus @ SV943 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5221]) ).
thf(6475,plain,
! [SV944: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV944 ) )
= $true )
| ( ( class_HOL_Ozero @ SV944 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5222]) ).
thf(6476,plain,
! [SV945: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV945 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV945 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5223]) ).
thf(6477,plain,
! [SV946: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV946 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV946 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5224]) ).
thf(6478,plain,
! [SV947: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV947 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV947 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5225]) ).
thf(6479,plain,
! [SV948: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV948 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV948 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5226]) ).
thf(6480,plain,
! [SV949: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV949 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV949 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5227]) ).
thf(6481,plain,
! [SV950: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV950 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV950 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5228]) ).
thf(6482,plain,
! [SV951: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV951 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV951 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5229]) ).
thf(6483,plain,
! [SV952: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV952 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV952 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5230]) ).
thf(6484,plain,
! [SV953: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV953 ) )
= $true )
| ( ( class_HOL_Oplus @ SV953 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(6485,plain,
! [SV954: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV954 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV954 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5232]) ).
thf(6486,plain,
! [SV955: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV955 ) )
= $true )
| ( ( class_HOL_Otimes @ SV955 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5233]) ).
thf(6487,plain,
! [SV956: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV956 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV956 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(6488,plain,
! [SV957: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV957 ) )
= $true )
| ( ( class_HOL_Ominus @ SV957 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5235]) ).
thf(6489,plain,
! [SV958: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV958 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV958 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5236]) ).
thf(6490,plain,
! [SV959: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV959 ) )
= $true )
| ( ( class_HOL_Ozero @ SV959 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5237]) ).
thf(6491,plain,
! [SV960: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV960 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV960 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5238]) ).
thf(6492,plain,
! [SV961: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV961 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV961 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5239]) ).
thf(6493,plain,
! [SV962: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV962 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV962 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5240]) ).
thf(6494,plain,
! [SV963: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV963 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV963 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5241]) ).
thf(6495,plain,
! [SV964: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV964 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV964 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5242]) ).
thf(6496,plain,
! [SV965: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV965 ) )
= $true )
| ( ( class_HOL_Oplus @ SV965 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5243]) ).
thf(6497,plain,
! [SV966: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV966 ) )
= $true )
| ( ( class_HOL_Ozero @ SV966 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5244]) ).
thf(6498,plain,
! [SV967: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV967 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV967 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5245]) ).
thf(6499,plain,
! [SV968: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV968 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV968 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5246]) ).
thf(6500,plain,
! [SV969: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV969 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV969 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5247]) ).
thf(6501,plain,
! [SV970: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV970 ) )
= $true )
| ( ( class_HOL_Oone @ SV970 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5248]) ).
thf(6502,plain,
! [SV971: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV971 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV971 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5249]) ).
thf(6503,plain,
! [SV972: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV972 ) )
= $true )
| ( ( class_HOL_Ominus @ SV972 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(6504,plain,
! [SV973: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV973 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV973 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5251]) ).
thf(6505,plain,
! [SV974: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV974 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV974 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5252]) ).
thf(6506,plain,
! [SV975: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV975 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV975 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5253]) ).
thf(6507,plain,
! [SV976: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV976 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV976 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5254]) ).
thf(6508,plain,
! [SV977: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV977 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV977 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(6509,plain,
! [SV978: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV978 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV978 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5256]) ).
thf(6510,plain,
! [SV979: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV979 ) )
= $true )
| ( ( class_HOL_Otimes @ SV979 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5257]) ).
thf(6511,plain,
! [SV980: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV980 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV980 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5258]) ).
thf(6512,plain,
! [SV981: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV981 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV981 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5259]) ).
thf(6513,plain,
! [SV982: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV982 ) )
= $true )
| ( ( class_HOL_Oplus @ SV982 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5260]) ).
thf(6514,plain,
! [SV983: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV983 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV983 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5261]) ).
thf(6515,plain,
! [SV984: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV984 ) )
= $true )
| ( ( class_HOL_Otimes @ SV984 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5262]) ).
thf(6516,plain,
! [SV985: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV985 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV985 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5263]) ).
thf(6517,plain,
! [SV986: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV986 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV986 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5264]) ).
thf(6518,plain,
! [SV987: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV987 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV987 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5265]) ).
thf(6519,plain,
! [SV988: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV988 ) )
= $true )
| ( ( class_HOL_Oplus @ SV988 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5266]) ).
thf(6520,plain,
! [SV989: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV989 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV989 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(6521,plain,
! [SV990: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV990 ) )
= $true )
| ( ( class_HOL_Otimes @ SV990 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5268]) ).
thf(6522,plain,
! [SV991: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV991 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV991 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5269]) ).
thf(6523,plain,
! [SV992: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV992 ) )
= $true )
| ( ( class_HOL_Ozero @ SV992 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5270]) ).
thf(6524,plain,
! [SV993: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV993 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV993 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5271]) ).
thf(6525,plain,
! [SV994: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV994 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV994 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5272]) ).
thf(6526,plain,
! [SV995: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV995 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV995 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5273]) ).
thf(6527,plain,
! [SV996: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV996 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV996 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5274]) ).
thf(6528,plain,
! [SV997: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV997 ) )
= $true )
| ( ( class_HOL_Otimes @ SV997 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5275]) ).
thf(6529,plain,
! [SV998: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV998 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV998 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5276]) ).
thf(6530,plain,
! [SV999: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV999 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV999 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5277]) ).
thf(6531,plain,
! [SV1000: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1000 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV1000 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5278]) ).
thf(6532,plain,
! [SV1001: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1001 ) )
= $true )
| ( ( class_HOL_Oplus @ SV1001 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5279]) ).
thf(6533,plain,
! [SV1002: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1002 ) )
= $true )
| ( ( class_HOL_Ozero @ SV1002 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5280]) ).
thf(6534,plain,
! [SV1003: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ SV1003 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1003 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5281]) ).
thf(6535,plain,
! [SV1004: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1004 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1004 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5282]) ).
thf(6536,plain,
! [SV1005: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1005 ) )
= $true )
| ( ( class_HOL_Ozero @ SV1005 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5283]) ).
thf(6537,plain,
! [SV1006: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1006 ) )
= $true )
| ( ( class_HOL_Oplus @ SV1006 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5284]) ).
thf(6538,plain,
! [SV1007: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1007 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV1007 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5285]) ).
thf(6539,plain,
! [SV1008: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1008 ) )
= $true )
| ( ( class_HOL_Oone @ SV1008 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5286]) ).
thf(6540,plain,
! [SV1009: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1009 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV1009 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5287]) ).
thf(6541,plain,
! [SV1010: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1010 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV1010 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5288]) ).
thf(6542,plain,
! [SV1011: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1011 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV1011 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5289]) ).
thf(6543,plain,
! [SV1012: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1012 ) )
= $true )
| ( ( class_HOL_Otimes @ SV1012 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5290]) ).
thf(6544,plain,
! [SV1013: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1013 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1013 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5291]) ).
thf(6545,plain,
! [SV1014: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1014 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV1014 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5292]) ).
thf(6546,plain,
! [SV1015: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV1015 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV1015 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5293]) ).
thf(6547,plain,
! [SV1016: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1016 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV1016 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5294]) ).
thf(6548,plain,
! [SV1017: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1017 ) )
= $true )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1017 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5295]) ).
thf(6549,plain,
! [SV1018: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1018 ) )
= $true )
| ( ( class_HOL_Oone @ SV1018 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5296]) ).
thf(6550,plain,
! [SV1019: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1019 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV1019 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5297]) ).
thf(6551,plain,
! [SV1020: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1020 ) )
= $true )
| ( ( class_HOL_Otimes @ SV1020 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5298]) ).
thf(6552,plain,
! [SV1021: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1021 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1021 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(6553,plain,
! [SV1022: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1022 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV1022 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5300]) ).
thf(6554,plain,
! [SV1023: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1023 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1023 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5301]) ).
thf(6555,plain,
! [SV1024: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1024 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV1024 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5302]) ).
thf(6556,plain,
! [SV1025: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1025 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring @ SV1025 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5303]) ).
thf(6557,plain,
! [SV1026: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1026 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1026 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5304]) ).
thf(6558,plain,
! [SV1027: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1027 ) )
= $true )
| ( ( class_HOL_Ozero @ SV1027 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5305]) ).
thf(6559,plain,
! [SV1028: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1028 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV1028 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5306]) ).
thf(6560,plain,
! [SV1029: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1029 ) )
= $true )
| ( ( class_OrderedGroup_Osemigroup__add @ SV1029 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5307]) ).
thf(6561,plain,
! [SV1030: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1030 ) )
= $true )
| ( ( class_HOL_Oplus @ SV1030 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5308]) ).
thf(6562,plain,
! [SV1031: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ SV1031 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV1031 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5309]) ).
thf(6563,plain,
! [SV1032: $i] :
( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1032 ) )
= $true )
| ( ( class_Orderings_Oord @ SV1032 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5310]) ).
thf(6564,plain,
! [SV1033: $i] :
( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1033 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV1033 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5311]) ).
thf(6565,plain,
! [SV1034: $i] :
( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1034 ) )
= $true )
| ( ( class_LOrder_Omeet__semilorder @ SV1034 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5312]) ).
thf(6566,plain,
! [SV1035: $i] :
( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1035 ) )
= $true )
| ( ( class_LOrder_Ojoin__semilorder @ SV1035 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5313]) ).
thf(6567,plain,
! [SV1036: $i] :
( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1036 ) )
= $true )
| ( ( class_LOrder_Olorder @ SV1036 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5314]) ).
thf(6568,plain,
! [SV1037: $i] :
( ( ( ~ ( class_Wellfounded__Recursion_Owellorder @ SV1037 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV1037 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5315]) ).
thf(6569,plain,
! [SV1370: $i,SV1038: $i] :
( ( ! [SY2894: $i] :
( ~ ( c_in @ SV1038 @ ( c_Datatype_Oo2s @ SV1370 @ SY2894 ) @ SY2894 )
| ( SV1370
= ( c_Datatype_Ooption_OSome @ SV1038 @ SY2894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5316]) ).
thf(6570,plain,
! [SV1371: $i,SV1039: $i] :
( ( c_in @ SV1039 @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ SV1039 @ SV1371 ) @ SV1371 ) @ SV1371 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5317]) ).
thf(6571,plain,
! [SV1372: $i,SV1040: $i] :
( ( ( SV1040 = c_Datatype_Ooption_ONone )
| ( SV1040
= ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ SV1040 @ SV1372 ) @ SV1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5318]) ).
thf(6572,plain,
! [SV1373: $i,SV1041: $i] :
( ( ( SV1041 = c_Datatype_Ooption_ONone )
| ( SV1041
= ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ SV1041 @ SV1373 ) @ SV1373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5319]) ).
thf(6573,plain,
! [SV1042: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1042 @ tc_nat ) )
= $true )
| ( ( SV1042 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5320]) ).
thf(6574,plain,
! [SV1374: $i,SV1043: $i] :
( ( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1043 @ SV1374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5321]) ).
thf(6575,plain,
! [SV1375: $i,SV1044: $i] :
( ( ( c_Equiv__Relations_Oquotient @ c_emptyset @ SV1044 @ SV1375 )
= c_emptyset )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5322]) ).
thf(6576,plain,
! [SV1376: $i,SV1045: $i] :
( ( ! [SY2895: $i,SY2896: $i] :
( ~ ( c_in @ ( c_minus @ SV1045 @ ( c_insert @ SV1376 @ SY2895 @ SY2896 ) @ ( tc_set @ SY2896 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2896 ) )
| ( c_in @ ( c_minus @ SV1045 @ SY2895 @ ( tc_set @ SY2896 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5323]) ).
thf(6577,plain,
! [SV1377: $i,SV1046: $i] :
( ( ! [SY2897: $i,SY2898: $i] :
( ~ ( c_in @ ( c_minus @ SV1046 @ SV1377 @ ( tc_set @ SY2897 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2897 ) )
| ( c_in @ ( c_minus @ SV1046 @ ( c_insert @ SY2898 @ SV1377 @ SY2897 ) @ ( tc_set @ SY2897 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5324]) ).
thf(6578,plain,
! [SV1378: $i,SV1047: $i] :
( ( ~ ( c_in @ ( c_Pow @ SV1047 @ SV1378 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1378 ) ) )
| ( c_in @ SV1047 @ c_Finite__Set_OFinites @ ( tc_set @ SV1378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5325]) ).
thf(6579,plain,
! [SV1379: $i,SV1048: $i] :
( ( ~ ( c_in @ SV1048 @ c_Finite__Set_OFinites @ ( tc_set @ SV1379 ) )
| ( c_in @ ( c_Pow @ SV1048 @ SV1379 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5326]) ).
thf(6580,plain,
! [SV1380: $i,SV1049: $i] :
( ( ! [SY2899: $i] :
( ~ ( c_in @ ( c_union @ SV1049 @ SV1380 @ SY2899 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2899 ) )
| ( c_in @ SV1049 @ c_Finite__Set_OFinites @ ( tc_set @ SY2899 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5327]) ).
thf(6581,plain,
! [SV1381: $i,SV1050: $i] :
( ( ! [SY2900: $i] :
( ~ ( c_in @ ( c_union @ SV1050 @ SV1381 @ SY2900 ) @ c_Finite__Set_OFinites @ ( tc_set @ SY2900 ) )
| ( c_in @ SV1381 @ c_Finite__Set_OFinites @ ( tc_set @ SY2900 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5328]) ).
thf(6582,plain,
! [SV1382: $i,SV1051: $i] :
( ( ! [SY2901: $i] :
( ~ ( c_in @ SV1051 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
| ~ ( c_in @ SY2901 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
| ( c_in @ ( c_union @ SY2901 @ SV1051 @ SV1382 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5329]) ).
thf(6583,plain,
! [SV1383: $i,SV1052: $i] :
( ( ! [SY2902: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ SV1052 @ SV1383 @ SY2902 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2902 @ SV1383 ) ) )
| ( c_in @ SV1052 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1383 @ SY2902 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5330]) ).
thf(6584,plain,
! [SV1384: $i,SV1053: $i] :
( ( ! [SY2903: $i] :
( ~ ( c_in @ SV1053 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1384 @ SY2903 ) ) )
| ( c_in @ ( c_Relation_Oconverse @ SV1053 @ SV1384 @ SY2903 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SY2903 @ SV1384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5331]) ).
thf(6585,plain,
! [SV1385: $i,SV1054: $i] :
( ( ! [SY2904: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1054 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1385 @ SY2904 @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1054 @ SV1385 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5332]) ).
thf(6586,plain,
! [SV1386: $i,SV1055: $i] :
( ( ! [SY2905: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1055 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1386 @ SY2905 @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1055 @ SY2905 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5333]) ).
thf(6587,plain,
! [SV1387: $i,SV1056: $i] :
( ( ! [SY2906: $i] :
( ~ ( c_Divides_Oop_Advd @ SV1056 @ SV1387 @ tc_nat )
| ~ ( c_Divides_Oop_Advd @ SV1056 @ SY2906 @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1056 @ ( c_GCD_Ogcd @ ( c_Pair @ SY2906 @ SV1387 @ tc_nat @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5334]) ).
thf(6588,plain,
! [SV1388: $i,SV1057: $i] :
( ( ~ ( c_Divides_Oop_Advd @ SV1057 @ ( c_uminus @ SV1388 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ SV1057 @ SV1388 @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5336]) ).
thf(6589,plain,
! [SV1389: $i,SV1058: $i] :
( ( ~ ( c_Divides_Oop_Advd @ SV1058 @ SV1389 @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ SV1058 @ ( c_uminus @ SV1389 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5337]) ).
thf(6590,plain,
! [SV1059: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ c_0 @ SV1059 @ tc_IntDef_Oint ) )
= $true )
| ( ( SV1059 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5338]) ).
thf(6591,plain,
! [SV1390: $i,SV1060: $i] :
( ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ SV1060 @ tc_IntDef_Oint ) @ SV1390 @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ SV1060 @ SV1390 @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5339]) ).
thf(6592,plain,
! [SV1391: $i,SV1061: $i] :
( ( ~ ( c_Divides_Oop_Advd @ SV1061 @ SV1391 @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ ( c_uminus @ SV1061 @ tc_IntDef_Oint ) @ SV1391 @ tc_IntDef_Oint ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5340]) ).
thf(6593,plain,
! [SV1392: $i,SV1062: $i] :
( ( ! [SY2907: $i] :
~ ( c_in @ ( c_Pair @ SV1062 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1392 ) @ ( tc_List_Olist @ SV1392 ) ) @ ( c_List_Olex @ SY2907 @ SV1392 ) @ ( tc_prod @ ( tc_List_Olist @ SV1392 ) @ ( tc_List_Olist @ SV1392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5341]) ).
thf(6594,plain,
! [SV1393: $i,SV1065: $i] :
( ( ! [SY2908: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1065 @ ( tc_List_Olist @ SV1393 ) @ ( tc_List_Olist @ SV1393 ) ) @ ( c_List_Olex @ SY2908 @ SV1393 ) @ ( tc_prod @ ( tc_List_Olist @ SV1393 ) @ ( tc_List_Olist @ SV1393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5344]) ).
thf(6595,plain,
! [SV1394: $i,SV1066: $i] :
( ( ! [SY2909: $i,SY2910: $i] :
( ~ ( c_in @ ( c_append @ SV1066 @ SV1394 @ SY2909 ) @ ( c_List_Olists @ SY2910 @ SY2909 ) @ ( tc_List_Olist @ SY2909 ) )
| ( c_in @ SV1066 @ ( c_List_Olists @ SY2910 @ SY2909 ) @ ( tc_List_Olist @ SY2909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5345]) ).
thf(6596,plain,
! [SV1395: $i,SV1067: $i] :
( ( ! [SY2911: $i,SY2912: $i] :
( ~ ( c_in @ ( c_append @ SV1067 @ SV1395 @ SY2911 ) @ ( c_List_Olists @ SY2912 @ SY2911 ) @ ( tc_List_Olist @ SY2911 ) )
| ( c_in @ SV1395 @ ( c_List_Olists @ SY2912 @ SY2911 ) @ ( tc_List_Olist @ SY2911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5346]) ).
thf(6597,plain,
! [SV1396: $i,SV1068: $i] :
( ( ! [SY2913: $i,SY2914: $i] :
( ~ ( c_in @ SV1068 @ ( c_List_Olists @ SV1396 @ SY2913 ) @ ( tc_List_Olist @ SY2913 ) )
| ~ ( c_in @ SY2914 @ ( c_List_Olists @ SV1396 @ SY2913 ) @ ( tc_List_Olist @ SY2913 ) )
| ( c_in @ ( c_append @ SY2914 @ SV1068 @ SY2913 ) @ ( c_List_Olists @ SV1396 @ SY2913 ) @ ( tc_List_Olist @ SY2913 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5347]) ).
thf(6598,plain,
! [SV1397: $i,SV1070: $i] :
( ( ( c_append @ c_List_Olist_ONil @ SV1070 @ SV1397 )
= SV1070 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5349]) ).
thf(6599,plain,
! [SV1398: $i,SV1071: $i] :
( ( ( c_append @ SV1071 @ c_List_Olist_ONil @ SV1398 )
= SV1071 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5350]) ).
thf(6600,plain,
! [SV1073: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1073 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5352]) ).
thf(6601,plain,
! [SV1399: $i,SV1074: $i] :
( ( ( c_less @ c_0 @ ( c_Nat_Osize @ SV1074 @ ( tc_List_Olist @ SV1399 ) ) @ tc_nat )
| ( SV1074 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5353]) ).
thf(6602,plain,
! [SV1400: $i,SV1075: $i] :
( ( ! [SY2915: $i] :
( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ SV1075 @ SV1400 ) @ ( c_List_Olist_OCons @ SY2915 @ c_List_Olist_ONil @ SV1400 ) @ SV1400 ) @ SV1400 )
= ( c_List_Olist_OCons @ SY2915 @ SV1075 @ SV1400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5354]) ).
thf(6603,plain,
! [SV1401: $i,SV1077: $i] :
( ( SV1077
= ( c_append @ c_List_Olist_ONil @ SV1077 @ SV1401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5356]) ).
thf(6604,plain,
! [SV1402: $i,SV1078: $i] :
( ( SV1078
= ( c_append @ SV1078 @ c_List_Olist_ONil @ SV1402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5357]) ).
thf(6605,plain,
! [SV1403: $i,SV1081: $i] :
( ( ~ ( c_lessequals @ ( c_Suc @ SV1081 ) @ ( c_Suc @ SV1403 ) @ tc_nat )
| ( c_lessequals @ SV1081 @ SV1403 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5360]) ).
thf(6606,plain,
! [SV1404: $i,SV1082: $i] :
( ( ~ ( c_lessequals @ SV1082 @ SV1404 @ tc_nat )
| ( c_lessequals @ ( c_Suc @ SV1082 ) @ ( c_Suc @ SV1404 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5361]) ).
thf(6607,plain,
! [SV1405: $i,SV1083: $i] :
( ( ~ ( c_less @ ( c_Suc @ SV1083 ) @ ( c_Suc @ SV1405 ) @ tc_nat )
| ( c_less @ SV1083 @ SV1405 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5362]) ).
thf(6608,plain,
! [SV1406: $i,SV1084: $i] :
( ( ~ ( c_less @ SV1084 @ SV1406 @ tc_nat )
| ( c_less @ ( c_Suc @ SV1084 ) @ ( c_Suc @ SV1406 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5363]) ).
thf(6609,plain,
! [SV1407: $i,SV1085: $i] :
( ( ~ ( c_less @ c_0 @ ( c_plus @ SV1085 @ SV1407 @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ SV1407 @ tc_nat )
| ( c_less @ c_0 @ SV1085 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5364]) ).
thf(6610,plain,
! [SV1408: $i,SV1086: $i] :
( ( ~ ( c_less @ c_0 @ SV1086 @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ SV1086 @ SV1408 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5365]) ).
thf(6611,plain,
! [SV1409: $i,SV1087: $i] :
( ( ~ ( c_less @ c_0 @ SV1087 @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ SV1409 @ SV1087 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5366]) ).
thf(6612,plain,
! [SV1088: $i] :
( ( ( ~ ( c_lessequals @ SV1088 @ c_0 @ tc_nat ) )
= $true )
| ( ( SV1088 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5367]) ).
thf(6613,plain,
! [SV1089: $i] :
( ( ( ~ ( c_less @ SV1089 @ ( c_Suc @ c_0 ) @ tc_nat ) )
= $true )
| ( ( SV1089 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5368]) ).
thf(6614,plain,
! [SV1090: $i] :
( ( ( ~ ( c_less @ SV1090 @ c_1 @ tc_nat ) )
= $true )
| ( ( SV1090 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5369]) ).
thf(6615,plain,
! [SV1091: $i] :
( ( ( c_less @ c_0 @ SV1091 @ tc_nat )
= $true )
| ( ( SV1091 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5370]) ).
thf(6616,plain,
! [SV1410: $i,SV1092: $i] :
( ( ~ ( c_less @ ( c_plus @ SV1092 @ SV1410 @ tc_nat ) @ SV1092 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5372]) ).
thf(6617,plain,
! [SV1411: $i,SV1093: $i] :
( ( ~ ( c_less @ ( c_plus @ SV1093 @ SV1411 @ tc_nat ) @ SV1411 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5373]) ).
thf(6618,plain,
! [SV1094: $i] :
( ( c_less @ SV1094 @ c_0 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(6619,plain,
! [SV1412: $i,SV1095: $i] :
( ( ~ ( class_Orderings_Oorder @ SV1095 )
| ~ ( c_less @ SV1412 @ SV1412 @ SV1095 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5375]) ).
thf(6620,plain,
! [SV1413: $i,SV1096: $i] :
( ( c_in @ ( c_Pair @ SV1096 @ SV1096 @ SV1413 @ SV1413 ) @ c_Relation_OId @ ( tc_prod @ SV1413 @ SV1413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5376]) ).
thf(6621,plain,
! [SV1414: $i,SV1097: $i] :
( ( ! [SY2916: $i,SY2917: $i,SY2918: $i] :
( ~ ( c_in @ SV1097 @ ( c_Relation_OImage @ SV1414 @ ( c_insert @ SY2916 @ c_emptyset @ SY2917 ) @ SY2917 @ SY2918 ) @ SY2918 )
| ( c_in @ ( c_Pair @ SY2916 @ SV1097 @ SY2917 @ SY2918 ) @ SV1414 @ ( tc_prod @ SY2917 @ SY2918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5377]) ).
thf(6622,plain,
! [SV1415: $i,SV1098: $i] :
( ( ! [SY2919: $i,SY2920: $i,SY2921: $i] :
( ~ ( c_in @ ( c_Pair @ SV1098 @ SV1415 @ SY2919 @ SY2920 ) @ SY2921 @ ( tc_prod @ SY2919 @ SY2920 ) )
| ( c_in @ SV1415 @ ( c_Relation_OImage @ SY2921 @ ( c_insert @ SV1098 @ c_emptyset @ SY2919 ) @ SY2919 @ SY2920 ) @ SY2920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5378]) ).
thf(6623,plain,
! [SV1416: $i,SV1099: $i] :
( ( ! [SY2922: $i,SY2923: $i,SY2924: $i] :
( ~ ( c_in @ ( c_Pair @ SV1099 @ SV1416 @ SY2922 @ SY2923 ) @ ( c_Relation_Oconverse @ SY2924 @ SY2923 @ SY2922 ) @ ( tc_prod @ SY2922 @ SY2923 ) )
| ( c_in @ ( c_Pair @ SV1416 @ SV1099 @ SY2923 @ SY2922 ) @ SY2924 @ ( tc_prod @ SY2923 @ SY2922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5379]) ).
thf(6624,plain,
! [SV1417: $i,SV1100: $i] :
( ( ! [SY2925: $i,SY2926: $i,SY2927: $i] :
( ~ ( c_in @ ( c_Pair @ SV1100 @ SV1417 @ SY2925 @ SY2926 ) @ SY2927 @ ( tc_prod @ SY2925 @ SY2926 ) )
| ( c_in @ ( c_Pair @ SV1417 @ SV1100 @ SY2926 @ SY2925 ) @ ( c_Relation_Oconverse @ SY2927 @ SY2925 @ SY2926 ) @ ( tc_prod @ SY2926 @ SY2925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5380]) ).
thf(6625,plain,
! [SV1418: $i,SV1101: $i] :
( ( ! [SY2928: $i] :
( ~ ( c_in @ ( c_Pair @ SV1101 @ SV1418 @ SY2928 @ SY2928 ) @ c_Relation_OId @ ( tc_prod @ SY2928 @ SY2928 ) )
| ( SV1101 = SV1418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5381]) ).
thf(6626,plain,
! [SV1419: $i,SV1102: $i] :
( ( ! [SY2929: $i] :
( ~ ( class_Orderings_Oord @ SV1102 )
| ~ ( c_in @ SV1419 @ ( c_SetInterval_OatLeast @ SY2929 @ SV1102 ) @ SV1102 )
| ( c_lessequals @ SY2929 @ SV1419 @ SV1102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5382]) ).
thf(6627,plain,
! [SV1420: $i,SV1103: $i] :
( ( ! [SY2930: $i] :
( ~ ( class_Orderings_Oord @ SV1103 )
| ~ ( c_lessequals @ SV1420 @ SY2930 @ SV1103 )
| ( c_in @ SY2930 @ ( c_SetInterval_OatLeast @ SV1420 @ SV1103 ) @ SV1103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5383]) ).
thf(6628,plain,
! [SV1421: $i,SV1104: $i] :
( ( ! [SY2931: $i] :
( ~ ( class_Orderings_Oorder @ SV1104 )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1421 @ SV1104 ) @ ( c_SetInterval_OatLeast @ SY2931 @ SV1104 ) @ ( tc_set @ SV1104 ) )
| ( c_lessequals @ SY2931 @ SV1421 @ SV1104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5384]) ).
thf(6629,plain,
! [SV1422: $i,SV1105: $i] :
( ( ! [SY2932: $i] :
( ~ ( class_Orderings_Oorder @ SV1105 )
| ~ ( c_lessequals @ SV1422 @ SY2932 @ SV1105 )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ SY2932 @ SV1105 ) @ ( c_SetInterval_OatLeast @ SV1422 @ SV1105 ) @ ( tc_set @ SV1105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5385]) ).
thf(6630,plain,
! [SV1423: $i,SV1106: $i] :
( ( ! [SY2933: $i] :
( ~ ( class_Orderings_Oord @ SV1106 )
| ~ ( c_in @ SV1423 @ ( c_SetInterval_OatMost @ SY2933 @ SV1106 ) @ SV1106 )
| ( c_lessequals @ SV1423 @ SY2933 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5386]) ).
thf(6631,plain,
! [SV1424: $i,SV1107: $i] :
( ( ! [SY2934: $i] :
( ~ ( class_Orderings_Oord @ SV1107 )
| ~ ( c_lessequals @ SV1424 @ SY2934 @ SV1107 )
| ( c_in @ SV1424 @ ( c_SetInterval_OatMost @ SY2934 @ SV1107 ) @ SV1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5387]) ).
thf(6632,plain,
! [SV1425: $i,SV1108: $i] :
( ( ! [SY2935: $i] :
( ~ ( class_Orderings_Oorder @ SV1108 )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1425 @ SV1108 ) @ ( c_SetInterval_OatMost @ SY2935 @ SV1108 ) @ ( tc_set @ SV1108 ) )
| ( c_lessequals @ SV1425 @ SY2935 @ SV1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5388]) ).
thf(6633,plain,
! [SV1426: $i,SV1109: $i] :
( ( ! [SY2936: $i] :
( ~ ( class_Orderings_Oorder @ SV1109 )
| ~ ( c_lessequals @ SV1426 @ SY2936 @ SV1109 )
| ( c_lessequals @ ( c_SetInterval_OatMost @ SV1426 @ SV1109 ) @ ( c_SetInterval_OatMost @ SY2936 @ SV1109 ) @ ( tc_set @ SV1109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5389]) ).
thf(6634,plain,
! [SV1427: $i,SV1110: $i] :
( ( ! [SY2937: $i] :
( ~ ( class_Orderings_Oord @ SV1110 )
| ~ ( c_in @ SV1427 @ ( c_SetInterval_OgreaterThan @ SY2937 @ SV1110 ) @ SV1110 )
| ( c_less @ SY2937 @ SV1427 @ SV1110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5390]) ).
thf(6635,plain,
! [SV1428: $i,SV1111: $i] :
( ( ! [SY2938: $i] :
( ~ ( class_Orderings_Oord @ SV1111 )
| ~ ( c_less @ SV1428 @ SY2938 @ SV1111 )
| ( c_in @ SY2938 @ ( c_SetInterval_OgreaterThan @ SV1428 @ SV1111 ) @ SV1111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5391]) ).
thf(6636,plain,
! [SV1429: $i,SV1112: $i] :
( ( ! [SY2939: $i] :
( ~ ( class_Orderings_Olinorder @ SV1112 )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1429 @ SV1112 ) @ ( c_SetInterval_OgreaterThan @ SY2939 @ SV1112 ) @ ( tc_set @ SV1112 ) )
| ( c_lessequals @ SY2939 @ SV1429 @ SV1112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5392]) ).
thf(6637,plain,
! [SV1430: $i,SV1113: $i] :
( ( ! [SY2940: $i] :
( ~ ( class_Orderings_Olinorder @ SV1113 )
| ~ ( c_lessequals @ SV1430 @ SY2940 @ SV1113 )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SY2940 @ SV1113 ) @ ( c_SetInterval_OgreaterThan @ SV1430 @ SV1113 ) @ ( tc_set @ SV1113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5393]) ).
thf(6638,plain,
! [SV1431: $i,SV1114: $i] :
( ( ! [SY2941: $i] :
( ~ ( class_Orderings_Oord @ SV1114 )
| ~ ( c_in @ SV1431 @ ( c_SetInterval_OlessThan @ SY2941 @ SV1114 ) @ SV1114 )
| ( c_less @ SV1431 @ SY2941 @ SV1114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5394]) ).
thf(6639,plain,
! [SV1432: $i,SV1115: $i] :
( ( ! [SY2942: $i] :
( ~ ( class_Orderings_Oord @ SV1115 )
| ~ ( c_less @ SV1432 @ SY2942 @ SV1115 )
| ( c_in @ SV1432 @ ( c_SetInterval_OlessThan @ SY2942 @ SV1115 ) @ SV1115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5395]) ).
thf(6640,plain,
! [SV1433: $i,SV1116: $i] :
( ( ! [SY2943: $i] :
( ~ ( class_Orderings_Olinorder @ SV1116 )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1433 @ SV1116 ) @ ( c_SetInterval_OlessThan @ SY2943 @ SV1116 ) @ ( tc_set @ SV1116 ) )
| ( c_lessequals @ SV1433 @ SY2943 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5396]) ).
thf(6641,plain,
! [SV1434: $i,SV1117: $i] :
( ( ! [SY2944: $i] :
( ~ ( class_Orderings_Olinorder @ SV1117 )
| ~ ( c_lessequals @ SV1434 @ SY2944 @ SV1117 )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1434 @ SV1117 ) @ ( c_SetInterval_OlessThan @ SY2944 @ SV1117 ) @ ( tc_set @ SV1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5397]) ).
thf(6642,plain,
! [SV1435: $i,SV1118: $i] :
( ( ! [SY2945: $i] :
( ~ ( c_in @ SV1118 @ SV1435 @ SY2945 )
| ~ ( c_in @ SV1118 @ ( c_uminus @ SV1435 @ ( tc_set @ SY2945 ) ) @ SY2945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5398]) ).
thf(6643,plain,
! [SV1436: $i,SV1119: $i] :
( ( ! [SY2946: $i] :
( ( c_in @ SV1119 @ SV1436 @ SY2946 )
| ( c_in @ SV1119 @ ( c_uminus @ SV1436 @ ( tc_set @ SY2946 ) ) @ SY2946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5399]) ).
thf(6644,plain,
! [SV1437: $i,SV1120: $i] :
( ( ! [SY2947: $i] :
( ~ ( c_lessequals @ ( c_uminus @ SV1120 @ ( tc_set @ SV1437 ) ) @ ( c_uminus @ SY2947 @ ( tc_set @ SV1437 ) ) @ ( tc_set @ SV1437 ) )
| ( c_lessequals @ SY2947 @ SV1120 @ ( tc_set @ SV1437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5400]) ).
thf(6645,plain,
! [SV1438: $i,SV1121: $i] :
( ( ! [SY2948: $i] :
( ~ ( c_lessequals @ SV1121 @ SV1438 @ ( tc_set @ SY2948 ) )
| ( c_lessequals @ ( c_uminus @ SV1438 @ ( tc_set @ SY2948 ) ) @ ( c_uminus @ SV1121 @ ( tc_set @ SY2948 ) ) @ ( tc_set @ SY2948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5401]) ).
thf(6646,plain,
! [SV1439: $i,SV1122: $i] :
( ( ! [SY2949: $i,SY2950: $i] :
( ~ ( c_in @ SV1122 @ SV1439 @ SY2949 )
| ~ ( c_in @ SV1122 @ ( c_minus @ SY2950 @ SV1439 @ ( tc_set @ SY2949 ) ) @ SY2949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5402]) ).
thf(6647,plain,
! [SV1440: $i,SV1123: $i] :
( ( ! [SY2951: $i,SY2952: $i] :
( ~ ( c_in @ SV1123 @ ( c_minus @ SV1440 @ SY2951 @ ( tc_set @ SY2952 ) ) @ SY2952 )
| ( c_in @ SV1123 @ SV1440 @ SY2952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5403]) ).
thf(6648,plain,
! [SV1441: $i,SV1124: $i] :
( ( ! [SY2953: $i,SY2954: $i] :
( ~ ( c_in @ SV1124 @ SV1441 @ SY2953 )
| ( c_in @ SV1124 @ SY2954 @ SY2953 )
| ( c_in @ SV1124 @ ( c_minus @ SV1441 @ SY2954 @ ( tc_set @ SY2953 ) ) @ SY2953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5404]) ).
thf(6649,plain,
! [SV1442: $i,SV1125: $i] :
( ( ! [SY2955: $i,SY2956: $i] :
( ~ ( c_in @ SV1125 @ ( c_inter @ SV1442 @ SY2955 @ SY2956 ) @ SY2956 )
| ( c_in @ SV1125 @ SY2955 @ SY2956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5405]) ).
thf(6650,plain,
! [SV1443: $i,SV1126: $i] :
( ( ! [SY2957: $i,SY2958: $i] :
( ~ ( c_in @ SV1126 @ ( c_inter @ SV1443 @ SY2957 @ SY2958 ) @ SY2958 )
| ( c_in @ SV1126 @ SV1443 @ SY2958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5406]) ).
thf(6651,plain,
! [SV1444: $i,SV1127: $i] :
( ( ! [SY2959: $i,SY2960: $i] :
( ~ ( c_in @ SV1127 @ SV1444 @ SY2959 )
| ~ ( c_in @ SV1127 @ SY2960 @ SY2959 )
| ( c_in @ SV1127 @ ( c_inter @ SY2960 @ SV1444 @ SY2959 ) @ SY2959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5407]) ).
thf(6652,plain,
! [SV1445: $i,SV1128: $i] :
( ( ! [SY2961: $i,SY2962: $i] :
( ~ ( c_in @ SV1128 @ SV1445 @ ( tc_set @ SY2961 ) )
| ~ ( c_in @ SY2962 @ ( c_Inter @ SV1445 @ SY2961 ) @ SY2961 )
| ( c_in @ SY2962 @ SV1128 @ SY2961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5408]) ).
thf(6653,plain,
! [SV1446: $i,SV1129: $i] :
( ( ! [SY2963: $i] :
( ~ ( c_in @ SV1129 @ ( c_Pow @ SV1446 @ SY2963 ) @ ( tc_set @ SY2963 ) )
| ( c_lessequals @ SV1129 @ SV1446 @ ( tc_set @ SY2963 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5409]) ).
thf(6654,plain,
! [SV1447: $i,SV1130: $i] :
( ( ! [SY2964: $i] :
( ~ ( c_lessequals @ SV1130 @ SV1447 @ ( tc_set @ SY2964 ) )
| ( c_in @ SV1130 @ ( c_Pow @ SV1447 @ SY2964 ) @ ( tc_set @ SY2964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5410]) ).
thf(6655,plain,
! [SV1448: $i,SV1131: $i] :
( ( ! [SY2965: $i,SY2966: $i] :
( ~ ( c_in @ SV1131 @ SV1448 @ SY2965 )
| ( c_in @ SV1131 @ ( c_union @ SY2966 @ SV1448 @ SY2965 ) @ SY2965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5411]) ).
thf(6656,plain,
! [SV1449: $i,SV1132: $i] :
( ( ! [SY2967: $i,SY2968: $i] :
( ~ ( c_in @ SV1132 @ SV1449 @ SY2967 )
| ( c_in @ SV1132 @ ( c_union @ SV1449 @ SY2968 @ SY2967 ) @ SY2967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5412]) ).
thf(6657,plain,
! [SV1450: $i,SV1133: $i] :
( ( ! [SY2969: $i,SY2970: $i] :
( ~ ( c_in @ SV1133 @ ( c_union @ SV1450 @ SY2969 @ SY2970 ) @ SY2970 )
| ( c_in @ SV1133 @ SY2969 @ SY2970 )
| ( c_in @ SV1133 @ SV1450 @ SY2970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5413]) ).
thf(6658,plain,
! [SV1451: $i,SV1135: $i] :
( ( ! [SY2971: $i,SY2972: $i] :
( ~ ( c_in @ SV1135 @ SV1451 @ SY2971 )
| ~ ( c_in @ SV1451 @ SY2972 @ ( tc_set @ SY2971 ) )
| ( c_in @ SV1135 @ ( c_Union @ SY2972 @ SY2971 ) @ SY2971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5415]) ).
thf(6659,plain,
! [SV1452: $i,SV1136: $i] :
( ( ~ ( c_in @ SV1136 @ c_emptyset @ SV1452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5416]) ).
thf(6660,plain,
! [SV1453: $i,SV1137: $i] :
( ( ! [SY2973: $i,SY2974: $i] :
( ~ ( c_in @ SV1137 @ SV1453 @ SY2973 )
| ( c_in @ SV1137 @ ( c_insert @ SY2974 @ SV1453 @ SY2973 ) @ SY2973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5417]) ).
thf(6661,plain,
! [SV1454: $i,SV1138: $i] :
( ( ! [SY2975: $i] : ( c_in @ SV1138 @ ( c_insert @ SV1138 @ SV1454 @ SY2975 ) @ SY2975 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5418]) ).
thf(6662,plain,
! [SV1455: $i,SV1139: $i] :
( ( ! [SY2976: $i,SY2977: $i] :
( ~ ( c_in @ SV1139 @ ( c_insert @ SV1455 @ SY2976 @ SY2977 ) @ SY2977 )
| ( c_in @ SV1139 @ SY2976 @ SY2977 )
| ( SV1139 = SV1455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5419]) ).
thf(6663,plain,
! [SV1456: $i,SV1140: $i] :
( ( ~ ( c_less @ SV1140 @ c_emptyset @ ( tc_set @ SV1456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5420]) ).
thf(6664,plain,
! [SV1457: $i,SV1141: $i] :
( ( ! [SY2978: $i] :
( ~ ( c_lessequals @ SV1141 @ ( c_insert @ SV1457 @ c_emptyset @ SY2978 ) @ ( tc_set @ SY2978 ) )
| ( ( c_insert @ SV1457 @ SV1141 @ SY2978 )
= ( c_insert @ SV1457 @ c_emptyset @ SY2978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5421]) ).
thf(6665,plain,
! [SV1458: $i,SV1142: $i] :
( ( ! [SY2979: $i] :
( ~ ( c_lessequals @ SV1142 @ ( c_insert @ SV1458 @ c_emptyset @ SY2979 ) @ ( tc_set @ SY2979 ) )
| ( ( c_insert @ SV1458 @ c_emptyset @ SY2979 )
= ( c_insert @ SV1458 @ SV1142 @ SY2979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5422]) ).
thf(6666,plain,
! [SV1459: $i,SV1143: $i] :
( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1143 @ SV1459 @ SV1459 ) @ SV1459 )
| ( c_Wellfounded__Recursion_Oacyclic @ SV1143 @ SV1459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5423]) ).
thf(6667,plain,
! [SV1460: $i,SV1144: $i] :
( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1144 @ SV1460 )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1144 @ SV1460 @ SV1460 ) @ SV1460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5424]) ).
thf(6668,plain,
! [SV1461: $i,SV1145: $i] :
( ( ! [SY2980: $i,SY2981: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1145 @ SV1461 @ SY2980 @ SY2980 ) @ SY2981 @ ( tc_prod @ SY2980 @ SY2980 ) ) @ SY2980 )
| ( c_Wellfounded__Recursion_Oacyclic @ SY2981 @ SY2980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5425]) ).
thf(6669,plain,
! [SV1462: $i,SV1146: $i] :
( ( ! [SY2982: $i,SY2983: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1146 @ SV1462 @ SY2982 @ SY2982 ) @ SY2983 @ ( tc_prod @ SY2982 @ SY2982 ) ) @ SY2982 )
| ~ ( c_in @ ( c_Pair @ SV1462 @ SV1146 @ SY2982 @ SY2982 ) @ ( c_Transitive__Closure_Ortrancl @ SY2983 @ SY2982 ) @ ( tc_prod @ SY2982 @ SY2982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5426]) ).
thf(6670,plain,
! [SV1463: $i,SV1147: $i] :
( ( ! [SY2984: $i,SY2985: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1147 @ SV1463 )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SY2984 @ SY2985 @ SV1463 @ SV1463 ) @ SV1147 @ ( tc_prod @ SV1463 @ SV1463 ) ) @ SV1463 )
| ( c_in @ ( c_Pair @ SY2985 @ SY2984 @ SV1463 @ SV1463 ) @ ( c_Transitive__Closure_Ortrancl @ SV1147 @ SV1463 ) @ ( tc_prod @ SV1463 @ SV1463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5427]) ).
thf(6671,plain,
! [SV1464: $i,SV1148: $i] :
( ( ! [SY2986: $i,SY2987: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1148 @ SV1464 @ SY2986 @ SY2986 ) @ SY2987 @ ( tc_prod @ SY2986 @ SY2986 ) ) @ SY2986 )
| ( c_Wellfounded__Recursion_Owf @ SY2987 @ SY2986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5428]) ).
thf(6672,plain,
! [SV1465: $i,SV1149: $i] :
( ( ! [SY2988: $i,SY2989: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1149 @ SV1465 @ SY2988 @ SY2988 ) @ SY2989 @ ( tc_prod @ SY2988 @ SY2988 ) ) @ SY2988 )
| ~ ( c_in @ ( c_Pair @ SV1465 @ SV1149 @ SY2988 @ SY2988 ) @ ( c_Transitive__Closure_Ortrancl @ SY2989 @ SY2988 ) @ ( tc_prod @ SY2988 @ SY2988 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5429]) ).
thf(6673,plain,
! [SV1466: $i,SV1150: $i] :
( ( ! [SY2990: $i,SY2991: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV1150 @ SV1466 )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SY2990 @ SY2991 @ SV1466 @ SV1466 ) @ SV1150 @ ( tc_prod @ SV1466 @ SV1466 ) ) @ SV1466 )
| ( c_in @ ( c_Pair @ SY2991 @ SY2990 @ SV1466 @ SV1466 ) @ ( c_Transitive__Closure_Ortrancl @ SV1150 @ SV1466 ) @ ( tc_prod @ SV1466 @ SV1466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5430]) ).
thf(6674,plain,
! [SV1467: $i,SV1151: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV1151 @ SV1467 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ SV1151 @ SV1467 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5431]) ).
thf(6675,plain,
! [SV1468: $i,SV1152: $i] :
( ( ~ ( c_less @ SV1152 @ SV1468 @ tc_nat )
| ( c_in @ ( c_Pair @ SV1152 @ SV1468 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5432]) ).
thf(6676,plain,
! [SV1469: $i,SV1153: $i] :
( ( ! [SY2992: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1153 @ SV1469 ) @ ( c_Message_Oanalz @ SY2992 ) @ tc_Message_Omsg )
| ( c_in @ SV1469 @ ( c_Message_Oanalz @ SY2992 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5433]) ).
thf(6677,plain,
! [SV1470: $i,SV1154: $i] :
( ( ! [SY2993: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1154 @ SV1470 ) @ ( c_Message_Oanalz @ SY2993 ) @ tc_Message_Omsg )
| ( c_in @ SV1154 @ ( c_Message_Oanalz @ SY2993 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5434]) ).
thf(6678,plain,
! [SV1471: $i,SV1155: $i] :
( ( ! [SY2994: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1155 @ SV1471 ) @ ( c_Message_Oparts @ SY2994 ) @ tc_Message_Omsg )
| ( c_in @ SV1471 @ ( c_Message_Oparts @ SY2994 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5435]) ).
thf(6679,plain,
! [SV1472: $i,SV1156: $i] :
( ( ! [SY2995: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1156 @ SV1472 ) @ ( c_Message_Oparts @ SY2995 ) @ tc_Message_Omsg )
| ( c_in @ SV1156 @ ( c_Message_Oparts @ SY2995 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5436]) ).
thf(6680,plain,
! [SV1473: $i,SV1157: $i] :
( ( ! [SY2996: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1157 @ SV1473 ) @ ( c_Message_Oanalz @ SY2996 ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1157 ) ) @ ( c_Message_Oanalz @ SY2996 ) @ tc_Message_Omsg )
| ( c_in @ SV1473 @ ( c_Message_Oanalz @ SY2996 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5437]) ).
thf(6681,plain,
! [SV1474: $i,SV1158: $i] :
( ( ~ ( c_in @ SV1158 @ SV1474 @ tc_Message_Omsg )
| ( c_in @ SV1158 @ ( c_Message_Oanalz @ SV1474 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5438]) ).
thf(6682,plain,
! [SV1475: $i,SV1159: $i] :
( ( ~ ( c_in @ SV1159 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SV1475 ) ) @ tc_Message_Omsg )
| ( c_in @ SV1159 @ ( c_Message_Oanalz @ SV1475 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5439]) ).
thf(6683,plain,
! [SV1476: $i,SV1160: $i] :
( ( ~ ( c_lessequals @ SV1160 @ SV1476 @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ SV1160 ) @ ( c_Message_Oanalz @ SV1476 ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5440]) ).
thf(6684,plain,
! [SV1477: $i,SV1161: $i] :
( ( ! [SY2997: $i] :
( ~ ( c_in @ SV1161 @ ( c_Message_Oparts @ ( c_union @ SV1477 @ SY2997 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SY2997 ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1477 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5441]) ).
thf(6685,plain,
! [SV1478: $i,SV1162: $i] :
( ( ! [SY2998: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1162 @ SV1478 ) @ ( c_Message_Oparts @ SY2998 ) @ tc_Message_Omsg )
| ( c_in @ SV1478 @ ( c_Message_Oparts @ SY2998 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5442]) ).
thf(6686,plain,
! [SV1479: $i,SV1163: $i] :
( ( ~ ( c_in @ SV1163 @ SV1479 @ tc_Message_Omsg )
| ( c_in @ SV1163 @ ( c_Message_Oparts @ SV1479 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5443]) ).
thf(6687,plain,
! [SV1164: $i] :
( ( c_in @ SV1164 @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5444]) ).
thf(6688,plain,
! [SV1480: $i,SV1165: $i] :
( ( ~ ( c_in @ SV1165 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SV1480 ) ) @ tc_Message_Omsg )
| ( c_in @ SV1165 @ ( c_Message_Oparts @ SV1480 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5445]) ).
thf(6689,plain,
! [SV1481: $i,SV1166: $i] :
( ( ! [SY2999: $i] : ( c_lessequals @ SV1166 @ ( c_union @ SV1166 @ SV1481 @ SY2999 ) @ ( tc_set @ SY2999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5446]) ).
thf(6690,plain,
! [SV1482: $i,SV1167: $i] :
( ( ! [SY3000: $i] : ( c_lessequals @ SV1167 @ ( c_union @ SV1482 @ SV1167 @ SY3000 ) @ ( tc_set @ SY3000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5447]) ).
thf(6691,plain,
! [SV1483: $i,SV1168: $i] :
( ( ! [SY3001: $i,SY3002: $i] :
( ~ ( c_lessequals @ SV1168 @ SV1483 @ ( tc_set @ SY3001 ) )
| ~ ( c_lessequals @ SY3002 @ SV1168 @ ( tc_set @ SY3001 ) )
| ( c_lessequals @ SY3002 @ SV1483 @ ( tc_set @ SY3001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5448]) ).
thf(6692,plain,
! [SV1484: $i,SV1169: $i] :
( ( ! [SY3003: $i,SY3004: $i] :
( ( c_Datatype__Universe_OIn0 @ SV1169 @ SV1484 @ SY3003 )
!= ( c_Datatype__Universe_OIn1 @ SY3004 @ SV1484 @ SY3003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5450]) ).
thf(6693,plain,
! [SV1485: $i,SV1170: $i] :
( ( ! [SY3005: $i,SY3006: $i] :
( ( ( c_Message_Omsg_OCrypt @ SV1170 @ SV1485 )
!= ( c_Message_Omsg_OCrypt @ SY3005 @ SY3006 ) )
| ( SV1170 = SY3005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5451]) ).
thf(6694,plain,
! [SV1486: $i,SV1171: $i] :
( ( ( ( c_List_Orev @ SV1171 @ SV1486 )
!= c_List_Olist_ONil )
| ( SV1171 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5452]) ).
thf(6695,plain,
! [SV1487: $i,SV1172: $i] :
( ( ! [SY3007: $i,SY3008: $i,SY3009: $i] :
( ( ( c_append @ SV1172 @ ( c_List_Olist_OCons @ SV1487 @ c_List_Olist_ONil @ SY3007 ) @ SY3007 )
!= ( c_append @ SY3008 @ ( c_List_Olist_OCons @ SY3009 @ c_List_Olist_ONil @ SY3007 ) @ SY3007 ) )
| ( SV1487 = SY3009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5453]) ).
thf(6696,plain,
! [SV1488: $i,SV1173: $i] :
( ( ! [SY3010: $i,SY3011: $i,SY3012: $i] :
( ( c_Datatype__Universe_OScons @ SV1173 @ SV1488 @ SY3010 @ SY3011 )
!= ( c_Datatype__Universe_ONumb @ SY3012 @ SY3010 @ SY3011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5454]) ).
thf(6697,plain,
! [SV1489: $i,SV1174: $i] :
( ( ( ( c_List_Oset @ SV1174 @ SV1489 )
!= c_emptyset )
| ( SV1174 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5455]) ).
thf(6698,plain,
! [SV1490: $i,SV1175: $i] :
( ( c_Datatype_Ooption_ONone
!= ( c_Datatype_Ooption_OSome @ SV1175 @ SV1490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5456]) ).
thf(6699,plain,
! [SV1491: $i,SV1176: $i] :
( ( ! [SY3013: $i,SY3014: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SV1176 @ SV1491 @ SY3013 )
!= ( c_Datatype__Universe_OLeaf @ SY3014 @ SV1491 @ SY3013 ) )
| ( SV1176 = SY3014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5457]) ).
thf(6700,plain,
! [SV1492: $i,SV1177: $i] :
( ( ! [SY3015: $i,SY3016: $i] :
( ( c_Datatype__Universe_OIn1 @ SV1177 @ SV1492 @ SY3015 )
!= ( c_Datatype__Universe_OIn0 @ SY3016 @ SV1492 @ SY3015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5458]) ).
thf(6701,plain,
! [SV1493: $i,SV1178: $i] :
( ( ( ( c_List_Oremdups @ SV1178 @ SV1493 )
!= SV1178 )
| ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1178 @ SV1493 ) @ ( tc_List_Olist @ SV1493 ) )
= ( c_Nat_Osize @ SV1178 @ ( tc_List_Olist @ SV1493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5459]) ).
thf(6702,plain,
! [SV1179: $i] :
( ( ( c_Message_Oagent_OFriend @ SV1179 )
= c_Message_Oagent_OSpy )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(6703,plain,
! [SV1494: $i,SV1180: $i] :
( ( ! [SY3017: $i,SY3018: $i] :
( ( ( c_Datatype__Universe_ONumb @ SV1180 @ SV1494 @ SY3017 )
!= ( c_Datatype__Universe_ONumb @ SY3018 @ SV1494 @ SY3017 ) )
| ( SV1180 = SY3018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5463]) ).
thf(6704,plain,
! [SV1181: $i] :
( ( c_Message_Oagent_OSpy
= ( c_Message_Oagent_OFriend @ SV1181 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(6705,plain,
! [SV1495: $i,SV1182: $i] :
( ( ! [SY3019: $i] :
( ( ( c_Equiv__Relations_Oquotient @ SV1182 @ SV1495 @ SY3019 )
!= c_emptyset )
| ( SV1182 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5465]) ).
thf(6706,plain,
! [SV1496: $i,SV1183: $i] :
( ( ( ( c_Nat_Osize @ SV1183 @ ( tc_List_Olist @ SV1496 ) )
!= c_0 )
| ( SV1183 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5466]) ).
thf(6707,plain,
! [SV1497: $i,SV1184: $i] :
( ( ! [SY3020: $i,SY3021: $i] :
( ( ( c_Message_Omsg_OMPair @ SV1184 @ SV1497 )
!= ( c_Message_Omsg_OMPair @ SY3020 @ SY3021 ) )
| ( SV1184 = SY3020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5467]) ).
thf(6708,plain,
! [SV1498: $i,SV1185: $i] :
( ( ! [SY3022: $i,SY3023: $i,SY3024: $i] :
( ( ( c_List_Olist_OCons @ SV1185 @ SV1498 @ SY3022 )
!= ( c_List_Olist_OCons @ SY3023 @ SY3024 @ SY3022 ) )
| ( SV1498 = SY3024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5468]) ).
thf(6709,plain,
! [SV1499: $i,SV1186: $i] :
( ( ! [SY3025: $i,SY3026: $i] :
( ( c_Sum__Type_OInr @ SV1186 @ SV1499 @ SY3025 )
!= ( c_Sum__Type_OInl @ SY3026 @ SY3025 @ SV1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5469]) ).
thf(6710,plain,
! [SV1500: $i,SV1187: $i] :
( ( ( ( c_Message_Omsg_OHash @ SV1187 )
!= ( c_Message_Omsg_OHash @ SV1500 ) )
| ( SV1187 = SV1500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5470]) ).
thf(6711,plain,
! [SV1501: $i,SV1188: $i] :
( ( ! [SY3027: $i,SY3028: $i,SY3029: $i] :
( ( ( c_append @ SV1188 @ ( c_List_Olist_OCons @ SV1501 @ c_List_Olist_ONil @ SY3027 ) @ SY3027 )
!= ( c_append @ SY3028 @ ( c_List_Olist_OCons @ SY3029 @ c_List_Olist_ONil @ SY3027 ) @ SY3027 ) )
| ( SV1188 = SY3028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5473]) ).
thf(6712,plain,
! [SV1502: $i,SV1189: $i] :
( ( ! [SY3030: $i,SY3031: $i] :
( ( ( c_Datatype__Universe_OAtom @ SV1189 @ SV1502 @ SY3030 )
!= ( c_Datatype__Universe_OAtom @ SY3031 @ SV1502 @ SY3030 ) )
| ( SV1189 = SY3031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5474]) ).
thf(6713,plain,
! [SV1190: $i] :
( ( c_Message_Oagent_OServer
= ( c_Message_Oagent_OFriend @ SV1190 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(6714,plain,
! [SV1503: $i,SV1191: $i] :
( ( ! [SY3032: $i] :
( ( ( c_append @ SV1191 @ SV1503 @ SY3032 )
!= c_List_Olist_ONil )
| ( SV1503 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5476]) ).
thf(6715,plain,
! [SV1504: $i,SV1192: $i] :
( ( ! [SY3033: $i,SY3034: $i] :
( ( ( c_Datatype__Universe_OIn1 @ SV1192 @ SV1504 @ SY3033 )
!= ( c_Datatype__Universe_OIn1 @ SY3034 @ SV1504 @ SY3033 ) )
| ( SV1192 = SY3034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5477]) ).
thf(6716,plain,
! [SV1505: $i,SV1193: $i] :
( ( ! [SY3035: $i] :
( ( ( c_union @ SV1193 @ SV1505 @ SY3035 )
!= c_emptyset )
| ( SV1505 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5478]) ).
thf(6717,plain,
! [SV1506: $i,SV1194: $i] :
( ( ! [SY3036: $i] :
( ~ ( class_Orderings_Olinorder @ SV1194 )
| ( ( c_SetInterval_OlessThan @ SV1506 @ SV1194 )
!= ( c_SetInterval_OlessThan @ SY3036 @ SV1194 ) )
| ( SV1506 = SY3036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5479]) ).
thf(6718,plain,
! [SV1507: $i,SV1195: $i] :
( ( ! [SY3037: $i,SY3038: $i,SY3039: $i,SY3040: $i] :
( ( ( c_Pair @ SV1195 @ SV1507 @ SY3037 @ SY3038 )
!= ( c_Pair @ SY3039 @ SY3040 @ SY3037 @ SY3038 ) )
| ( SV1195 = SY3039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5480]) ).
thf(6719,plain,
! [SV1508: $i,SV1196: $i] :
( ( ! [SY3041: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SV1196 @ SV1508 @ SY3041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5482]) ).
thf(6720,plain,
! [SV1509: $i,SV1197: $i] :
( ( ( ( c_Message_Omsg_OKey @ SV1197 )
!= ( c_Message_Omsg_OKey @ SV1509 ) )
| ( SV1197 = SV1509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5483]) ).
thf(6721,plain,
! [SV1510: $i,SV1198: $i] :
( ( ! [SY3042: $i,SY3043: $i] :
( ( ( c_List_Ochar_OChar @ SV1198 @ SV1510 )
!= ( c_List_Ochar_OChar @ SY3042 @ SY3043 ) )
| ( SV1510 = SY3043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5484]) ).
thf(6722,plain,
! [SV1511: $i,SV1199: $i] :
( ( ( ( c_plus @ SV1199 @ SV1511 @ tc_nat )
!= c_0 )
| ( SV1511 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5485]) ).
thf(6723,plain,
! [SV1512: $i,SV1200: $i] :
( ( ! [SY3044: $i,SY3045: $i,SY3046: $i] :
( ( c_Datatype__Universe_OLeaf @ SV1200 @ SV1512 @ SY3044 )
!= ( c_Datatype__Universe_OScons @ SY3045 @ SY3046 @ SV1512 @ SY3044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5486]) ).
thf(6724,plain,
! [SV1513: $i,SV1201: $i] :
( ( ! [SY3047: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ SV1201 @ SV1513 @ SY3047 ) )
| ( SV1513 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5487]) ).
thf(6725,plain,
! [SV1514: $i,SV1202: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ( ( c_append @ SV1202 @ SV1514 @ SY3048 )
!= ( c_append @ SV1202 @ SY3049 @ SY3048 ) )
| ( SV1514 = SY3049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5488]) ).
thf(6726,plain,
! [SV1515: $i,SV1203: $i] :
( ( ! [SY3050: $i] :
( ( ( c_union @ SV1203 @ SV1515 @ SY3050 )
!= c_emptyset )
| ( SV1203 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5489]) ).
thf(6727,plain,
! [SV1204: $i] :
( ( ( c_Suc @ SV1204 )
= c_0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5490]) ).
thf(6728,plain,
! [SV1516: $i,SV1205: $i] :
( ( ! [SY3051: $i,SY3052: $i] :
( ( ( c_Datatype__Universe_OIn0 @ SV1205 @ SV1516 @ SY3051 )
!= ( c_Datatype__Universe_OIn0 @ SY3052 @ SV1516 @ SY3051 ) )
| ( SV1205 = SY3052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5491]) ).
thf(6729,plain,
! [SV1517: $i,SV1206: $i] :
( ( ! [SY3053: $i,SY3054: $i,SY3055: $i,SY3056: $i] :
( ( ( c_Pair @ SV1206 @ SV1517 @ SY3053 @ SY3054 )
!= ( c_Pair @ SY3055 @ SY3056 @ SY3053 @ SY3054 ) )
| ( SV1517 = SY3056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5493]) ).
thf(6730,plain,
! [SV1518: $i,SV1207: $i] :
( ( ! [SY3057: $i,SY3058: $i,SY3059: $i] :
( ( c_Datatype__Universe_OAtom @ SV1207 @ SV1518 @ SY3057 )
!= ( c_Datatype__Universe_OScons @ SY3058 @ SY3059 @ SV1518 @ SY3057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5494]) ).
thf(6731,plain,
! [SV1208: $i] :
( ( ( c_Message_Oagent_OFriend @ SV1208 )
= c_Message_Oagent_OServer )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(6732,plain,
! [SV1519: $i,SV1209: $i] :
( ( ! [SY3060: $i,SY3061: $i] :
( ( ( c_List_Orev @ SV1209 @ SV1519 )
!= ( c_List_Olist_OCons @ SY3060 @ SY3061 @ SV1519 ) )
| ( SV1209
= ( c_append @ ( c_List_Orev @ SY3061 @ SV1519 ) @ ( c_List_Olist_OCons @ SY3060 @ c_List_Olist_ONil @ SV1519 ) @ SV1519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5496]) ).
thf(6733,plain,
! [SV1520: $i,SV1210: $i] :
( ( ! [SY3062: $i] :
( ~ ( class_Orderings_Olinorder @ SV1210 )
| ( ( c_SetInterval_OatLeast @ SV1520 @ SV1210 )
!= ( c_SetInterval_OatLeast @ SY3062 @ SV1210 ) )
| ( SV1520 = SY3062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5497]) ).
thf(6734,plain,
! [SV1521: $i,SV1211: $i] :
( ( ! [SY3063: $i] :
( ( ( c_uminus @ SV1211 @ ( tc_set @ SV1521 ) )
!= ( c_uminus @ SY3063 @ ( tc_set @ SV1521 ) ) )
| ( SV1211 = SY3063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5498]) ).
thf(6735,plain,
! [SV1522: $i,SV1212: $i] :
( ( ! [SY3064: $i,SY3065: $i,SY3066: $i] :
( ( c_Datatype__Universe_ONumb @ SV1212 @ SV1522 @ SY3064 )
!= ( c_Datatype__Universe_OScons @ SY3065 @ SY3066 @ SV1522 @ SY3064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5499]) ).
thf(6736,plain,
! [SV1523: $i,SV1213: $i] :
( ( ! [SY3067: $i,SY3068: $i] :
( ( ( c_insert @ SV1213 @ c_emptyset @ SV1523 )
!= ( c_insert @ SY3067 @ SY3068 @ SV1523 ) )
| ( SY3067 = SV1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5500]) ).
thf(6737,plain,
! [SV1524: $i,SV1214: $i] :
( ( ! [SY3069: $i] :
( ( SV1214
!= ( c_append @ SV1524 @ SV1214 @ SY3069 ) )
| ( SV1524 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5501]) ).
thf(6738,plain,
! [SV1525: $i,SV1215: $i] :
( ( ( ( c_Message_Oagent_OFriend @ SV1215 )
!= ( c_Message_Oagent_OFriend @ SV1525 ) )
| ( SV1215 = SV1525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5502]) ).
thf(6739,plain,
! [SV1216: $i] :
( ( c_0
= ( c_Suc @ SV1216 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5503]) ).
thf(6740,plain,
! [SV1526: $i,SV1217: $i] :
( ( ! [SY3070: $i] :
( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ SV1217 @ SV1526 @ SY3070 ) )
| ( SV1217 = c_emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5504]) ).
thf(6741,plain,
! [SV1527: $i,SV1218: $i] :
( ( ! [SY3071: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ SV1218 @ SV1527 @ SY3071 ) )
| ( SV1218 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5505]) ).
thf(6742,plain,
! [SV1528: $i,SV1219: $i] :
( ( ( c_Datatype_Ooption_OSome @ SV1219 @ SV1528 )
!= c_Datatype_Ooption_ONone )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5506]) ).
thf(6743,plain,
! [SV1529: $i,SV1220: $i] :
( ( ! [SY3072: $i] :
( ( ( c_append @ SV1220 @ SV1529 @ SY3072 )
!= SV1220 )
| ( SV1529 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5507]) ).
thf(6744,plain,
! [SV1530: $i,SV1221: $i] :
( ( ! [SY3073: $i] :
( ~ ( class_Orderings_Olinorder @ SV1221 )
| ( ( c_SetInterval_OgreaterThan @ SV1530 @ SV1221 )
!= ( c_SetInterval_OgreaterThan @ SY3073 @ SV1221 ) )
| ( SV1530 = SY3073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5508]) ).
thf(6745,plain,
! [SV1531: $i,SV1222: $i] :
( ( ! [SY3074: $i,SY3075: $i] :
( ( ( c_Message_Omsg_OCrypt @ SV1222 @ SV1531 )
!= ( c_Message_Omsg_OCrypt @ SY3074 @ SY3075 ) )
| ( SV1531 = SY3075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5510]) ).
thf(6746,plain,
! [SV1532: $i,SV1223: $i] :
( ( ( ( c_Message_Omsg_OAgent @ SV1223 )
!= ( c_Message_Omsg_OAgent @ SV1532 ) )
| ( SV1223 = SV1532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5511]) ).
thf(6747,plain,
! [SV1533: $i,SV1224: $i] :
( ( ! [SY3076: $i] :
( ( ( c_Datatype_Ooption_OSome @ SV1224 @ SV1533 )
!= ( c_Datatype_Ooption_OSome @ SY3076 @ SV1533 ) )
| ( SV1224 = SY3076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5512]) ).
thf(6748,plain,
! [SV1534: $i,SV1225: $i] :
( ( ( ( c_Message_Omsg_ONonce @ SV1225 )
!= ( c_Message_Omsg_ONonce @ SV1534 ) )
| ( SV1225 = SV1534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5513]) ).
thf(6749,plain,
! [SV1535: $i,SV1226: $i] :
( ( ! [SY3077: $i] :
( ( ( c_append @ SV1226 @ SV1535 @ SY3077 )
!= SV1535 )
| ( SV1226 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5514]) ).
thf(6750,plain,
! [SV1536: $i,SV1227: $i] :
( ( ! [SY3078: $i] :
( ( SV1227
!= ( c_append @ SV1227 @ SV1536 @ SY3078 ) )
| ( SV1536 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5515]) ).
thf(6751,plain,
! [SV1537: $i,SV1228: $i] :
( ( ( ( c_Message_Omsg_ONumber @ SV1228 )
!= ( c_Message_Omsg_ONumber @ SV1537 ) )
| ( SV1228 = SV1537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5516]) ).
thf(6752,plain,
! [SV1538: $i,SV1229: $i] :
( ( ( c_emptyset
!= ( c_List_Oset @ SV1229 @ SV1538 ) )
| ( SV1229 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5517]) ).
thf(6753,plain,
! [SV1539: $i,SV1230: $i] :
( ( ! [SY3079: $i] :
( ( ( c_insert @ SV1230 @ c_emptyset @ SV1539 )
!= ( c_insert @ SY3079 @ c_emptyset @ SV1539 ) )
| ( SV1230 = SY3079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5518]) ).
thf(6754,plain,
! [SV1540: $i,SV1231: $i] :
( ( ( ( c_Divides_Oop_Amod @ SV1231 @ SV1540 @ tc_nat )
!= c_0 )
| ( SV1231
= ( c_times @ SV1540 @ ( c_Main_Omod__eq__0D__dest__1 @ SV1540 @ SV1231 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5519]) ).
thf(6755,plain,
! [SV1541: $i,SV1232: $i] :
( ( ! [SY3080: $i,SY3081: $i] :
( ( c_Sum__Type_OInl @ SV1232 @ SV1541 @ SY3080 )
!= ( c_Sum__Type_OInr @ SY3081 @ SY3080 @ SV1541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5520]) ).
thf(6756,plain,
! [SV1542: $i,SV1233: $i] :
( ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1233 @ SV1542 ) @ ( tc_List_Olist @ SV1542 ) )
!= ( c_Nat_Osize @ SV1233 @ ( tc_List_Olist @ SV1542 ) ) )
| ( ( c_List_Oremdups @ SV1233 @ SV1542 )
= SV1233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5521]) ).
thf(6757,plain,
! [SV1543: $i,SV1234: $i] :
( ( ! [SY3082: $i,SY3083: $i,SY3084: $i] :
( ( c_Datatype__Universe_OScons @ SV1234 @ SV1543 @ SY3082 @ SY3083 )
!= ( c_Datatype__Universe_OLeaf @ SY3084 @ SY3082 @ SY3083 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5522]) ).
thf(6758,plain,
! [SV1544: $i,SV1235: $i] :
( ( ! [SY3085: $i,SY3086: $i,SY3087: $i] :
( ( ( c_List_Olist_OCons @ SV1235 @ SV1544 @ SY3085 )
!= ( c_List_Olist_OCons @ SY3086 @ SY3087 @ SY3085 ) )
| ( SV1235 = SY3086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5523]) ).
thf(6759,plain,
! [SV1545: $i,SV1236: $i] :
( ( ( ( c_Suc @ SV1236 )
!= ( c_Suc @ SV1545 ) )
| ( SV1236 = SV1545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(6760,plain,
! [SV1546: $i,SV1237: $i] :
( ( ! [SY3088: $i,SY3089: $i] :
( ( c_Datatype__Universe_ONumb @ SV1237 @ SV1546 @ SY3088 )
!= ( c_Datatype__Universe_OLeaf @ SY3089 @ SV1546 @ SY3088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5525]) ).
thf(6761,plain,
! [SV1547: $i,SV1238: $i] :
( ( ! [SY3090: $i] :
( ( c_List_Olist_OCons @ SV1238 @ SV1547 @ SY3090 )
!= c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5526]) ).
thf(6762,plain,
! [SV1548: $i,SV1239: $i] :
( ( ( ( c_plus @ SV1239 @ SV1548 @ tc_nat )
!= c_0 )
| ( SV1239 = c_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5527]) ).
thf(6763,plain,
! [SV1549: $i,SV1240: $i] :
( ( ! [SY3091: $i,SY3092: $i] :
( ( ( c_Sum__Type_OInl @ SV1240 @ SV1549 @ SY3091 )
!= ( c_Sum__Type_OInl @ SY3092 @ SV1549 @ SY3091 ) )
| ( SV1240 = SY3092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5528]) ).
thf(6764,plain,
! [SV1550: $i,SV1241: $i] :
( ( ! [SY3093: $i,SY3094: $i,SY3095: $i,SY3096: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1241 @ SV1550 @ SY3093 @ SY3094 )
!= ( c_Datatype__Universe_OScons @ SY3095 @ SY3096 @ SY3093 @ SY3094 ) )
| ( SV1241 = SY3095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5529]) ).
thf(6765,plain,
! [SV1551: $i,SV1242: $i] :
( ( ! [SY3097: $i,SY3098: $i] :
( ( ( c_append @ SV1242 @ SV1551 @ SY3097 )
!= ( c_append @ SY3098 @ SV1551 @ SY3097 ) )
| ( SV1242 = SY3098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5530]) ).
thf(6766,plain,
! [SV1552: $i,SV1243: $i] :
( ( ( c_List_Olist_ONil
!= ( c_List_Orev @ SV1243 @ SV1552 ) )
| ( SV1243 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5531]) ).
thf(6767,plain,
! [SV1553: $i,SV1244: $i] :
( ( ! [SY3099: $i,SY3100: $i,SY3101: $i] :
( ( c_Datatype__Universe_OScons @ SV1244 @ SV1553 @ SY3099 @ SY3100 )
!= ( c_Datatype__Universe_OAtom @ SY3101 @ SY3099 @ SY3100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5532]) ).
thf(6768,plain,
! [SV1554: $i,SV1245: $i] :
( ( ! [SY3102: $i,SY3103: $i] :
( ( c_Datatype__Universe_OLeaf @ SV1245 @ SV1554 @ SY3102 )
!= ( c_Datatype__Universe_ONumb @ SY3103 @ SV1554 @ SY3102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5533]) ).
thf(6769,plain,
! [SV1555: $i,SV1246: $i] :
( ( ! [SY3104: $i,SY3105: $i] :
( ( ( c_List_Ochar_OChar @ SV1246 @ SV1555 )
!= ( c_List_Ochar_OChar @ SY3104 @ SY3105 ) )
| ( SV1246 = SY3104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5534]) ).
thf(6770,plain,
! [SV1556: $i,SV1247: $i] :
( ( ! [SY3106: $i] :
( ( ( c_append @ SV1247 @ SV1556 @ SY3106 )
!= c_List_Olist_ONil )
| ( SV1247 = c_List_Olist_ONil ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5535]) ).
thf(6771,plain,
! [SV1557: $i,SV1248: $i] :
( ( ! [SY3107: $i,SY3108: $i,SY3109: $i,SY3110: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1248 @ SV1557 @ SY3107 @ SY3108 )
!= ( c_Datatype__Universe_OScons @ SY3109 @ SY3110 @ SY3107 @ SY3108 ) )
| ( SV1557 = SY3110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5536]) ).
thf(6772,plain,
! [SV1558: $i,SV1249: $i] :
( ( ! [SY3111: $i] :
( ~ ( class_Orderings_Olinorder @ SV1249 )
| ( ( c_SetInterval_OatMost @ SV1558 @ SV1249 )
!= ( c_SetInterval_OatMost @ SY3111 @ SV1249 ) )
| ( SV1558 = SY3111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5537]) ).
thf(6773,plain,
! [SV1559: $i,SV1250: $i] :
( ( ( ( c_Divides_Oop_Amod @ SV1250 @ SV1559 @ tc_IntDef_Oint )
!= c_0 )
| ( SV1250
= ( c_times @ SV1559 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SV1559 @ SV1250 ) @ tc_IntDef_Oint ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5538]) ).
thf(6774,plain,
! [SV1560: $i,SV1251: $i] :
( ( ! [SY3112: $i] :
( ( ( c_List_Orev @ SV1251 @ SV1560 )
!= ( c_List_Orev @ SY3112 @ SV1560 ) )
| ( SV1251 = SY3112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5539]) ).
thf(6775,plain,
! [SV1561: $i,SV1252: $i] :
( ( ! [SY3113: $i,SY3114: $i] :
( ( ( c_Message_Omsg_OMPair @ SV1252 @ SV1561 )
!= ( c_Message_Omsg_OMPair @ SY3113 @ SY3114 ) )
| ( SV1561 = SY3114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5540]) ).
thf(6776,plain,
! [SV1562: $i,SV1253: $i] :
( ( ! [SY3115: $i,SY3116: $i] :
( ( ( c_insert @ SV1253 @ c_emptyset @ SV1562 )
!= ( c_insert @ SY3115 @ SY3116 @ SV1562 ) )
| ( c_lessequals @ SY3116 @ ( c_insert @ SV1253 @ c_emptyset @ SV1562 ) @ ( tc_set @ SV1562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5541]) ).
thf(6777,plain,
! [SV1563: $i,SV1254: $i] :
( ( ( ( c_IntDef_Oint @ SV1254 )
!= ( c_IntDef_Oint @ SV1563 ) )
| ( SV1254 = SV1563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5542]) ).
thf(6778,plain,
! [SV1564: $i,SV1255: $i] :
( ( ! [SY3117: $i,SY3118: $i] :
( ( ( c_Sum__Type_OInr @ SV1255 @ SV1564 @ SY3117 )
!= ( c_Sum__Type_OInr @ SY3118 @ SV1564 @ SY3117 ) )
| ( SV1255 = SY3118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5543]) ).
thf(6779,plain,
! [SV1565: $i,SV1256: $i] :
( ( ! [SY3119: $i,SY3120: $i] :
( ( ( c_insert @ SV1256 @ SV1565 @ SY3119 )
!= ( c_insert @ SY3120 @ c_emptyset @ SY3119 ) )
| ( c_lessequals @ SV1565 @ ( c_insert @ SY3120 @ c_emptyset @ SY3119 ) @ ( tc_set @ SY3119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5544]) ).
thf(6780,plain,
! [SV1566: $i,SV1257: $i] :
( ( ! [SY3121: $i,SY3122: $i] :
( ( ( c_insert @ SV1257 @ SV1566 @ SY3121 )
!= ( c_insert @ SY3122 @ c_emptyset @ SY3121 ) )
| ( SV1257 = SY3122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5545]) ).
thf(6781,plain,
( ( ( c_lessequals @ v_G @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ v_H @ ( c_Message_Oanalz @ ( c_union @ v_G_H @ v_H_H @ tc_Message_Omsg ) ) @ ( tc_set @ tc_Message_Omsg ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5546]) ).
thf(6782,plain,
! [SV1567: $i,SV1258: $i,SV1: $i] :
( ( ! [SY3123: $i,SY3124: $i] :
( ~ ( c_in @ SV1 @ ( c_Datatype__Universe_Odprod @ SV1258 @ SV1567 @ SY3123 @ SY3124 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3123 @ SY3124 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3123 @ SY3124 ) ) ) )
| ( SV1
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV1 @ SV1258 @ SV1567 @ SY3123 @ SY3124 ) @ ( c_Main_OdprodE__2 @ SV1 @ SV1258 @ SV1567 @ SY3123 @ SY3124 ) @ SY3123 @ SY3124 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV1 @ SV1258 @ SV1567 @ SY3123 @ SY3124 ) @ ( c_Main_OdprodE__4 @ SV1 @ SV1258 @ SV1567 @ SY3123 @ SY3124 ) @ SY3123 @ SY3124 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3123 @ SY3124 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3123 @ SY3124 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5547]) ).
thf(6783,plain,
! [SV1568: $i,SV1259: $i,SV2: $i] :
( ( ! [SY3125: $i,SY3126: $i] :
( ~ ( c_in @ SV2 @ ( c_Datatype__Universe_Odprod @ SV1259 @ SV1568 @ SY3125 @ SY3126 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3125 @ SY3126 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3125 @ SY3126 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV2 @ SV1259 @ SV1568 @ SY3125 @ SY3126 ) @ ( c_Main_OdprodE__4 @ SV2 @ SV1259 @ SV1568 @ SY3125 @ SY3126 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3125 @ SY3126 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3125 @ SY3126 ) ) ) @ SV1568 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3125 @ SY3126 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3125 @ SY3126 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5548]) ).
thf(6784,plain,
! [SV1569: $i,SV1260: $i,SV3: $i] :
( ( ! [SY3127: $i,SY3128: $i] :
( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1260 @ SV1569 @ SY3127 @ SY3128 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3127 @ SY3128 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3127 @ SY3128 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV3 @ SV1260 @ SV1569 @ SY3127 @ SY3128 ) @ ( c_Main_OdprodE__3 @ SV3 @ SV1260 @ SV1569 @ SY3127 @ SY3128 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3127 @ SY3128 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3127 @ SY3128 ) ) ) @ SV1260 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3127 @ SY3128 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3127 @ SY3128 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5549]) ).
thf(6785,plain,
! [SV1570: $i,SV1261: $i,SV4: $i] :
( ( ! [SY3129: $i,SY3130: $i,SY3131: $i,SY3132: $i,SY3133: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) ) @ SY3130 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SY3131 @ SY3132 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) ) @ SY3133 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY3131 @ SV4 @ SV1570 @ SY3129 ) @ ( c_Datatype__Universe_OScons @ SY3132 @ SV1261 @ SV1570 @ SY3129 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3133 @ SY3130 @ SV1570 @ SY3129 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SY3129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5550]) ).
thf(6786,plain,
! [SV1571: $i,SV1262: $i,SV5: $i] :
( ( ! [SY3134: $i,SY3135: $i] :
( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SV1262 @ SV1571 @ SY3134 @ SY3135 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3134 @ SY3135 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3134 @ SY3135 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1262 @ SV5 @ SY3134 @ SY3135 ) @ SY3134 @ SY3135 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1262 @ SV5 @ SY3134 @ SY3135 ) @ SY3134 @ SY3135 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3134 @ SY3135 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3134 @ SY3135 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1571 @ SV5 @ SY3134 @ SY3135 ) @ SY3134 @ SY3135 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1571 @ SV5 @ SY3134 @ SY3135 ) @ SY3134 @ SY3135 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3134 @ SY3135 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3134 @ SY3135 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5551]) ).
thf(6787,plain,
! [SV1572: $i,SV1263: $i,SV6: $i] :
( ( ! [SY3136: $i,SY3137: $i] :
( ~ ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SV1263 @ SV1572 @ SY3136 @ SY3137 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1572 @ SV6 @ SY3136 @ SY3137 ) @ ( c_Main_OdsumE__4 @ SV1572 @ SV6 @ SY3136 @ SY3137 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) ) @ SV1572 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3136 @ SY3137 ) ) ) )
| ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1263 @ SV6 @ SY3136 @ SY3137 ) @ SY3136 @ SY3137 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1263 @ SV6 @ 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)],[5552]) ).
thf(6788,plain,
! [SV1573: $i,SV1264: $i,SV7: $i] :
( ( ! [SY3138: $i,SY3139: $i] :
( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1264 @ SV1573 @ 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_OdsumE__1 @ SV1264 @ SV7 @ SY3138 @ SY3139 ) @ ( c_Main_OdsumE__2 @ SV1264 @ SV7 @ SY3138 @ SY3139 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) ) @ SV1264 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) ) )
| ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1573 @ SV7 @ SY3138 @ SY3139 ) @ SY3138 @ SY3139 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1573 @ SV7 @ SY3138 @ SY3139 ) @ SY3138 @ SY3139 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3138 @ SY3139 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5553]) ).
thf(6789,plain,
! [SV1574: $i,SV1265: $i,SV8: $i] :
( ( ! [SY3140: $i,SY3141: $i] :
( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1265 @ SV1574 @ 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_OdsumE__1 @ SV1265 @ SV8 @ SY3140 @ SY3141 ) @ ( c_Main_OdsumE__2 @ SV1265 @ SV8 @ SY3140 @ SY3141 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) ) @ SV1265 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1574 @ SV8 @ SY3140 @ SY3141 ) @ ( c_Main_OdsumE__4 @ SV1574 @ SV8 @ SY3140 @ SY3141 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3140 @ SY3141 ) ) ) @ SV1574 @ ( 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)],[5554]) ).
thf(6790,plain,
! [SV1575: $i,SV1266: $i,SV9: $i] :
( ( ! [SY3142: $i,SY3143: $i,SY3144: $i] :
( ~ ( c_in @ ( c_Pair @ SV9 @ SV1266 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) ) @ SY3143 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SV1575 @ SY3142 ) @ ( c_Datatype__Universe_OIn0 @ SV1266 @ SV1575 @ SY3142 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3143 @ SY3144 @ SV1575 @ SY3142 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SY3142 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5555]) ).
thf(6791,plain,
! [SV1576: $i,SV1267: $i,SV10: $i] :
( ( ! [SY3145: $i,SY3146: $i,SY3147: $i] :
( ~ ( c_in @ ( c_Pair @ SV10 @ SV1267 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) ) @ SY3146 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SV1576 @ SY3145 ) @ ( c_Datatype__Universe_OIn1 @ SV1267 @ SV1576 @ SY3145 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3147 @ SY3146 @ SV1576 @ SY3145 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SY3145 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5556]) ).
thf(6792,plain,
! [SV1577: $i,SV1268: $i,SV11: $i] :
( ( ! [SY3148: $i,SY3149: $i] :
( ~ ( c_in @ SV11 @ ( c_Datatype__Universe_Ouprod @ SV1268 @ SV1577 @ SY3148 @ SY3149 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3148 @ SY3149 ) ) )
| ( SV11
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1268 @ SV1577 @ SV11 @ SY3148 @ SY3149 ) @ ( c_Main_OuprodE__2 @ SV1268 @ SV1577 @ SV11 @ SY3148 @ SY3149 ) @ SY3148 @ SY3149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5557]) ).
thf(6793,plain,
! [SV1578: $i,SV1269: $i,SV12: $i] :
( ( ! [SY3150: $i,SY3151: $i] :
( ~ ( c_in @ SV12 @ ( c_Datatype__Universe_Ouprod @ SV1269 @ SV1578 @ SY3150 @ SY3151 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3150 @ SY3151 ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ SV1269 @ SV1578 @ SV12 @ SY3150 @ SY3151 ) @ SV1578 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3150 @ SY3151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5558]) ).
thf(6794,plain,
! [SV1579: $i,SV1270: $i,SV13: $i] :
( ( ! [SY3152: $i,SY3153: $i] :
( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1270 @ SV1579 @ SY3152 @ SY3153 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3152 @ SY3153 ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ SV1270 @ SV1579 @ SV13 @ SY3152 @ SY3153 ) @ SV1270 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3152 @ SY3153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5559]) ).
thf(6795,plain,
! [SV1580: $i,SV1271: $i,SV14: $i] :
( ( ! [SY3154: $i,SY3155: $i,SY3156: $i] :
( ~ ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SY3154 ) ) )
| ~ ( c_in @ SY3155 @ SY3156 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SY3154 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SY3155 @ SV14 @ SV1580 @ SY3154 ) @ ( c_Datatype__Universe_Ouprod @ SY3156 @ SV1271 @ SV1580 @ SY3154 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SY3154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5560]) ).
thf(6796,plain,
! [SV1581: $i,SV1272: $i,SV15: $i] :
( ( ! [SY3157: $i,SY3158: $i] :
( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SV1272 @ SV1581 @ SY3157 @ SY3158 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3157 @ SY3158 ) ) )
| ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1272 @ SV15 @ SY3157 @ SY3158 ) @ SY3157 @ SY3158 ) )
| ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1581 @ SV15 @ SY3157 @ SY3158 ) @ SY3157 @ SY3158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5561]) ).
thf(6797,plain,
! [SV1582: $i,SV1273: $i,SV16: $i] :
( ( ! [SY3159: $i,SY3160: $i] :
( ~ ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SV1273 @ SV1582 @ SY3159 @ SY3160 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3159 @ SY3160 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1582 @ SV16 @ SY3159 @ SY3160 ) @ SV1582 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3159 @ SY3160 ) ) )
| ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1273 @ SV16 @ SY3159 @ SY3160 ) @ SY3159 @ SY3160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5562]) ).
thf(6798,plain,
! [SV1583: $i,SV1274: $i,SV17: $i] :
( ( ! [SY3161: $i,SY3162: $i] :
( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1274 @ SV1583 @ SY3161 @ SY3162 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3161 @ SY3162 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1274 @ SV17 @ SY3161 @ SY3162 ) @ SV1274 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3161 @ SY3162 ) ) )
| ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1583 @ SV17 @ SY3161 @ SY3162 ) @ SY3161 @ SY3162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5563]) ).
thf(6799,plain,
! [SV1584: $i,SV1275: $i,SV18: $i] :
( ( ! [SY3163: $i,SY3164: $i] :
( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1275 @ SV1584 @ SY3163 @ SY3164 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3163 @ SY3164 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1275 @ SV18 @ SY3163 @ SY3164 ) @ SV1275 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3163 @ SY3164 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1584 @ SV18 @ SY3163 @ SY3164 ) @ SV1584 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SY3163 @ SY3164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5564]) ).
thf(6800,plain,
! [SV1585: $i,SV1276: $i,SV19: $i] :
( ( ! [SY3165: $i,SY3166: $i] :
( ~ ( c_in @ SV19 @ SV1276 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SY3165 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn0 @ SV19 @ SV1585 @ SY3165 ) @ ( c_Datatype__Universe_Ousum @ SV1276 @ SY3166 @ SV1585 @ SY3165 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SY3165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5565]) ).
thf(6801,plain,
! [SV1586: $i,SV1277: $i,SV20: $i] :
( ( ! [SY3167: $i,SY3168: $i] :
( ~ ( c_in @ SV20 @ SV1277 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SY3167 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn1 @ SV20 @ SV1586 @ SY3167 ) @ ( c_Datatype__Universe_Ousum @ SY3168 @ SV1277 @ SV1586 @ SY3167 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SY3167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5566]) ).
thf(6802,plain,
! [SV1587: $i,SV1280: $i,SV26: $i] :
( ( ~ ( c_in @ SV26 @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) )
| ( c_in @ ( c_insert @ SV1587 @ SV26 @ SV1280 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5569]) ).
thf(6803,plain,
! [SV1588: $i,SV1281: $i,SV27: $i] :
( ( ~ ( c_in @ SV27 @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) )
| ( c_in @ ( c_inter @ SV27 @ SV1588 @ SV1281 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5570]) ).
thf(6804,plain,
! [SV1589: $i,SV1282: $i,SV28: $i] :
( ( ~ ( c_in @ SV28 @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) )
| ( c_in @ ( c_inter @ SV1589 @ SV28 @ SV1282 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5571]) ).
thf(6805,plain,
! [SV1283: $i,SV29: $i] :
( ( ( ~ ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1283 ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV29 @ SV1283 ) @ SV29 @ ( tc_set @ SV1283 ) )
| ( c_in @ ( c_Union @ SV29 @ SV1283 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5572]) ).
thf(6806,plain,
! [SV1284: $i,SV30: $i] :
( ( ( ~ ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1284 ) ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) )
| ( c_in @ ( c_Union @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5573]) ).
thf(6807,plain,
! [SV1590: $i,SV1287: $i,SV33: $i] :
( ( ! [SY3169: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
| ~ ( c_in @ SV1590 @ SV33 @ SV1287 )
| ~ ( c_in @ SY3169 @ SV33 @ SV1287 )
| ( SV1590 = SY3169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5576]) ).
thf(6808,plain,
! [SV1591: $i,SV1294: $i,SV42: $i] :
( ( ! [SY3170: $i] :
( ~ ( c_in @ SV42 @ ( c_List_Olists @ SV1294 @ SV1591 ) @ ( tc_List_Olist @ SV1591 ) )
| ~ ( c_in @ SY3170 @ ( c_List_Oset @ SV42 @ SV1591 ) @ SV1591 )
| ( c_in @ SY3170 @ SV1294 @ SV1591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5583]) ).
thf(6809,plain,
! [SV1592: $i,SV1295: $i,SV43: $i] :
( ( ( c_in @ SV43 @ ( c_List_Olists @ SV1295 @ SV1592 ) @ ( tc_List_Olist @ SV1592 ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ SV1295 @ SV43 @ SV1592 ) @ ( c_List_Oset @ SV43 @ SV1592 ) @ SV1592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5584]) ).
thf(6810,plain,
! [SV1593: $i,SV1296: $i,SV44: $i] :
( ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV44 @ SV1296 @ SV1593 ) @ SV44 @ SV1593 )
| ( c_in @ SV1296 @ ( c_List_Olists @ SV44 @ SV1593 ) @ ( tc_List_Olist @ SV1593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5585]) ).
thf(6811,plain,
! [SV1594: $i,SV1298: $i,SV46: $i] :
( ( ! [SY3171: $i,SY3172: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV46 @ SV1298 @ SV1594 ) @ SY3171 @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) @ ( c_List_Olistrel @ SY3172 @ SV1594 ) @ ( tc_prod @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) )
| ( SY3171
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY3172 @ SY3171 @ SV46 @ SV1298 @ SV1594 ) @ ( c_Main_Olistrel__Cons1__2 @ SY3172 @ SY3171 @ SV46 @ SV1298 @ SV1594 ) @ SV1594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(6812,plain,
! [SV1595: $i,SV1299: $i,SV47: $i] :
( ( ! [SY3173: $i,SY3174: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV47 @ SV1299 @ SV1595 ) @ SY3173 @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SY3174 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) )
| ( c_in @ ( c_Pair @ SV1299 @ ( c_Main_Olistrel__Cons1__2 @ SY3174 @ SY3173 @ SV47 @ SV1299 @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SY3174 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(6813,plain,
! [SV1596: $i,SV1300: $i,SV48: $i] :
( ( ! [SY3175: $i,SY3176: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV48 @ SV1300 @ SV1596 ) @ SY3175 @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) @ ( c_List_Olistrel @ SY3176 @ SV1596 ) @ ( tc_prod @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) )
| ( c_in @ ( c_Pair @ SV48 @ ( c_Main_Olistrel__Cons1__1 @ SY3176 @ SY3175 @ SV48 @ SV1300 @ SV1596 ) @ SV1596 @ SV1596 ) @ SY3176 @ ( tc_prod @ SV1596 @ SV1596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5589]) ).
thf(6814,plain,
! [SV1597: $i,SV1301: $i,SV49: $i] :
( ( ! [SY3177: $i,SY3178: $i] :
( ~ ( c_in @ ( c_Pair @ SV49 @ ( c_List_Olist_OCons @ SV1301 @ SV1597 @ SY3177 ) @ ( tc_List_Olist @ SY3177 ) @ ( tc_List_Olist @ SY3177 ) ) @ ( c_List_Olistrel @ SY3178 @ SY3177 ) @ ( tc_prod @ ( tc_List_Olist @ SY3177 ) @ ( tc_List_Olist @ SY3177 ) ) )
| ( SV49
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY3178 @ SV49 @ SV1301 @ SV1597 @ SY3177 ) @ ( c_Main_Olistrel__Cons2__2 @ SY3178 @ SV49 @ SV1301 @ SV1597 @ SY3177 ) @ SY3177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5590]) ).
thf(6815,plain,
! [SV1598: $i,SV1302: $i,SV50: $i] :
( ( ! [SY3179: $i,SY3180: $i] :
( ~ ( c_in @ ( c_Pair @ SV50 @ ( c_List_Olist_OCons @ SV1302 @ SV1598 @ SY3179 ) @ ( tc_List_Olist @ SY3179 ) @ ( tc_List_Olist @ SY3179 ) ) @ ( c_List_Olistrel @ SY3180 @ SY3179 ) @ ( tc_prod @ ( tc_List_Olist @ SY3179 ) @ ( tc_List_Olist @ SY3179 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY3180 @ SV50 @ SV1302 @ SV1598 @ SY3179 ) @ SV1598 @ ( tc_List_Olist @ SY3179 ) @ ( tc_List_Olist @ SY3179 ) ) @ ( c_List_Olistrel @ SY3180 @ SY3179 ) @ ( tc_prod @ ( tc_List_Olist @ SY3179 ) @ ( tc_List_Olist @ SY3179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5591]) ).
thf(6816,plain,
! [SV1599: $i,SV1303: $i,SV51: $i] :
( ( ! [SY3181: $i,SY3182: $i] :
( ~ ( c_in @ ( c_Pair @ SV51 @ ( c_List_Olist_OCons @ SV1303 @ SV1599 @ SY3181 ) @ ( tc_List_Olist @ SY3181 ) @ ( tc_List_Olist @ SY3181 ) ) @ ( c_List_Olistrel @ SY3182 @ SY3181 ) @ ( tc_prod @ ( tc_List_Olist @ SY3181 ) @ ( tc_List_Olist @ SY3181 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY3182 @ SV51 @ SV1303 @ SV1599 @ SY3181 ) @ SV1303 @ SY3181 @ SY3181 ) @ SY3182 @ ( tc_prod @ SY3181 @ SY3181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5592]) ).
thf(6817,plain,
! [SV1600: $i,SV1304: $i,SV52: $i] :
( ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV52 @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) @ ( c_List_Olistrel @ SV1600 @ SV1304 ) @ ( tc_prod @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) )
| ( SV52 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5593]) ).
thf(6818,plain,
! [SV1601: $i,SV1305: $i,SV53: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV53 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) @ ( c_List_Olistrel @ SV1601 @ SV1305 ) @ ( tc_prod @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) )
| ( SV53 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5594]) ).
thf(6819,plain,
! [SV1602: $i,SV1306: $i,SV54: $i] :
( ( ! [SY3183: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ SV54 @ SV1306 @ SV1602 ) @ ( c_List_Olists @ SY3183 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) )
| ( c_in @ SV1306 @ ( c_List_Olists @ SY3183 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5595]) ).
thf(6820,plain,
! [SV1603: $i,SV1307: $i,SV55: $i] :
( ( ! [SY3184: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ SV55 @ SV1307 @ SV1603 ) @ ( c_List_Olists @ SY3184 @ SV1603 ) @ ( tc_List_Olist @ SV1603 ) )
| ( c_in @ SV55 @ SY3184 @ SV1603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5596]) ).
thf(6821,plain,
! [SV1604: $i,SV1308: $i,SV56: $i] :
( ( ! [SY3185: $i] :
( ~ ( c_in @ SV56 @ SV1308 @ SV1604 )
| ~ ( c_in @ SY3185 @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) )
| ( c_in @ ( c_List_Olist_OCons @ SV56 @ SY3185 @ SV1604 ) @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5597]) ).
thf(6822,plain,
! [SV1310: $i,SV58: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV58 @ SV1310 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV58 @ SV1310 ) @ ( tc_List_Olist @ SV1310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5599]) ).
thf(6823,plain,
! [SV1311: $i,SV59: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV59 @ SV1311 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV59 @ SV1311 ) @ ( tc_List_Olist @ SV1311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5600]) ).
thf(6824,plain,
! [SV1312: $i,SV64: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV64 ) )
= $true )
| ( ( c_lessequals @ SV1312 @ SV1312 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5602]) ).
thf(6825,plain,
! [SV1605: $i,SV1313: $i,SV65: $i] :
( ( ! [SY3186: $i] :
( ~ ( c_in @ SV65 @ ( c_Relation_ODomain @ SV1313 @ SV1605 @ SY3186 ) @ SV1605 )
| ( c_in @ ( c_Pair @ SV65 @ ( c_Main_ODomainE__1 @ SV65 @ SV1313 @ SV1605 @ SY3186 ) @ SV1605 @ SY3186 ) @ SV1313 @ ( tc_prod @ SV1605 @ SY3186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5603]) ).
thf(6826,plain,
! [SV1606: $i,SV1314: $i,SV66: $i] :
( ( ! [SY3187: $i,SY3188: $i] :
( ~ ( c_in @ ( c_Pair @ SV66 @ SV1314 @ SV1606 @ SY3187 ) @ SY3188 @ ( tc_prod @ SV1606 @ SY3187 ) )
| ( c_in @ SV66 @ ( c_Relation_ODomain @ SY3188 @ SV1606 @ SY3187 ) @ SV1606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5604]) ).
thf(6827,plain,
! [SV1315: $i,SV67: $i] :
( ( ( ~ ( c_in @ SV67 @ c_Relation_OId @ ( tc_prod @ SV1315 @ SV1315 ) ) )
= $true )
| ( ( SV67
= ( c_Pair @ ( c_Main_OIdE__1 @ SV67 @ SV1315 ) @ ( c_Main_OIdE__1 @ SV67 @ SV1315 ) @ SV1315 @ SV1315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5605]) ).
thf(6828,plain,
! [SV1607: $i,SV1316: $i,SV68: $i] :
( ( ! [SY3189: $i,SY3190: $i] :
( ~ ( c_in @ SV68 @ ( c_Relation_OImage @ SV1316 @ SV1607 @ SY3189 @ SY3190 ) @ SY3190 )
| ( c_in @ ( c_Main_OImageE__1 @ SV1607 @ SV68 @ SV1316 @ SY3189 @ SY3190 ) @ SV1607 @ SY3189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5606]) ).
thf(6829,plain,
! [SV1608: $i,SV1317: $i,SV69: $i] :
( ( ! [SY3191: $i,SY3192: $i] :
( ~ ( c_in @ SV69 @ ( c_Relation_OImage @ SV1317 @ SV1608 @ SY3191 @ SY3192 ) @ SY3192 )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1608 @ SV69 @ SV1317 @ SY3191 @ SY3192 ) @ SV69 @ SY3191 @ SY3192 ) @ SV1317 @ ( tc_prod @ SY3191 @ SY3192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5607]) ).
thf(6830,plain,
! [SV1609: $i,SV1318: $i,SV70: $i] :
( ( ! [SY3193: $i,SY3194: $i,SY3195: $i] :
( ~ ( c_in @ SV70 @ SV1318 @ SV1609 )
| ~ ( c_in @ ( c_Pair @ SV70 @ SY3193 @ SV1609 @ SY3194 ) @ SY3195 @ ( tc_prod @ SV1609 @ SY3194 ) )
| ( c_in @ SY3193 @ ( c_Relation_OImage @ SY3195 @ SV1318 @ SV1609 @ SY3194 ) @ SY3194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5608]) ).
thf(6831,plain,
! [SV1610: $i,SV1319: $i,SV71: $i] :
( ( ! [SY3196: $i] :
( ~ ( c_in @ SV71 @ ( c_Relation_ORange @ SV1319 @ SV1610 @ SY3196 ) @ SY3196 )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV71 @ SV1319 @ SY3196 @ SV1610 ) @ SV71 @ SV1610 @ SY3196 ) @ SV1319 @ ( tc_prod @ SV1610 @ SY3196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5609]) ).
thf(6832,plain,
! [SV1611: $i,SV1320: $i,SV72: $i] :
( ( ! [SY3197: $i,SY3198: $i] :
( ~ ( c_in @ ( c_Pair @ SV72 @ SV1320 @ SV1611 @ SY3197 ) @ SY3198 @ ( tc_prod @ SV1611 @ SY3197 ) )
| ( c_in @ SV1320 @ ( c_Relation_ORange @ SY3198 @ SV1611 @ SY3197 ) @ SY3197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5610]) ).
thf(6833,plain,
! [SV1612: $i,SV1321: $i,SV73: $i] :
( ( ! [SY3199: $i] :
( ~ ( c_in @ SV73 @ ( c_Relation_Oconverse @ SV1321 @ SV1612 @ SY3199 ) @ ( tc_prod @ SY3199 @ SV1612 ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1321 @ SV73 @ SV1612 @ SY3199 ) @ ( c_Main_OconverseE__2 @ SV1321 @ SV73 @ SV1612 @ SY3199 ) @ SV1612 @ SY3199 ) @ SV1321 @ ( tc_prod @ SV1612 @ SY3199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5611]) ).
thf(6834,plain,
! [SV1613: $i,SV1322: $i,SV74: $i] :
( ( ! [SY3200: $i] :
( ~ ( c_in @ SV74 @ ( c_Relation_Oconverse @ SV1322 @ SV1613 @ SY3200 ) @ ( tc_prod @ SY3200 @ SV1613 ) )
| ( SV74
= ( c_Pair @ ( c_Main_OconverseE__2 @ SV1322 @ SV74 @ SV1613 @ SY3200 ) @ ( c_Main_OconverseE__1 @ SV1322 @ SV74 @ SV1613 @ SY3200 ) @ SY3200 @ SV1613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5612]) ).
thf(6835,plain,
! [SV1614: $i,SV1323: $i,SV75: $i] :
( ( ~ ( c_in @ SV75 @ ( c_Relation_Odiag @ SV1323 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
| ( SV75
= ( c_Pair @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SV1614 ) @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SV1614 ) @ SV1614 @ SV1614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5613]) ).
thf(6836,plain,
! [SV1615: $i,SV1324: $i,SV76: $i] :
( ( ~ ( c_in @ SV76 @ ( c_Relation_Odiag @ SV1324 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ( c_in @ ( c_Main_OdiagE__1 @ SV1324 @ SV76 @ SV1615 ) @ SV1324 @ SV1615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5614]) ).
thf(6837,plain,
! [SV1616: $i,SV1325: $i,SV77: $i] :
( ( ~ ( c_in @ SV77 @ SV1325 @ SV1616 )
| ( c_in @ ( c_Pair @ SV77 @ SV77 @ SV1616 @ SV1616 ) @ ( c_Relation_Odiag @ SV1325 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5615]) ).
thf(6838,plain,
! [SV1617: $i,SV1326: $i,SV78: $i] :
( ( ! [SY3201: $i,SY3202: $i,SY3203: $i] :
( ~ ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SV1326 @ SV1617 @ SY3201 @ SY3202 @ SY3203 ) @ ( tc_prod @ SY3203 @ SY3202 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1326 @ SV1617 @ SV78 @ SY3201 @ SY3202 @ SY3203 ) @ ( c_Main_Orel__compE__3 @ SV1326 @ SV1617 @ SV78 @ SY3201 @ SY3202 @ SY3203 ) @ SY3201 @ SY3202 ) @ SV1326 @ ( tc_prod @ SY3201 @ SY3202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5616]) ).
thf(6839,plain,
! [SV1618: $i,SV1327: $i,SV79: $i] :
( ( ! [SY3204: $i,SY3205: $i,SY3206: $i] :
( ~ ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SV1327 @ SV1618 @ SY3204 @ SY3205 @ SY3206 ) @ ( tc_prod @ SY3206 @ SY3205 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1327 @ SV1618 @ SV79 @ SY3204 @ SY3205 @ SY3206 ) @ ( c_Main_Orel__compE__2 @ SV1327 @ SV1618 @ SV79 @ SY3204 @ SY3205 @ SY3206 ) @ SY3206 @ SY3204 ) @ SV1618 @ ( tc_prod @ SY3206 @ SY3204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5617]) ).
thf(6840,plain,
! [SV1619: $i,SV1328: $i,SV80: $i] :
( ( ! [SY3207: $i,SY3208: $i,SY3209: $i] :
( ~ ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SV1328 @ SV1619 @ SY3207 @ SY3208 @ SY3209 ) @ ( tc_prod @ SY3209 @ SY3208 ) )
| ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1328 @ SV1619 @ SV80 @ SY3207 @ SY3208 @ SY3209 ) @ ( c_Main_Orel__compE__3 @ SV1328 @ SV1619 @ SV80 @ SY3207 @ SY3208 @ SY3209 ) @ SY3209 @ SY3208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5618]) ).
thf(6841,plain,
! [SV1620: $i,SV1329: $i,SV81: $i] :
( ( ! [SY3210: $i,SY3211: $i,SY3212: $i,SY3213: $i,SY3214: $i] :
( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SY3210 ) @ SY3211 @ ( tc_prod @ SV1620 @ SY3210 ) )
| ~ ( c_in @ ( c_Pair @ SY3212 @ SV81 @ SY3213 @ SV1620 ) @ SY3214 @ ( tc_prod @ SY3213 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SY3212 @ SV1329 @ SY3213 @ SY3210 ) @ ( c_Relation_Orel__comp @ SY3211 @ SY3214 @ SV1620 @ SY3210 @ SY3213 ) @ ( tc_prod @ SY3213 @ SY3210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5619]) ).
thf(6842,plain,
! [SV1621: $i,SV1338: $i,SV92: $i] :
( ( ( c_in @ SV92 @ ( c_Inter @ SV1338 @ SV1621 ) @ SV1621 )
| ( c_in @ ( c_Main_OInterI__1 @ SV92 @ SV1338 @ SV1621 ) @ SV1338 @ ( tc_set @ SV1621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5628]) ).
thf(6843,plain,
! [SV1622: $i,SV1339: $i,SV93: $i] :
( ( ~ ( c_in @ SV93 @ ( c_Main_OInterI__1 @ SV93 @ SV1339 @ SV1622 ) @ SV1622 )
| ( c_in @ SV93 @ ( c_Inter @ SV1339 @ SV1622 ) @ SV1622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5629]) ).
thf(6844,plain,
! [SV1623: $i,SV1341: $i,SV95: $i] :
( ( ~ ( c_in @ SV95 @ ( c_Union @ SV1341 @ SV1623 ) @ SV1623 )
| ( c_in @ ( c_Main_OUnionE__1 @ SV95 @ SV1341 @ SV1623 ) @ SV1341 @ ( tc_set @ SV1623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5631]) ).
thf(6845,plain,
! [SV1624: $i,SV1342: $i,SV96: $i] :
( ( ~ ( c_in @ SV96 @ ( c_Union @ SV1342 @ SV1624 ) @ SV1624 )
| ( c_in @ SV96 @ ( c_Main_OUnionE__1 @ SV96 @ SV1342 @ SV1624 ) @ SV1624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5632]) ).
thf(6846,plain,
! [SV1625: $i,SV1344: $i,SV98: $i] :
( ( ~ ( c_less @ SV98 @ SV1344 @ ( tc_set @ SV1625 ) )
| ~ ( c_lessequals @ SV1344 @ SV98 @ ( tc_set @ SV1625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5634]) ).
thf(6847,plain,
! [SV1626: $i,SV1345: $i,SV99: $i] :
( ( ~ ( c_less @ SV99 @ SV1345 @ ( tc_set @ SV1626 ) )
| ( c_lessequals @ SV99 @ SV1345 @ ( tc_set @ SV1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5635]) ).
thf(6848,plain,
! [SV1627: $i,SV1346: $i,SV100: $i] :
( ( ~ ( c_lessequals @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) )
| ( c_less @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) )
| ( SV100 = SV1346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5636]) ).
thf(6849,plain,
! [SV1628: $i,SV1347: $i,SV101: $i] :
( ( ~ ( c_in @ SV101 @ ( c_insert @ SV1347 @ c_emptyset @ SV1628 ) @ SV1628 )
| ( SV101 = SV1347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5637]) ).
thf(6850,plain,
! [SV1629: $i,SV1349: $i,SV103: $i] :
( ( ! [SY3215: $i] :
( ~ ( c_in @ SV103 @ SV1349 @ SV1629 )
| ~ ( c_lessequals @ SV1349 @ SY3215 @ ( tc_set @ SV1629 ) )
| ( c_in @ SV103 @ SY3215 @ SV1629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5639]) ).
thf(6851,plain,
! [SV1630: $i,SV1350: $i,SV104: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV104 @ SV1350 @ SV1630 ) @ SV104 @ SV1630 )
| ( c_lessequals @ SV104 @ SV1350 @ ( tc_set @ SV1630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5640]) ).
thf(6852,plain,
! [SV1631: $i,SV1351: $i,SV105: $i] :
( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV105 @ SV1351 @ SV1631 ) @ SV1351 @ SV1631 )
| ( c_lessequals @ SV105 @ SV1351 @ ( tc_set @ SV1631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5641]) ).
thf(6853,plain,
! [SV1632: $i,SV1352: $i,SV106: $i] :
( ( ~ ( c_lessequals @ SV106 @ SV1352 @ ( tc_set @ SV1632 ) )
| ~ ( c_lessequals @ SV1352 @ SV106 @ ( tc_set @ SV1632 ) )
| ( SV1352 = SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5642]) ).
thf(6854,plain,
! [SV1633: $i,SV1354: $i,SV108: $i] :
( ( ! [SY3216: $i,SY3217: $i] :
( ~ ( c_in @ SV108 @ SV1354 @ SV1633 )
| ( c_in @ ( c_Sum__Type_OInl @ SV108 @ SV1633 @ SY3216 ) @ ( c_Sum__Type_OPlus @ SV1354 @ SY3217 @ SV1633 @ SY3216 ) @ ( tc_sum @ SV1633 @ SY3216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5644]) ).
thf(6855,plain,
! [SV1634: $i,SV1355: $i,SV109: $i] :
( ( ! [SY3218: $i,SY3219: $i] :
( ~ ( c_in @ SV109 @ SV1355 @ SV1634 )
| ( c_in @ ( c_Sum__Type_OInr @ SV109 @ SV1634 @ SY3218 ) @ ( c_Sum__Type_OPlus @ SY3219 @ SV1355 @ SY3218 @ SV1634 ) @ ( tc_sum @ SY3218 @ SV1634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5645]) ).
thf(6856,plain,
! [SV1635: $i,SV1356: $i,SV110: $i] :
( ( ! [SY3220: $i,SY3221: $i] :
( ~ ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SV1356 @ SV1635 @ SY3220 @ SY3221 ) @ ( tc_sum @ SY3220 @ SY3221 ) )
| ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1356 @ SV110 @ SY3220 @ SY3221 ) @ SY3220 @ SY3221 ) )
| ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1635 @ SV110 @ SY3221 @ SY3220 ) @ SY3221 @ SY3220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5646]) ).
thf(6857,plain,
! [SV1636: $i,SV1357: $i,SV111: $i] :
( ( ! [SY3222: $i,SY3223: $i] :
( ~ ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SV1357 @ SV1636 @ SY3222 @ SY3223 ) @ ( tc_sum @ SY3222 @ SY3223 ) )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1636 @ SV111 @ SY3223 @ SY3222 ) @ SV1636 @ SY3223 )
| ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1357 @ SV111 @ SY3222 @ SY3223 ) @ SY3222 @ SY3223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5647]) ).
thf(6858,plain,
! [SV1637: $i,SV1358: $i,SV112: $i] :
( ( ! [SY3224: $i,SY3225: $i] :
( ~ ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SV1358 @ SV1637 @ SY3224 @ SY3225 ) @ ( tc_sum @ SY3224 @ SY3225 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1358 @ SV112 @ SY3224 @ SY3225 ) @ SV1358 @ SY3224 )
| ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1637 @ SV112 @ SY3225 @ SY3224 ) @ SY3225 @ SY3224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5648]) ).
thf(6859,plain,
! [SV1638: $i,SV1359: $i,SV113: $i] :
( ( ! [SY3226: $i,SY3227: $i] :
( ~ ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SV1359 @ SV1638 @ SY3226 @ SY3227 ) @ ( tc_sum @ SY3226 @ SY3227 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1359 @ SV113 @ SY3226 @ SY3227 ) @ SV1359 @ SY3226 )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1638 @ SV113 @ SY3227 @ SY3226 ) @ SV1638 @ SY3227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5649]) ).
thf(6860,plain,
! [SV1639: $i,SV1360: $i,SV114: $i] :
( ( ~ ( c_in @ SV114 @ SV1360 @ ( tc_prod @ SV1639 @ SV1639 ) )
| ( c_in @ SV114 @ ( c_Transitive__Closure_Ortrancl @ SV1360 @ SV1639 ) @ ( tc_prod @ SV1639 @ SV1639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5650]) ).
thf(6861,plain,
! [SV1640: $i,SV1361: $i,SV115: $i] :
( ( c_in @ ( c_Pair @ SV115 @ SV115 @ SV1361 @ SV1361 ) @ ( c_Transitive__Closure_Ortrancl @ SV1640 @ SV1361 ) @ ( tc_prod @ SV1361 @ SV1361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5651]) ).
thf(6862,plain,
! [SV1641: $i,SV1362: $i,SV116: $i] :
( ( ! [SY3228: $i] :
( ~ ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ SY3228 @ ( tc_prod @ SV1641 @ SV1641 ) )
| ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ ( c_Transitive__Closure_Otrancl @ SY3228 @ SV1641 ) @ ( tc_prod @ SV1641 @ SV1641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5652]) ).
thf(6863,plain,
! [SV1642: $i,SV1363: $i,SV117: $i] :
( ( ! [SY3229: $i] :
( ~ ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Otrancl @ SY3229 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
| ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Ortrancl @ SY3229 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5653]) ).
thf(6864,plain,
! [SV1643: $i,SV1364: $i,SV119: $i] :
( ( ! [SY3230: $i] :
( ~ ( c_Relation_Otrans @ SV119 @ SV1364 )
| ~ ( c_Relation_Otrans @ SV1643 @ SY3230 )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1643 @ SV119 @ SY3230 @ SV1364 ) @ ( tc_prod @ SY3230 @ SV1364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5654]) ).
thf(6865,plain,
! [SV1644: $i,SV1365: $i,SV120: $i] :
( ( ! [SY3231: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV120 @ SV1365 )
| ~ ( c_Wellfounded__Recursion_Owf @ SV1644 @ SY3231 )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1644 @ SV120 @ SY3231 @ SV1365 ) @ ( tc_prod @ SY3231 @ SV1365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5655]) ).
thf(6866,plain,
! [SV121: $i] :
( ( ( class_Finite__Set_Ofinite @ SV121 )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_Datatype_Ooption @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5656]) ).
thf(6867,plain,
! [SV1366: $i,SV122: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV122 @ SV1366 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV1366 )
| ~ ( class_Finite__Set_Ofinite @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5657]) ).
thf(6868,plain,
! [SV1368: $i,SV124: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV124 @ SV1368 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV1368 )
| ~ ( class_Finite__Set_Ofinite @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5659]) ).
thf(6869,plain,
! [SV128: $i] :
( ( ( class_Finite__Set_Ofinite @ SV128 )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_set @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5660]) ).
thf(6870,plain,
! [SV1369: $i,SV130: $i] :
( ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV130 @ SV1369 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV1369 )
| ~ ( class_Finite__Set_Ofinite @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5661]) ).
thf(6871,plain,
! [SV131: $i] :
( ( ( class_LOrder_Ojoin__semilorder @ SV131 )
= $false )
| ( ( class_Orderings_Oord @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(6872,plain,
! [SV132: $i] :
( ( ( class_LOrder_Ojoin__semilorder @ SV132 )
= $false )
| ( ( class_Orderings_Oorder @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(6873,plain,
! [SV133: $i] :
( ( ( class_LOrder_Olorder @ SV133 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(6874,plain,
! [SV134: $i] :
( ( ( class_LOrder_Olorder @ SV134 )
= $false )
| ( ( class_Orderings_Oord @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5665]) ).
thf(6875,plain,
! [SV135: $i] :
( ( ( class_LOrder_Olorder @ SV135 )
= $false )
| ( ( class_Orderings_Oorder @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5666]) ).
thf(6876,plain,
! [SV136: $i] :
( ( ( class_LOrder_Olorder @ SV136 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5667]) ).
thf(6877,plain,
! [SV137: $i] :
( ( ( class_LOrder_Omeet__semilorder @ SV137 )
= $false )
| ( ( class_Orderings_Oord @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5668]) ).
thf(6878,plain,
! [SV138: $i] :
( ( ( class_LOrder_Omeet__semilorder @ SV138 )
= $false )
| ( ( class_Orderings_Oorder @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5669]) ).
thf(6879,plain,
! [SV139: $i] :
( ( ( class_Numeral_Onumber__ring @ SV139 )
= $false )
| ( ( class_HOL_Oplus @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5670]) ).
thf(6880,plain,
! [SV140: $i] :
( ( ( class_Numeral_Onumber__ring @ SV140 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5671]) ).
thf(6881,plain,
! [SV141: $i] :
( ( ( class_Numeral_Onumber__ring @ SV141 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(6882,plain,
! [SV142: $i] :
( ( ( class_Numeral_Onumber__ring @ SV142 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5673]) ).
thf(6883,plain,
! [SV143: $i] :
( ( ( class_Numeral_Onumber__ring @ SV143 )
= $false )
| ( ( class_HOL_Ominus @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5674]) ).
thf(6884,plain,
! [SV144: $i] :
( ( ( class_Numeral_Onumber__ring @ SV144 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5675]) ).
thf(6885,plain,
! [SV145: $i] :
( ( ( class_Numeral_Onumber__ring @ SV145 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5676]) ).
thf(6886,plain,
! [SV146: $i] :
( ( ( class_Numeral_Onumber__ring @ SV146 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5677]) ).
thf(6887,plain,
! [SV147: $i] :
( ( ( class_Numeral_Onumber__ring @ SV147 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5678]) ).
thf(6888,plain,
! [SV148: $i] :
( ( ( class_Numeral_Onumber__ring @ SV148 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5679]) ).
thf(6889,plain,
! [SV149: $i] :
( ( ( class_Numeral_Onumber__ring @ SV149 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5680]) ).
thf(6890,plain,
! [SV150: $i] :
( ( ( class_Numeral_Onumber__ring @ SV150 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5681]) ).
thf(6891,plain,
! [SV151: $i] :
( ( ( class_Numeral_Onumber__ring @ SV151 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5682]) ).
thf(6892,plain,
! [SV152: $i] :
( ( ( class_Numeral_Onumber__ring @ SV152 )
= $false )
| ( ( class_HOL_Oone @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(6893,plain,
! [SV153: $i] :
( ( ( class_Numeral_Onumber__ring @ SV153 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5684]) ).
thf(6894,plain,
! [SV154: $i] :
( ( ( class_Numeral_Onumber__ring @ SV154 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5685]) ).
thf(6895,plain,
! [SV155: $i] :
( ( ( class_Numeral_Onumber__ring @ SV155 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5686]) ).
thf(6896,plain,
! [SV156: $i] :
( ( ( class_Numeral_Onumber__ring @ SV156 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5687]) ).
thf(6897,plain,
! [SV157: $i] :
( ( ( class_Numeral_Onumber__ring @ SV157 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5688]) ).
thf(6898,plain,
! [SV158: $i] :
( ( ( class_Numeral_Onumber__ring @ SV158 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5689]) ).
thf(6899,plain,
! [SV159: $i] :
( ( ( class_Numeral_Onumber__ring @ SV159 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5690]) ).
thf(6900,plain,
! [SV160: $i] :
( ( ( class_Numeral_Onumber__ring @ SV160 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5691]) ).
thf(6901,plain,
! [SV161: $i] :
( ( ( class_Numeral_Onumber__ring @ SV161 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5692]) ).
thf(6902,plain,
! [SV162: $i] :
( ( ( class_Numeral_Onumber__ring @ SV162 )
= $false )
| ( ( class_HOL_Otimes @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5693]) ).
thf(6903,plain,
! [SV163: $i] :
( ( ( class_Numeral_Onumber__ring @ SV163 )
= $false )
| ( ( class_Numeral_Onumber @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(6904,plain,
! [SV164: $i] :
( ( ( class_Numeral_Onumber__ring @ SV164 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(6905,plain,
! [SV165: $i] :
( ( ( class_Numeral_Onumber__ring @ SV165 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(6906,plain,
! [SV166: $i] :
( ( ( class_Numeral_Onumber__ring @ SV166 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(6907,plain,
! [SV167: $i] :
( ( ( class_Numeral_Onumber__ring @ SV167 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5698]) ).
thf(6908,plain,
! [SV168: $i] :
( ( ( class_Numeral_Onumber__ring @ SV168 )
= $false )
| ( ( class_HOL_Ozero @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(6909,plain,
! [SV169: $i] :
( ( ( class_Numeral_Onumber__ring @ SV169 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5700]) ).
thf(6910,plain,
! [SV170: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV170 )
= $false )
| ( ( class_HOL_Ominus @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5701]) ).
thf(6911,plain,
! [SV171: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV171 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5702]) ).
thf(6912,plain,
! [SV172: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV172 )
= $false )
| ( ( class_HOL_Ozero @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5703]) ).
thf(6913,plain,
! [SV173: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV173 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5704]) ).
thf(6914,plain,
! [SV174: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV174 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(6915,plain,
! [SV175: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV175 )
= $false )
| ( ( class_HOL_Oplus @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(6916,plain,
! [SV176: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV176 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5707]) ).
thf(6917,plain,
! [SV177: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV177 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5708]) ).
thf(6918,plain,
! [SV178: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV178 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(6919,plain,
! [SV179: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV179 )
= $false )
| ( ( class_HOL_Oplus @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(6920,plain,
! [SV180: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV180 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5711]) ).
thf(6921,plain,
! [SV181: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV181 )
= $false )
| ( ( class_HOL_Otimes @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5712]) ).
thf(6922,plain,
! [SV182: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV182 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5713]) ).
thf(6923,plain,
! [SV183: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV183 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5714]) ).
thf(6924,plain,
! [SV184: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV184 )
= $false )
| ( ( class_HOL_Oplus @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5715]) ).
thf(6925,plain,
! [SV185: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV185 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5716]) ).
thf(6926,plain,
! [SV186: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV186 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(6927,plain,
! [SV187: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV187 )
= $false )
| ( ( class_HOL_Oplus @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5718]) ).
thf(6928,plain,
! [SV188: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV188 )
= $false )
| ( ( class_HOL_Ozero @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(6929,plain,
! [SV189: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV189 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5720]) ).
thf(6930,plain,
! [SV190: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV190 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5721]) ).
thf(6931,plain,
! [SV191: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV191 )
= $false )
| ( ( class_HOL_Oplus @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5722]) ).
thf(6932,plain,
! [SV192: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV192 )
= $false )
| ( ( class_HOL_Oone @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5723]) ).
thf(6933,plain,
! [SV193: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV193 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(6934,plain,
! [SV194: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV194 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5725]) ).
thf(6935,plain,
! [SV195: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV195 )
= $false )
| ( ( class_HOL_Otimes @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(6936,plain,
! [SV196: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV196 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5727]) ).
thf(6937,plain,
! [SV197: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV197 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5728]) ).
thf(6938,plain,
! [SV198: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV198 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5729]) ).
thf(6939,plain,
! [SV199: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV199 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5730]) ).
thf(6940,plain,
! [SV200: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV200 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5731]) ).
thf(6941,plain,
! [SV201: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV201 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5732]) ).
thf(6942,plain,
! [SV202: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV202 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5733]) ).
thf(6943,plain,
! [SV203: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV203 )
= $false )
| ( ( class_HOL_Oplus @ SV203 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5734]) ).
thf(6944,plain,
! [SV204: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV204 )
= $false )
| ( ( class_LOrder_Olorder @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5735]) ).
thf(6945,plain,
! [SV205: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV205 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5736]) ).
thf(6946,plain,
! [SV206: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV206 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5737]) ).
thf(6947,plain,
! [SV207: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV207 )
= $false )
| ( ( class_HOL_Ominus @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5738]) ).
thf(6948,plain,
! [SV208: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV208 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5739]) ).
thf(6949,plain,
! [SV209: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV209 )
= $false )
| ( ( class_HOL_Ozero @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5740]) ).
thf(6950,plain,
! [SV210: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV210 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5741]) ).
thf(6951,plain,
! [SV211: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV211 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5742]) ).
thf(6952,plain,
! [SV212: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV212 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(6953,plain,
! [SV213: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV213 )
= $false )
| ( ( class_Orderings_Oorder @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5744]) ).
thf(6954,plain,
! [SV214: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group @ SV214 )
= $false )
| ( ( class_Orderings_Oord @ SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5745]) ).
thf(6955,plain,
! [SV215: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV215 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5746]) ).
thf(6956,plain,
! [SV216: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV216 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5747]) ).
thf(6957,plain,
! [SV217: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV217 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5748]) ).
thf(6958,plain,
! [SV218: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV218 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV218 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5749]) ).
thf(6959,plain,
! [SV219: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV219 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(6960,plain,
! [SV220: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV220 )
= $false )
| ( ( class_HOL_Oplus @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5751]) ).
thf(6961,plain,
! [SV221: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV221 )
= $false )
| ( ( class_LOrder_Olorder @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5752]) ).
thf(6962,plain,
! [SV222: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV222 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5753]) ).
thf(6963,plain,
! [SV223: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV223 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5754]) ).
thf(6964,plain,
! [SV224: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV224 )
= $false )
| ( ( class_Orderings_Oorder @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(6965,plain,
! [SV225: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV225 )
= $false )
| ( ( class_Orderings_Oord @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(6966,plain,
! [SV226: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV226 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(6967,plain,
! [SV227: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV227 )
= $false )
| ( ( class_HOL_Ominus @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5758]) ).
thf(6968,plain,
! [SV228: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV228 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5759]) ).
thf(6969,plain,
! [SV229: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV229 )
= $false )
| ( ( class_HOL_Ozero @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5760]) ).
thf(6970,plain,
! [SV230: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV230 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5761]) ).
thf(6971,plain,
! [SV231: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV231 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5762]) ).
thf(6972,plain,
! [SV232: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV232 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5763]) ).
thf(6973,plain,
! [SV233: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV233 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5764]) ).
thf(6974,plain,
! [SV234: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV234 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(6975,plain,
! [SV235: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV235 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(6976,plain,
! [SV236: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV236 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5767]) ).
thf(6977,plain,
! [SV237: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV237 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5768]) ).
thf(6978,plain,
! [SV238: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV238 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5769]) ).
thf(6979,plain,
! [SV239: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV239 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(6980,plain,
! [SV240: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV240 )
= $false )
| ( ( class_HOL_Oplus @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5771]) ).
thf(6981,plain,
! [SV241: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV241 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5772]) ).
thf(6982,plain,
! [SV242: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV242 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(6983,plain,
! [SV243: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV243 )
= $false )
| ( ( class_LOrder_Olorder @ SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5774]) ).
thf(6984,plain,
! [SV244: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV244 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5775]) ).
thf(6985,plain,
! [SV245: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV245 )
= $false )
| ( ( class_HOL_Ominus @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5776]) ).
thf(6986,plain,
! [SV246: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV246 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5777]) ).
thf(6987,plain,
! [SV247: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV247 )
= $false )
| ( ( class_HOL_Ozero @ SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(6988,plain,
! [SV248: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV248 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5779]) ).
thf(6989,plain,
! [SV249: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV249 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5780]) ).
thf(6990,plain,
! [SV250: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV250 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5781]) ).
thf(6991,plain,
! [SV251: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV251 )
= $false )
| ( ( class_Orderings_Oorder @ SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(6992,plain,
! [SV252: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__join @ SV252 )
= $false )
| ( ( class_Orderings_Oord @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5783]) ).
thf(6993,plain,
! [SV253: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV253 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5784]) ).
thf(6994,plain,
! [SV254: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV254 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5785]) ).
thf(6995,plain,
! [SV255: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV255 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5786]) ).
thf(6996,plain,
! [SV256: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV256 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5787]) ).
thf(6997,plain,
! [SV257: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV257 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(6998,plain,
! [SV258: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV258 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(6999,plain,
! [SV259: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV259 )
= $false )
| ( ( class_HOL_Oplus @ SV259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5790]) ).
thf(7000,plain,
! [SV260: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV260 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5791]) ).
thf(7001,plain,
! [SV261: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV261 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5792]) ).
thf(7002,plain,
! [SV262: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV262 )
= $false )
| ( ( class_LOrder_Olorder @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5793]) ).
thf(7003,plain,
! [SV263: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV263 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5794]) ).
thf(7004,plain,
! [SV264: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV264 )
= $false )
| ( ( class_HOL_Ominus @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5795]) ).
thf(7005,plain,
! [SV265: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV265 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV265 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5796]) ).
thf(7006,plain,
! [SV266: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV266 )
= $false )
| ( ( class_HOL_Ozero @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5797]) ).
thf(7007,plain,
! [SV267: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV267 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5798]) ).
thf(7008,plain,
! [SV268: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV268 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV268 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5799]) ).
thf(7009,plain,
! [SV269: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV269 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5800]) ).
thf(7010,plain,
! [SV270: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV270 )
= $false )
| ( ( class_Orderings_Oorder @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5801]) ).
thf(7011,plain,
! [SV271: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV271 )
= $false )
| ( ( class_Orderings_Oord @ SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5802]) ).
thf(7012,plain,
! [SV272: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV272 )
= $false )
| ( ( class_HOL_Oone @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5803]) ).
thf(7013,plain,
! [SV273: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV273 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5804]) ).
thf(7014,plain,
! [SV274: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV274 )
= $false )
| ( ( class_HOL_Otimes @ SV274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5805]) ).
thf(7015,plain,
! [SV275: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV275 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5806]) ).
thf(7016,plain,
! [SV276: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV276 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5807]) ).
thf(7017,plain,
! [SV277: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV277 )
= $false )
| ( ( class_LOrder_Olorder @ SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5808]) ).
thf(7018,plain,
! [SV278: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV278 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5809]) ).
thf(7019,plain,
! [SV279: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV279 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5810]) ).
thf(7020,plain,
! [SV280: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV280 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5811]) ).
thf(7021,plain,
! [SV281: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV281 )
= $false )
| ( ( class_Orderings_Oorder @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5812]) ).
thf(7022,plain,
! [SV282: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV282 )
= $false )
| ( ( class_Orderings_Oord @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5813]) ).
thf(7023,plain,
! [SV283: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV283 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5814]) ).
thf(7024,plain,
! [SV284: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV284 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5815]) ).
thf(7025,plain,
! [SV285: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV285 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5816]) ).
thf(7026,plain,
! [SV286: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV286 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV286 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5817]) ).
thf(7027,plain,
! [SV287: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV287 )
= $false )
| ( ( class_HOL_Oplus @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5818]) ).
thf(7028,plain,
! [SV288: $i] :
( ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV288 )
= $false )
| ( ( class_Orderings_Olinorder @ SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5819]) ).
thf(7029,plain,
! [SV289: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV289 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(7030,plain,
! [SV290: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV290 )
= $false )
| ( ( class_HOL_Ominus @ SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(7031,plain,
! [SV291: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV291 )
= $false )
| ( ( class_Orderings_Oorder @ SV291 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5822]) ).
thf(7032,plain,
! [SV292: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV292 )
= $false )
| ( ( class_Orderings_Oord @ SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5823]) ).
thf(7033,plain,
! [SV293: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV293 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5824]) ).
thf(7034,plain,
! [SV294: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV294 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV294 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5825]) ).
thf(7035,plain,
! [SV295: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV295 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(7036,plain,
! [SV296: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV296 )
= $false )
| ( ( class_HOL_Ozero @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(7037,plain,
! [SV297: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV297 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5828]) ).
thf(7038,plain,
! [SV298: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV298 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(7039,plain,
! [SV299: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV299 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5830]) ).
thf(7040,plain,
! [SV300: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV300 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5831]) ).
thf(7041,plain,
! [SV301: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV301 )
= $false )
| ( ( class_HOL_Oplus @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5832]) ).
thf(7042,plain,
! [SV302: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV302 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5833]) ).
thf(7043,plain,
! [SV303: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV303 )
= $false )
| ( ( class_Orderings_Oorder @ SV303 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5834]) ).
thf(7044,plain,
! [SV304: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV304 )
= $false )
| ( ( class_Orderings_Oord @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5835]) ).
thf(7045,plain,
! [SV305: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV305 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV305 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5836]) ).
thf(7046,plain,
! [SV306: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV306 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5837]) ).
thf(7047,plain,
! [SV307: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV307 )
= $false )
| ( ( class_HOL_Oplus @ SV307 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5838]) ).
thf(7048,plain,
! [SV308: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV308 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5839]) ).
thf(7049,plain,
! [SV309: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV309 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5840]) ).
thf(7050,plain,
! [SV310: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV310 )
= $false )
| ( ( class_Orderings_Oorder @ SV310 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5841]) ).
thf(7051,plain,
! [SV311: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV311 )
= $false )
| ( ( class_Orderings_Oord @ SV311 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5842]) ).
thf(7052,plain,
! [SV312: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV312 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV312 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(7053,plain,
! [SV313: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV313 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5844]) ).
thf(7054,plain,
! [SV314: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV314 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV314 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5845]) ).
thf(7055,plain,
! [SV315: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV315 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV315 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(7056,plain,
! [SV316: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV316 )
= $false )
| ( ( class_HOL_Oplus @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5847]) ).
thf(7057,plain,
! [SV317: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV317 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV317 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5848]) ).
thf(7058,plain,
! [SV318: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV318 )
= $false )
| ( ( class_Orderings_Oorder @ SV318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5849]) ).
thf(7059,plain,
! [SV319: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV319 )
= $false )
| ( ( class_Orderings_Oord @ SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5850]) ).
thf(7060,plain,
! [SV320: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5851]) ).
thf(7061,plain,
! [SV321: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV321 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5852]) ).
thf(7062,plain,
! [SV322: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV322 )
= $false )
| ( ( class_HOL_Oplus @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5853]) ).
thf(7063,plain,
! [SV323: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV323 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV323 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5854]) ).
thf(7064,plain,
! [SV324: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV324 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV324 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5855]) ).
thf(7065,plain,
! [SV325: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV325 )
= $false )
| ( ( class_HOL_Oplus @ SV325 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5856]) ).
thf(7066,plain,
! [SV326: $i] :
( ( ( class_OrderedGroup_Osemigroup__mult @ SV326 )
= $false )
| ( ( class_HOL_Otimes @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5857]) ).
thf(7067,plain,
! [SV327: $i] :
( ( ( class_Orderings_Olinorder @ SV327 )
= $false )
| ( ( class_LOrder_Olorder @ SV327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(7068,plain,
! [SV328: $i] :
( ( ( class_Orderings_Olinorder @ SV328 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(7069,plain,
! [SV329: $i] :
( ( ( class_Orderings_Olinorder @ SV329 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5860]) ).
thf(7070,plain,
! [SV330: $i] :
( ( ( class_Orderings_Olinorder @ SV330 )
= $false )
| ( ( class_Orderings_Oord @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5861]) ).
thf(7071,plain,
! [SV331: $i] :
( ( ( class_Orderings_Olinorder @ SV331 )
= $false )
| ( ( class_Orderings_Oorder @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5862]) ).
thf(7072,plain,
! [SV332: $i] :
( ( ( class_Orderings_Oorder @ SV332 )
= $false )
| ( ( class_Orderings_Oord @ SV332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5863]) ).
thf(7073,plain,
! [SV333: $i] :
( ( ( class_Power_Orecpower @ SV333 )
= $false )
| ( ( class_Nat_Opower @ SV333 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5864]) ).
thf(7074,plain,
! [SV334: $i] :
( ( ( class_Power_Orecpower @ SV334 )
= $false )
| ( ( class_HOL_Ozero @ SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5865]) ).
thf(7075,plain,
! [SV335: $i] :
( ( ( class_Power_Orecpower @ SV335 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5866]) ).
thf(7076,plain,
! [SV336: $i] :
( ( ( class_Power_Orecpower @ SV336 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5867]) ).
thf(7077,plain,
! [SV337: $i] :
( ( ( class_Power_Orecpower @ SV337 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(7078,plain,
! [SV338: $i] :
( ( ( class_Power_Orecpower @ SV338 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV338 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(7079,plain,
! [SV339: $i] :
( ( ( class_Power_Orecpower @ SV339 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5870]) ).
thf(7080,plain,
! [SV340: $i] :
( ( ( class_Power_Orecpower @ SV340 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(7081,plain,
! [SV341: $i] :
( ( ( class_Power_Orecpower @ SV341 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5872]) ).
thf(7082,plain,
! [SV342: $i] :
( ( ( class_Power_Orecpower @ SV342 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5873]) ).
thf(7083,plain,
! [SV343: $i] :
( ( ( class_Power_Orecpower @ SV343 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5874]) ).
thf(7084,plain,
! [SV344: $i] :
( ( ( class_Power_Orecpower @ SV344 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5875]) ).
thf(7085,plain,
! [SV345: $i] :
( ( ( class_Power_Orecpower @ SV345 )
= $false )
| ( ( class_HOL_Oone @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5876]) ).
thf(7086,plain,
! [SV346: $i] :
( ( ( class_Power_Orecpower @ SV346 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5877]) ).
thf(7087,plain,
! [SV347: $i] :
( ( ( class_Power_Orecpower @ SV347 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV347 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5878]) ).
thf(7088,plain,
! [SV348: $i] :
( ( ( class_Power_Orecpower @ SV348 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV348 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5879]) ).
thf(7089,plain,
! [SV349: $i] :
( ( ( class_Power_Orecpower @ SV349 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV349 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5880]) ).
thf(7090,plain,
! [SV350: $i] :
( ( ( class_Power_Orecpower @ SV350 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5881]) ).
thf(7091,plain,
! [SV351: $i] :
( ( ( class_Power_Orecpower @ SV351 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV351 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5882]) ).
thf(7092,plain,
! [SV352: $i] :
( ( ( class_Power_Orecpower @ SV352 )
= $false )
| ( ( class_HOL_Oplus @ SV352 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5883]) ).
thf(7093,plain,
! [SV353: $i] :
( ( ( class_Power_Orecpower @ SV353 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5884]) ).
thf(7094,plain,
! [SV354: $i] :
( ( ( class_Power_Orecpower @ SV354 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV354 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5885]) ).
thf(7095,plain,
! [SV355: $i] :
( ( ( class_Power_Orecpower @ SV355 )
= $false )
| ( ( class_HOL_Otimes @ SV355 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5886]) ).
thf(7096,plain,
! [SV356: $i] :
( ( ( class_Power_Orecpower @ SV356 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV356 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5887]) ).
thf(7097,plain,
! [SV357: $i] :
( ( ( class_Power_Orecpower @ SV357 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5888]) ).
thf(7098,plain,
! [SV358: $i] :
( ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV358 )
= $false )
| ( ( class_HOL_Ozero @ SV358 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5889]) ).
thf(7099,plain,
! [SV359: $i] :
( ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV359 )
= $false )
| ( ( class_HOL_Oone @ SV359 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5890]) ).
thf(7100,plain,
! [SV360: $i] :
( ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV360 )
= $false )
| ( ( class_HOL_Ominus @ SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5891]) ).
thf(7101,plain,
! [SV361: $i] :
( ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV361 )
= $false )
| ( ( class_Orderings_Oord @ SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(7102,plain,
! [SV362: $i] :
( ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV362 )
= $false )
| ( ( class_HOL_Ozero @ SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5893]) ).
thf(7103,plain,
! [SV363: $i] :
( ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV363 )
= $false )
| ( ( class_HOL_Ozero @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5894]) ).
thf(7104,plain,
! [SV364: $i] :
( ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV364 )
= $false )
| ( ( class_HOL_Otimes @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5895]) ).
thf(7105,plain,
! [SV365: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV365 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5896]) ).
thf(7106,plain,
! [SV366: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV366 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5897]) ).
thf(7107,plain,
! [SV367: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV367 )
= $false )
| ( ( class_HOL_Oplus @ SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5898]) ).
thf(7108,plain,
! [SV368: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV368 )
= $false )
| ( ( class_HOL_Ozero @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5899]) ).
thf(7109,plain,
! [SV369: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV369 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5900]) ).
thf(7110,plain,
! [SV370: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV370 )
= $false )
| ( ( class_HOL_Ominus @ SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5901]) ).
thf(7111,plain,
! [SV371: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV371 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5902]) ).
thf(7112,plain,
! [SV372: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV372 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV372 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5903]) ).
thf(7113,plain,
! [SV373: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV373 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5904]) ).
thf(7114,plain,
! [SV374: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV374 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5905]) ).
thf(7115,plain,
! [SV375: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV375 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV375 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5906]) ).
thf(7116,plain,
! [SV376: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV376 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5907]) ).
thf(7117,plain,
! [SV377: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV377 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5908]) ).
thf(7118,plain,
! [SV378: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV378 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5909]) ).
thf(7119,plain,
! [SV379: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV379 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV379 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(7120,plain,
! [SV380: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV380 )
= $false )
| ( ( class_HOL_Otimes @ SV380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(7121,plain,
! [SV381: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV381 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5912]) ).
thf(7122,plain,
! [SV382: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV382 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5913]) ).
thf(7123,plain,
! [SV383: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV383 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5914]) ).
thf(7124,plain,
! [SV384: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV384 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5915]) ).
thf(7125,plain,
! [SV385: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV385 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5916]) ).
thf(7126,plain,
! [SV386: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV386 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5917]) ).
thf(7127,plain,
! [SV387: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV387 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV387 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5918]) ).
thf(7128,plain,
! [SV388: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV388 )
= $false )
| ( ( class_HOL_Otimes @ SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5919]) ).
thf(7129,plain,
! [SV389: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV389 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5920]) ).
thf(7130,plain,
! [SV390: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV390 )
= $false )
| ( ( class_HOL_Ozero @ SV390 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5921]) ).
thf(7131,plain,
! [SV391: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV391 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV391 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5922]) ).
thf(7132,plain,
! [SV392: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV392 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV392 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5923]) ).
thf(7133,plain,
! [SV393: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV393 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(7134,plain,
! [SV394: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV394 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5925]) ).
thf(7135,plain,
! [SV395: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV395 )
= $false )
| ( ( class_HOL_Oplus @ SV395 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5926]) ).
thf(7136,plain,
! [SV396: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV396 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV396 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5927]) ).
thf(7137,plain,
! [SV397: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV397 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV397 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5928]) ).
thf(7138,plain,
! [SV398: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV398 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV398 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5929]) ).
thf(7139,plain,
! [SV399: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV399 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5930]) ).
thf(7140,plain,
! [SV400: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV400 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(7141,plain,
! [SV401: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV401 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV401 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5932]) ).
thf(7142,plain,
! [SV402: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV402 )
= $false )
| ( ( class_HOL_Oone @ SV402 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5933]) ).
thf(7143,plain,
! [SV403: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV403 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ SV403 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5934]) ).
thf(7144,plain,
! [SV404: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV404 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV404 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5935]) ).
thf(7145,plain,
! [SV405: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV405 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV405 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5936]) ).
thf(7146,plain,
! [SV406: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV406 )
= $false )
| ( ( class_HOL_Ominus @ SV406 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(7147,plain,
! [SV407: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV407 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV407 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5938]) ).
thf(7148,plain,
! [SV408: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV408 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV408 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5939]) ).
thf(7149,plain,
! [SV409: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV409 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV409 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5940]) ).
thf(7150,plain,
! [SV410: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV410 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5941]) ).
thf(7151,plain,
! [SV411: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV411 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5942]) ).
thf(7152,plain,
! [SV412: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV412 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV412 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5943]) ).
thf(7153,plain,
! [SV413: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV413 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5944]) ).
thf(7154,plain,
! [SV414: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV414 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5945]) ).
thf(7155,plain,
! [SV415: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV415 )
= $false )
| ( ( class_HOL_Oplus @ SV415 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5946]) ).
thf(7156,plain,
! [SV416: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV416 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV416 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5947]) ).
thf(7157,plain,
! [SV417: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV417 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5948]) ).
thf(7158,plain,
! [SV418: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV418 )
= $false )
| ( ( class_HOL_Otimes @ SV418 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5949]) ).
thf(7159,plain,
! [SV419: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV419 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5950]) ).
thf(7160,plain,
! [SV420: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV420 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV420 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5951]) ).
thf(7161,plain,
! [SV421: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV421 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5952]) ).
thf(7162,plain,
! [SV422: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV422 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV422 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5953]) ).
thf(7163,plain,
! [SV423: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV423 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(7164,plain,
! [SV424: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV424 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5955]) ).
thf(7165,plain,
! [SV425: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV425 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV425 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5956]) ).
thf(7166,plain,
! [SV426: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV426 )
= $false )
| ( ( class_HOL_Oplus @ SV426 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5957]) ).
thf(7167,plain,
! [SV427: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV427 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5958]) ).
thf(7168,plain,
! [SV428: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV428 )
= $false )
| ( ( class_HOL_Otimes @ SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5959]) ).
thf(7169,plain,
! [SV429: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV429 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5960]) ).
thf(7170,plain,
! [SV430: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV430 )
= $false )
| ( ( class_HOL_Ozero @ SV430 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5961]) ).
thf(7171,plain,
! [SV431: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV431 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5962]) ).
thf(7172,plain,
! [SV432: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV432 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5963]) ).
thf(7173,plain,
! [SV433: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV433 )
= $false )
| ( ( class_HOL_Oplus @ SV433 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5964]) ).
thf(7174,plain,
! [SV434: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV434 )
= $false )
| ( ( class_HOL_Ozero @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5965]) ).
thf(7175,plain,
! [SV435: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV435 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5966]) ).
thf(7176,plain,
! [SV436: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV436 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5967]) ).
thf(7177,plain,
! [SV437: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV437 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV437 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5968]) ).
thf(7178,plain,
! [SV438: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV438 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV438 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5969]) ).
thf(7179,plain,
! [SV439: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV439 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5970]) ).
thf(7180,plain,
! [SV440: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV440 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV440 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5971]) ).
thf(7181,plain,
! [SV441: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV441 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV441 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5972]) ).
thf(7182,plain,
! [SV442: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV442 )
= $false )
| ( ( class_HOL_Otimes @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(7183,plain,
! [SV443: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV443 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV443 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5974]) ).
thf(7184,plain,
! [SV444: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV444 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV444 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5975]) ).
thf(7185,plain,
! [SV445: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV445 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV445 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5976]) ).
thf(7186,plain,
! [SV446: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV446 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV446 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5977]) ).
thf(7187,plain,
! [SV447: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV447 )
= $false )
| ( ( class_HOL_Ozero @ SV447 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5978]) ).
thf(7188,plain,
! [SV448: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV448 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5979]) ).
thf(7189,plain,
! [SV449: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5980]) ).
thf(7190,plain,
! [SV450: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV450 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5981]) ).
thf(7191,plain,
! [SV451: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV451 )
= $false )
| ( ( class_HOL_Oplus @ SV451 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5982]) ).
thf(7192,plain,
! [SV452: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV452 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV452 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5983]) ).
thf(7193,plain,
! [SV453: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV453 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5984]) ).
thf(7194,plain,
! [SV454: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV454 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(7195,plain,
! [SV455: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV455 )
= $false )
| ( ( class_HOL_Oone @ SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5986]) ).
thf(7196,plain,
! [SV456: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV456 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5987]) ).
thf(7197,plain,
! [SV457: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV457 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5988]) ).
thf(7198,plain,
! [SV458: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV458 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5989]) ).
thf(7199,plain,
! [SV459: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV459 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV459 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5990]) ).
thf(7200,plain,
! [SV460: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV460 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5991]) ).
thf(7201,plain,
! [SV461: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV461 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5992]) ).
thf(7202,plain,
! [SV462: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV462 )
= $false )
| ( ( class_HOL_Otimes @ SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5993]) ).
thf(7203,plain,
! [SV463: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV463 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5994]) ).
thf(7204,plain,
! [SV464: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV464 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV464 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5995]) ).
thf(7205,plain,
! [SV465: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV465 )
= $false )
| ( ( class_HOL_Ozero @ SV465 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5996]) ).
thf(7206,plain,
! [SV466: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV466 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV466 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5997]) ).
thf(7207,plain,
! [SV467: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV467 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV467 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5998]) ).
thf(7208,plain,
! [SV468: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV468 )
= $false )
| ( ( class_HOL_Oplus @ SV468 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5999]) ).
thf(7209,plain,
! [SV469: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV469 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV469 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6000]) ).
thf(7210,plain,
! [SV470: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV470 )
= $false )
| ( ( class_HOL_Oone @ SV470 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6001]) ).
thf(7211,plain,
! [SV471: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV471 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6002]) ).
thf(7212,plain,
! [SV472: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV472 )
= $false )
| ( ( class_HOL_Otimes @ SV472 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6003]) ).
thf(7213,plain,
! [SV473: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV473 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6004]) ).
thf(7214,plain,
! [SV474: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV474 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV474 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6005]) ).
thf(7215,plain,
! [SV475: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV475 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV475 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6006]) ).
thf(7216,plain,
! [SV476: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV476 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV476 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6007]) ).
thf(7217,plain,
! [SV477: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV477 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV477 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6008]) ).
thf(7218,plain,
! [SV478: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV478 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV478 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6009]) ).
thf(7219,plain,
! [SV479: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV479 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6010]) ).
thf(7220,plain,
! [SV480: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV480 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV480 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(7221,plain,
! [SV481: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV481 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV481 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6012]) ).
thf(7222,plain,
! [SV482: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV482 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6013]) ).
thf(7223,plain,
! [SV483: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV483 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV483 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6014]) ).
thf(7224,plain,
! [SV484: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV484 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV484 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6015]) ).
thf(7225,plain,
! [SV485: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV485 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV485 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6016]) ).
thf(7226,plain,
! [SV486: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV486 )
= $false )
| ( ( class_HOL_Ozero @ SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6017]) ).
thf(7227,plain,
! [SV487: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV487 )
= $false )
| ( ( class_HOL_Oinverse @ SV487 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(7228,plain,
! [SV488: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV488 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6019]) ).
thf(7229,plain,
! [SV489: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV489 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6020]) ).
thf(7230,plain,
! [SV490: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV490 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV490 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6021]) ).
thf(7231,plain,
! [SV491: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV491 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6022]) ).
thf(7232,plain,
! [SV492: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV492 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV492 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6023]) ).
thf(7233,plain,
! [SV493: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV493 )
= $false )
| ( ( class_HOL_Oone @ SV493 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6024]) ).
thf(7234,plain,
! [SV494: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV494 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6025]) ).
thf(7235,plain,
! [SV495: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV495 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV495 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6026]) ).
thf(7236,plain,
! [SV496: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV496 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6027]) ).
thf(7237,plain,
! [SV497: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV497 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV497 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6028]) ).
thf(7238,plain,
! [SV498: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV498 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV498 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6029]) ).
thf(7239,plain,
! [SV499: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV499 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6030]) ).
thf(7240,plain,
! [SV500: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV500 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ SV500 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6031]) ).
thf(7241,plain,
! [SV501: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV501 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV501 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6032]) ).
thf(7242,plain,
! [SV502: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV502 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6033]) ).
thf(7243,plain,
! [SV503: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV503 )
= $false )
| ( ( class_HOL_Otimes @ SV503 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6034]) ).
thf(7244,plain,
! [SV504: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV504 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV504 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6035]) ).
thf(7245,plain,
! [SV505: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV505 )
= $false )
| ( ( class_HOL_Ozero @ SV505 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6036]) ).
thf(7246,plain,
! [SV506: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV506 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV506 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6037]) ).
thf(7247,plain,
! [SV507: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV507 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6038]) ).
thf(7248,plain,
! [SV508: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV508 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6039]) ).
thf(7249,plain,
! [SV509: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV509 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV509 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6040]) ).
thf(7250,plain,
! [SV510: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV510 )
= $false )
| ( ( class_HOL_Oplus @ SV510 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6041]) ).
thf(7251,plain,
! [SV511: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV511 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV511 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6042]) ).
thf(7252,plain,
! [SV512: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV512 )
= $false )
| ( ( class_HOL_Oinverse @ SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6043]) ).
thf(7253,plain,
! [SV513: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV513 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6044]) ).
thf(7254,plain,
! [SV514: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV514 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(7255,plain,
! [SV515: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV515 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV515 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6046]) ).
thf(7256,plain,
! [SV516: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV516 )
= $false )
| ( ( class_HOL_Ominus @ SV516 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6047]) ).
thf(7257,plain,
! [SV517: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV517 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV517 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6048]) ).
thf(7258,plain,
! [SV518: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV518 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV518 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6049]) ).
thf(7259,plain,
! [SV519: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV519 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6050]) ).
thf(7260,plain,
! [SV520: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV520 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6051]) ).
thf(7261,plain,
! [SV521: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV521 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV521 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6052]) ).
thf(7262,plain,
! [SV522: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV522 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV522 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6053]) ).
thf(7263,plain,
! [SV523: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV523 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6054]) ).
thf(7264,plain,
! [SV524: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV524 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV524 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6055]) ).
thf(7265,plain,
! [SV525: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV525 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV525 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6056]) ).
thf(7266,plain,
! [SV526: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV526 )
= $false )
| ( ( class_HOL_Oone @ SV526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6057]) ).
thf(7267,plain,
! [SV527: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV527 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV527 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6058]) ).
thf(7268,plain,
! [SV528: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV528 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV528 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6059]) ).
thf(7269,plain,
! [SV529: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV529 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV529 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6060]) ).
thf(7270,plain,
! [SV530: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV530 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV530 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6061]) ).
thf(7271,plain,
! [SV531: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV531 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV531 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6062]) ).
thf(7272,plain,
! [SV532: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV532 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV532 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6063]) ).
thf(7273,plain,
! [SV533: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV533 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ SV533 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6064]) ).
thf(7274,plain,
! [SV534: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV534 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6065]) ).
thf(7275,plain,
! [SV535: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV535 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6066]) ).
thf(7276,plain,
! [SV536: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV536 )
= $false )
| ( ( class_HOL_Otimes @ SV536 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6067]) ).
thf(7277,plain,
! [SV537: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV537 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV537 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6068]) ).
thf(7278,plain,
! [SV538: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV538 )
= $false )
| ( ( class_HOL_Ozero @ SV538 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6069]) ).
thf(7279,plain,
! [SV539: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV539 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6070]) ).
thf(7280,plain,
! [SV540: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV540 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV540 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6071]) ).
thf(7281,plain,
! [SV541: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV541 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV541 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6072]) ).
thf(7282,plain,
! [SV542: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV542 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV542 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6073]) ).
thf(7283,plain,
! [SV543: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV543 )
= $false )
| ( ( class_HOL_Oplus @ SV543 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6074]) ).
thf(7284,plain,
! [SV544: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV544 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6075]) ).
thf(7285,plain,
! [SV545: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV545 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV545 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6076]) ).
thf(7286,plain,
! [SV546: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV546 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6077]) ).
thf(7287,plain,
! [SV547: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV547 )
= $false )
| ( ( class_HOL_Ominus @ SV547 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6078]) ).
thf(7288,plain,
! [SV548: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV548 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV548 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6079]) ).
thf(7289,plain,
! [SV549: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV549 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6080]) ).
thf(7290,plain,
! [SV550: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV550 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV550 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6081]) ).
thf(7291,plain,
! [SV551: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV551 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV551 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6082]) ).
thf(7292,plain,
! [SV552: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV552 )
= $false )
| ( ( class_Ring__and__Field_Opordered__ring @ SV552 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6083]) ).
thf(7293,plain,
! [SV553: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV553 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV553 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6084]) ).
thf(7294,plain,
! [SV554: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV554 )
= $false )
| ( ( class_Orderings_Oorder @ SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6085]) ).
thf(7295,plain,
! [SV555: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV555 )
= $false )
| ( ( class_Orderings_Oord @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6086]) ).
thf(7296,plain,
! [SV556: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV556 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6087]) ).
thf(7297,plain,
! [SV557: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV557 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV557 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6088]) ).
thf(7298,plain,
! [SV558: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV558 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV558 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6089]) ).
thf(7299,plain,
! [SV559: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV559 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6090]) ).
thf(7300,plain,
! [SV560: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV560 )
= $false )
| ( ( class_HOL_Otimes @ SV560 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6091]) ).
thf(7301,plain,
! [SV561: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV561 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV561 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6092]) ).
thf(7302,plain,
! [SV562: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV562 )
= $false )
| ( ( class_HOL_Ozero @ SV562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6093]) ).
thf(7303,plain,
! [SV563: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV563 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6094]) ).
thf(7304,plain,
! [SV564: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV564 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6095]) ).
thf(7305,plain,
! [SV565: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV565 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6096]) ).
thf(7306,plain,
! [SV566: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV566 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6097]) ).
thf(7307,plain,
! [SV567: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV567 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV567 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6098]) ).
thf(7308,plain,
! [SV568: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV568 )
= $false )
| ( ( class_HOL_Oplus @ SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6099]) ).
thf(7309,plain,
! [SV569: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV569 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6100]) ).
thf(7310,plain,
! [SV570: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV570 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6101]) ).
thf(7311,plain,
! [SV571: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV571 )
= $false )
| ( ( class_LOrder_Olorder @ SV571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6102]) ).
thf(7312,plain,
! [SV572: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV572 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6103]) ).
thf(7313,plain,
! [SV573: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV573 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6104]) ).
thf(7314,plain,
! [SV574: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV574 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6105]) ).
thf(7315,plain,
! [SV575: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV575 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6106]) ).
thf(7316,plain,
! [SV576: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV576 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV576 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6107]) ).
thf(7317,plain,
! [SV577: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV577 )
= $false )
| ( ( class_HOL_Ominus @ SV577 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6108]) ).
thf(7318,plain,
! [SV578: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV578 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV578 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6109]) ).
thf(7319,plain,
! [SV579: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV579 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV579 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6110]) ).
thf(7320,plain,
! [SV580: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV580 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV580 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6111]) ).
thf(7321,plain,
! [SV581: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV581 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV581 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6112]) ).
thf(7322,plain,
! [SV582: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV582 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV582 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6113]) ).
thf(7323,plain,
! [SV583: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV583 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV583 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6114]) ).
thf(7324,plain,
! [SV584: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV584 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV584 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6115]) ).
thf(7325,plain,
! [SV585: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV585 )
= $false )
| ( ( class_HOL_Oplus @ SV585 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6116]) ).
thf(7326,plain,
! [SV586: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV586 )
= $false )
| ( ( class_HOL_Ozero @ SV586 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6117]) ).
thf(7327,plain,
! [SV587: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV587 )
= $false )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6118]) ).
thf(7328,plain,
! [SV588: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV588 )
= $false )
| ( ( class_Orderings_Olinorder @ SV588 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6119]) ).
thf(7329,plain,
! [SV589: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV589 )
= $false )
| ( ( class_LOrder_Olorder @ SV589 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6120]) ).
thf(7330,plain,
! [SV590: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV590 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV590 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6121]) ).
thf(7331,plain,
! [SV591: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV591 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV591 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6122]) ).
thf(7332,plain,
! [SV592: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV592 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV592 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6123]) ).
thf(7333,plain,
! [SV593: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV593 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV593 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6124]) ).
thf(7334,plain,
! [SV594: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV594 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6125]) ).
thf(7335,plain,
! [SV595: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV595 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV595 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6126]) ).
thf(7336,plain,
! [SV596: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV596 )
= $false )
| ( ( class_Orderings_Oorder @ SV596 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6127]) ).
thf(7337,plain,
! [SV597: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV597 )
= $false )
| ( ( class_Orderings_Oord @ SV597 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6128]) ).
thf(7338,plain,
! [SV598: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV598 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV598 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6129]) ).
thf(7339,plain,
! [SV599: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV599 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV599 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6130]) ).
thf(7340,plain,
! [SV600: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV600 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6131]) ).
thf(7341,plain,
! [SV601: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV601 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV601 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6132]) ).
thf(7342,plain,
! [SV602: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV602 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV602 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6133]) ).
thf(7343,plain,
! [SV603: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV603 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV603 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6134]) ).
thf(7344,plain,
! [SV604: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV604 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV604 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6135]) ).
thf(7345,plain,
! [SV605: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV605 )
= $false )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6136]) ).
thf(7346,plain,
! [SV606: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV606 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6137]) ).
thf(7347,plain,
! [SV607: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV607 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV607 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6138]) ).
thf(7348,plain,
! [SV608: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV608 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV608 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6139]) ).
thf(7349,plain,
! [SV609: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV609 )
= $false )
| ( ( class_HOL_Otimes @ SV609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6140]) ).
thf(7350,plain,
! [SV610: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV610 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV610 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6141]) ).
thf(7351,plain,
! [SV611: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV611 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6142]) ).
thf(7352,plain,
! [SV612: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV612 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6143]) ).
thf(7353,plain,
! [SV613: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV613 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV613 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6144]) ).
thf(7354,plain,
! [SV614: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV614 )
= $false )
| ( ( class_HOL_Oinverse @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6145]) ).
thf(7355,plain,
! [SV615: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV615 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV615 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6146]) ).
thf(7356,plain,
! [SV616: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV616 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV616 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6147]) ).
thf(7357,plain,
! [SV617: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV617 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV617 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6148]) ).
thf(7358,plain,
! [SV618: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV618 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV618 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6149]) ).
thf(7359,plain,
! [SV619: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV619 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV619 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6150]) ).
thf(7360,plain,
! [SV620: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV620 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV620 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6151]) ).
thf(7361,plain,
! [SV621: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV621 )
= $false )
| ( ( class_HOL_Oone @ SV621 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6152]) ).
thf(7362,plain,
! [SV622: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV622 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV622 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6153]) ).
thf(7363,plain,
! [SV623: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV623 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6154]) ).
thf(7364,plain,
! [SV624: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV624 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6155]) ).
thf(7365,plain,
! [SV625: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV625 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV625 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6156]) ).
thf(7366,plain,
! [SV626: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV626 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV626 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6157]) ).
thf(7367,plain,
! [SV627: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV627 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV627 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6158]) ).
thf(7368,plain,
! [SV628: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV628 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6159]) ).
thf(7369,plain,
! [SV629: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV629 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV629 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6160]) ).
thf(7370,plain,
! [SV630: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV630 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6161]) ).
thf(7371,plain,
! [SV631: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV631 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV631 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6162]) ).
thf(7372,plain,
! [SV632: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV632 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV632 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6163]) ).
thf(7373,plain,
! [SV633: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV633 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV633 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6164]) ).
thf(7374,plain,
! [SV634: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV634 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV634 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6165]) ).
thf(7375,plain,
! [SV635: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV635 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV635 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6166]) ).
thf(7376,plain,
! [SV636: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV636 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV636 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6167]) ).
thf(7377,plain,
! [SV637: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV637 )
= $false )
| ( ( class_HOL_Oplus @ SV637 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6168]) ).
thf(7378,plain,
! [SV638: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV638 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV638 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6169]) ).
thf(7379,plain,
! [SV639: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV639 )
= $false )
| ( ( class_HOL_Ozero @ SV639 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6170]) ).
thf(7380,plain,
! [SV640: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV640 )
= $false )
| ( ( class_HOL_Otimes @ SV640 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6171]) ).
thf(7381,plain,
! [SV641: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Oordered__idom @ SV641 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6172]) ).
thf(7382,plain,
! [SV642: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV642 )
= $false )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV642 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6173]) ).
thf(7383,plain,
! [SV643: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV643 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV643 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6174]) ).
thf(7384,plain,
! [SV644: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV644 )
= $false )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV644 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6175]) ).
thf(7385,plain,
! [SV645: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV645 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV645 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6176]) ).
thf(7386,plain,
! [SV646: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV646 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV646 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6177]) ).
thf(7387,plain,
! [SV647: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV647 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6178]) ).
thf(7388,plain,
! [SV648: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV648 )
= $false )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV648 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6179]) ).
thf(7389,plain,
! [SV649: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV649 )
= $false )
| ( ( class_Orderings_Olinorder @ SV649 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6180]) ).
thf(7390,plain,
! [SV650: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV650 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV650 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6181]) ).
thf(7391,plain,
! [SV651: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV651 )
= $false )
| ( ( class_Ring__and__Field_Olordered__ring @ SV651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6182]) ).
thf(7392,plain,
! [SV652: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV652 )
= $false )
| ( ( class_Ring__and__Field_Opordered__ring @ SV652 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6183]) ).
thf(7393,plain,
! [SV653: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV653 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV653 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6184]) ).
thf(7394,plain,
! [SV654: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV654 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6185]) ).
thf(7395,plain,
! [SV655: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV655 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6186]) ).
thf(7396,plain,
! [SV656: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV656 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV656 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6187]) ).
thf(7397,plain,
! [SV657: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV657 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV657 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6188]) ).
thf(7398,plain,
! [SV658: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV658 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ SV658 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6189]) ).
thf(7399,plain,
! [SV659: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV659 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV659 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6190]) ).
thf(7400,plain,
! [SV660: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV660 )
= $false )
| ( ( class_LOrder_Olorder @ SV660 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6191]) ).
thf(7401,plain,
! [SV661: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV661 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV661 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6192]) ).
thf(7402,plain,
! [SV662: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV662 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV662 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6193]) ).
thf(7403,plain,
! [SV663: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV663 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV663 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6194]) ).
thf(7404,plain,
! [SV664: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV664 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV664 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6195]) ).
thf(7405,plain,
! [SV665: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV665 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV665 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6196]) ).
thf(7406,plain,
! [SV666: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV666 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV666 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6197]) ).
thf(7407,plain,
! [SV667: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV667 )
= $false )
| ( ( class_Orderings_Oorder @ SV667 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6198]) ).
thf(7408,plain,
! [SV668: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV668 )
= $false )
| ( ( class_Orderings_Oord @ SV668 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6199]) ).
thf(7409,plain,
! [SV669: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV669 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV669 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6200]) ).
thf(7410,plain,
! [SV670: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV670 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV670 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6201]) ).
thf(7411,plain,
! [SV671: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV671 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV671 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6202]) ).
thf(7412,plain,
! [SV672: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV672 )
= $false )
| ( ( class_HOL_Ominus @ SV672 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6203]) ).
thf(7413,plain,
! [SV673: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV673 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV673 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6204]) ).
thf(7414,plain,
! [SV674: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV674 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV674 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6205]) ).
thf(7415,plain,
! [SV675: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV675 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV675 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6206]) ).
thf(7416,plain,
! [SV676: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV676 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV676 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6207]) ).
thf(7417,plain,
! [SV677: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV677 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV677 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6208]) ).
thf(7418,plain,
! [SV678: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV678 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV678 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6209]) ).
thf(7419,plain,
! [SV679: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV679 )
= $false )
| ( ( class_HOL_Oone @ SV679 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6210]) ).
thf(7420,plain,
! [SV680: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV680 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV680 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6211]) ).
thf(7421,plain,
! [SV681: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV681 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV681 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6212]) ).
thf(7422,plain,
! [SV682: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV682 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV682 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6213]) ).
thf(7423,plain,
! [SV683: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV683 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV683 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6214]) ).
thf(7424,plain,
! [SV684: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV684 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV684 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6215]) ).
thf(7425,plain,
! [SV685: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV685 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV685 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6216]) ).
thf(7426,plain,
! [SV686: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV686 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ SV686 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6217]) ).
thf(7427,plain,
! [SV687: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV687 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV687 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6218]) ).
thf(7428,plain,
! [SV688: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV688 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV688 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6219]) ).
thf(7429,plain,
! [SV689: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV689 )
= $false )
| ( ( class_HOL_Otimes @ SV689 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6220]) ).
thf(7430,plain,
! [SV690: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV690 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV690 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6221]) ).
thf(7431,plain,
! [SV691: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV691 )
= $false )
| ( ( class_HOL_Ozero @ SV691 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6222]) ).
thf(7432,plain,
! [SV692: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV692 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV692 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6223]) ).
thf(7433,plain,
! [SV693: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV693 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV693 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6224]) ).
thf(7434,plain,
! [SV694: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV694 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV694 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6225]) ).
thf(7435,plain,
! [SV695: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV695 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV695 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6226]) ).
thf(7436,plain,
! [SV696: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV696 )
= $false )
| ( ( class_HOL_Oplus @ SV696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6227]) ).
thf(7437,plain,
! [SV697: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV697 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV697 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6228]) ).
thf(7438,plain,
! [SV698: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV698 )
= $false )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV698 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6229]) ).
thf(7439,plain,
! [SV699: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV699 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV699 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6230]) ).
thf(7440,plain,
! [SV700: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV700 )
= $false )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV700 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6231]) ).
thf(7441,plain,
! [SV701: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV701 )
= $false )
| ( ( class_Orderings_Olinorder @ SV701 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6232]) ).
thf(7442,plain,
! [SV702: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV702 )
= $false )
| ( ( class_LOrder_Olorder @ SV702 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6233]) ).
thf(7443,plain,
! [SV703: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV703 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV703 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6234]) ).
thf(7444,plain,
! [SV704: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV704 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV704 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6235]) ).
thf(7445,plain,
! [SV705: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV705 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV705 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6236]) ).
thf(7446,plain,
! [SV706: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV706 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV706 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6237]) ).
thf(7447,plain,
! [SV707: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV707 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV707 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6238]) ).
thf(7448,plain,
! [SV708: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV708 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV708 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6239]) ).
thf(7449,plain,
! [SV709: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV709 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6240]) ).
thf(7450,plain,
! [SV710: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV710 )
= $false )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV710 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6241]) ).
thf(7451,plain,
! [SV711: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV711 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV711 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6242]) ).
thf(7452,plain,
! [SV712: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV712 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV712 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6243]) ).
thf(7453,plain,
! [SV713: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV713 )
= $false )
| ( ( class_Orderings_Oorder @ SV713 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6244]) ).
thf(7454,plain,
! [SV714: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV714 )
= $false )
| ( ( class_Orderings_Oord @ SV714 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6245]) ).
thf(7455,plain,
! [SV715: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV715 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV715 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6246]) ).
thf(7456,plain,
! [SV716: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV716 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV716 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6247]) ).
thf(7457,plain,
! [SV717: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV717 )
= $false )
| ( ( class_Ring__and__Field_Olordered__ring @ SV717 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6248]) ).
thf(7458,plain,
! [SV718: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV718 )
= $false )
| ( ( class_Ring__and__Field_Opordered__ring @ SV718 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6249]) ).
thf(7459,plain,
! [SV719: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV719 )
= $false )
| ( ( class_HOL_Ominus @ SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6250]) ).
thf(7460,plain,
! [SV720: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV720 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6251]) ).
thf(7461,plain,
! [SV721: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV721 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6252]) ).
thf(7462,plain,
! [SV722: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV722 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6253]) ).
thf(7463,plain,
! [SV723: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV723 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV723 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6254]) ).
thf(7464,plain,
! [SV724: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV724 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV724 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6255]) ).
thf(7465,plain,
! [SV725: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV725 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV725 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6256]) ).
thf(7466,plain,
! [SV726: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV726 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV726 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(7467,plain,
! [SV727: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV727 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV727 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6258]) ).
thf(7468,plain,
! [SV728: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV728 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6259]) ).
thf(7469,plain,
! [SV729: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV729 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6260]) ).
thf(7470,plain,
! [SV730: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV730 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV730 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6261]) ).
thf(7471,plain,
! [SV731: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV731 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV731 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6262]) ).
thf(7472,plain,
! [SV732: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV732 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV732 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6263]) ).
thf(7473,plain,
! [SV733: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV733 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV733 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6264]) ).
thf(7474,plain,
! [SV734: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV734 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV734 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6265]) ).
thf(7475,plain,
! [SV735: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV735 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV735 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6266]) ).
thf(7476,plain,
! [SV736: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV736 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV736 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6267]) ).
thf(7477,plain,
! [SV737: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV737 )
= $false )
| ( ( class_HOL_Oplus @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6268]) ).
thf(7478,plain,
! [SV738: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV738 )
= $false )
| ( ( class_HOL_Ozero @ SV738 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6269]) ).
thf(7479,plain,
! [SV739: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV739 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV739 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6270]) ).
thf(7480,plain,
! [SV740: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV740 )
= $false )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV740 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6271]) ).
thf(7481,plain,
! [SV741: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV741 )
= $false )
| ( ( class_Orderings_Olinorder @ SV741 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6272]) ).
thf(7482,plain,
! [SV742: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV742 )
= $false )
| ( ( class_LOrder_Olorder @ SV742 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6273]) ).
thf(7483,plain,
! [SV743: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV743 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV743 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6274]) ).
thf(7484,plain,
! [SV744: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV744 )
= $false )
| ( ( class_HOL_Ominus @ SV744 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6275]) ).
thf(7485,plain,
! [SV745: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV745 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6276]) ).
thf(7486,plain,
! [SV746: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV746 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV746 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6277]) ).
thf(7487,plain,
! [SV747: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV747 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6278]) ).
thf(7488,plain,
! [SV748: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV748 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV748 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6279]) ).
thf(7489,plain,
! [SV749: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV749 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV749 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6280]) ).
thf(7490,plain,
! [SV750: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV750 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV750 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6281]) ).
thf(7491,plain,
! [SV751: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV751 )
= $false )
| ( ( class_Orderings_Oorder @ SV751 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6282]) ).
thf(7492,plain,
! [SV752: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV752 )
= $false )
| ( ( class_Orderings_Oord @ SV752 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6283]) ).
thf(7493,plain,
! [SV753: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV753 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__abs__if @ SV753 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6284]) ).
thf(7494,plain,
! [SV754: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV754 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group @ SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6285]) ).
thf(7495,plain,
! [SV755: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV755 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV755 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6286]) ).
thf(7496,plain,
! [SV756: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV756 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV756 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6287]) ).
thf(7497,plain,
! [SV757: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV757 )
= $false )
| ( ( class_Ring__and__Field_Olordered__ring @ SV757 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6288]) ).
thf(7498,plain,
! [SV758: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV758 )
= $false )
| ( ( class_Ring__and__Field_Opordered__ring @ SV758 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6289]) ).
thf(7499,plain,
! [SV759: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV759 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV759 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6290]) ).
thf(7500,plain,
! [SV760: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV760 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__meet @ SV760 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6291]) ).
thf(7501,plain,
! [SV761: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV761 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__join @ SV761 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6292]) ).
thf(7502,plain,
! [SV762: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV762 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ SV762 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6293]) ).
thf(7503,plain,
! [SV763: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV763 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV763 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6294]) ).
thf(7504,plain,
! [SV764: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV764 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV764 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6295]) ).
thf(7505,plain,
! [SV765: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV765 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV765 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6296]) ).
thf(7506,plain,
! [SV766: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV766 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6297]) ).
thf(7507,plain,
! [SV767: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV767 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV767 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6298]) ).
thf(7508,plain,
! [SV768: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV768 )
= $false )
| ( ( class_HOL_Otimes @ SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6299]) ).
thf(7509,plain,
! [SV769: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV769 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ SV769 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6300]) ).
thf(7510,plain,
! [SV770: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV770 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6301]) ).
thf(7511,plain,
! [SV771: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV771 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV771 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6302]) ).
thf(7512,plain,
! [SV772: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV772 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV772 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6303]) ).
thf(7513,plain,
! [SV773: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV773 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV773 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6304]) ).
thf(7514,plain,
! [SV774: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV774 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV774 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6305]) ).
thf(7515,plain,
! [SV775: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV775 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV775 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6306]) ).
thf(7516,plain,
! [SV776: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV776 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV776 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6307]) ).
thf(7517,plain,
! [SV777: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV777 )
= $false )
| ( ( class_HOL_Otimes @ SV777 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6308]) ).
thf(7518,plain,
! [SV778: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV778 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6309]) ).
thf(7519,plain,
! [SV779: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV779 )
= $false )
| ( ( class_HOL_Ozero @ SV779 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6310]) ).
thf(7520,plain,
! [SV780: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV780 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV780 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6311]) ).
thf(7521,plain,
! [SV781: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV781 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV781 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6312]) ).
thf(7522,plain,
! [SV782: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV782 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV782 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6313]) ).
thf(7523,plain,
! [SV783: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV783 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV783 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6314]) ).
thf(7524,plain,
! [SV784: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV784 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV784 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6315]) ).
thf(7525,plain,
! [SV785: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV785 )
= $false )
| ( ( class_HOL_Oplus @ SV785 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6316]) ).
thf(7526,plain,
! [SV786: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV786 )
= $false )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV786 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6317]) ).
thf(7527,plain,
! [SV787: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV787 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV787 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6318]) ).
thf(7528,plain,
! [SV788: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV788 )
= $false )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV788 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6319]) ).
thf(7529,plain,
! [SV789: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV789 )
= $false )
| ( ( class_Orderings_Olinorder @ SV789 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6320]) ).
thf(7530,plain,
! [SV790: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV790 )
= $false )
| ( ( class_LOrder_Olorder @ SV790 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6321]) ).
thf(7531,plain,
! [SV791: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV791 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV791 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6322]) ).
thf(7532,plain,
! [SV792: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV792 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6323]) ).
thf(7533,plain,
! [SV793: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV793 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV793 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6324]) ).
thf(7534,plain,
! [SV794: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV794 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV794 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6325]) ).
thf(7535,plain,
! [SV795: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV795 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV795 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6326]) ).
thf(7536,plain,
! [SV796: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV796 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV796 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6327]) ).
thf(7537,plain,
! [SV797: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV797 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV797 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6328]) ).
thf(7538,plain,
! [SV798: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV798 )
= $false )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV798 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6329]) ).
thf(7539,plain,
! [SV799: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV799 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV799 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6330]) ).
thf(7540,plain,
! [SV800: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV800 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV800 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6331]) ).
thf(7541,plain,
! [SV801: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV801 )
= $false )
| ( ( class_Orderings_Oorder @ SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6332]) ).
thf(7542,plain,
! [SV802: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV802 )
= $false )
| ( ( class_Orderings_Oord @ SV802 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6333]) ).
thf(7543,plain,
! [SV803: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV803 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV803 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6334]) ).
thf(7544,plain,
! [SV804: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV804 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV804 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6335]) ).
thf(7545,plain,
! [SV805: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV805 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV805 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6336]) ).
thf(7546,plain,
! [SV806: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV806 )
= $false )
| ( ( class_HOL_Oone @ SV806 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6337]) ).
thf(7547,plain,
! [SV807: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV807 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV807 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6338]) ).
thf(7548,plain,
! [SV808: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV808 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6339]) ).
thf(7549,plain,
! [SV809: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV809 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV809 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6340]) ).
thf(7550,plain,
! [SV810: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV810 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV810 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6341]) ).
thf(7551,plain,
! [SV811: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV811 )
= $false )
| ( ( class_Orderings_Olinorder @ SV811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6342]) ).
thf(7552,plain,
! [SV812: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV812 )
= $false )
| ( ( class_LOrder_Olorder @ SV812 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6343]) ).
thf(7553,plain,
! [SV813: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV813 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV813 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6344]) ).
thf(7554,plain,
! [SV814: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV814 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV814 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6345]) ).
thf(7555,plain,
! [SV815: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV815 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV815 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6346]) ).
thf(7556,plain,
! [SV816: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV816 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV816 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6347]) ).
thf(7557,plain,
! [SV817: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV817 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV817 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6348]) ).
thf(7558,plain,
! [SV818: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV818 )
= $false )
| ( ( class_Orderings_Oorder @ SV818 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6349]) ).
thf(7559,plain,
! [SV819: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV819 )
= $false )
| ( ( class_Orderings_Oord @ SV819 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6350]) ).
thf(7560,plain,
! [SV820: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV820 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV820 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6351]) ).
thf(7561,plain,
! [SV821: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV821 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV821 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6352]) ).
thf(7562,plain,
! [SV822: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV822 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV822 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6353]) ).
thf(7563,plain,
! [SV823: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV823 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV823 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6354]) ).
thf(7564,plain,
! [SV824: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV824 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV824 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6355]) ).
thf(7565,plain,
! [SV825: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV825 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV825 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6356]) ).
thf(7566,plain,
! [SV826: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV826 )
= $false )
| ( ( class_HOL_Otimes @ SV826 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6357]) ).
thf(7567,plain,
! [SV827: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV827 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV827 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6358]) ).
thf(7568,plain,
! [SV828: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV828 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV828 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6359]) ).
thf(7569,plain,
! [SV829: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV829 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV829 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6360]) ).
thf(7570,plain,
! [SV830: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV830 )
= $false )
| ( ( class_HOL_Oplus @ SV830 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6361]) ).
thf(7571,plain,
! [SV831: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV831 )
= $false )
| ( ( class_HOL_Ozero @ SV831 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6362]) ).
thf(7572,plain,
! [SV832: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV832 )
= $false )
| ( ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ SV832 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6363]) ).
thf(7573,plain,
! [SV833: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV833 )
= $false )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV833 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6364]) ).
thf(7574,plain,
! [SV834: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV834 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV834 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6365]) ).
thf(7575,plain,
! [SV835: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV835 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV835 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6366]) ).
thf(7576,plain,
! [SV836: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV836 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV836 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6367]) ).
thf(7577,plain,
! [SV837: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV837 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV837 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6368]) ).
thf(7578,plain,
! [SV838: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV838 )
= $false )
| ( ( class_HOL_Oplus @ SV838 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6369]) ).
thf(7579,plain,
! [SV839: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV839 )
= $false )
| ( ( class_Orderings_Oorder @ SV839 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6370]) ).
thf(7580,plain,
! [SV840: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV840 )
= $false )
| ( ( class_Orderings_Oord @ SV840 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6371]) ).
thf(7581,plain,
! [SV841: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV841 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV841 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6372]) ).
thf(7582,plain,
! [SV842: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV842 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV842 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6373]) ).
thf(7583,plain,
! [SV843: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV843 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV843 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6374]) ).
thf(7584,plain,
! [SV844: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV844 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV844 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6375]) ).
thf(7585,plain,
! [SV845: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV845 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV845 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6376]) ).
thf(7586,plain,
! [SV846: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV846 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV846 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6377]) ).
thf(7587,plain,
! [SV847: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV847 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV847 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6378]) ).
thf(7588,plain,
! [SV848: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV848 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV848 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6379]) ).
thf(7589,plain,
! [SV849: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV849 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV849 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6380]) ).
thf(7590,plain,
! [SV850: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV850 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV850 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6381]) ).
thf(7591,plain,
! [SV851: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV851 )
= $false )
| ( ( class_HOL_Otimes @ SV851 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6382]) ).
thf(7592,plain,
! [SV852: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV852 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV852 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6383]) ).
thf(7593,plain,
! [SV853: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ SV853 )
= $false )
| ( ( class_HOL_Ozero @ SV853 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6384]) ).
thf(7594,plain,
! [SV854: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV854 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV854 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6385]) ).
thf(7595,plain,
! [SV855: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV855 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV855 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6386]) ).
thf(7596,plain,
! [SV856: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV856 )
= $false )
| ( ( class_HOL_Oplus @ SV856 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6387]) ).
thf(7597,plain,
! [SV857: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV857 )
= $false )
| ( ( class_Orderings_Oorder @ SV857 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6388]) ).
thf(7598,plain,
! [SV858: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV858 )
= $false )
| ( ( class_Orderings_Oord @ SV858 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6389]) ).
thf(7599,plain,
! [SV859: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV859 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV859 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6390]) ).
thf(7600,plain,
! [SV860: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV860 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV860 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6391]) ).
thf(7601,plain,
! [SV861: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV861 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV861 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6392]) ).
thf(7602,plain,
! [SV862: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV862 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV862 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6393]) ).
thf(7603,plain,
! [SV863: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV863 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV863 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6394]) ).
thf(7604,plain,
! [SV864: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV864 )
= $false )
| ( ( class_HOL_Otimes @ SV864 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6395]) ).
thf(7605,plain,
! [SV865: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV865 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV865 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6396]) ).
thf(7606,plain,
! [SV866: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV866 )
= $false )
| ( ( class_HOL_Ozero @ SV866 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6397]) ).
thf(7607,plain,
! [SV867: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV867 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV867 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6398]) ).
thf(7608,plain,
! [SV868: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV868 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV868 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6399]) ).
thf(7609,plain,
! [SV869: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV869 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV869 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6400]) ).
thf(7610,plain,
! [SV870: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV870 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV870 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6401]) ).
thf(7611,plain,
! [SV871: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV871 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV871 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6402]) ).
thf(7612,plain,
! [SV872: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV872 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV872 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6403]) ).
thf(7613,plain,
! [SV873: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV873 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV873 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6404]) ).
thf(7614,plain,
! [SV874: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV874 )
= $false )
| ( ( class_HOL_Otimes @ SV874 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6405]) ).
thf(7615,plain,
! [SV875: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV875 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV875 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6406]) ).
thf(7616,plain,
! [SV876: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV876 )
= $false )
| ( ( class_HOL_Ozero @ SV876 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6407]) ).
thf(7617,plain,
! [SV877: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV877 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV877 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6408]) ).
thf(7618,plain,
! [SV878: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV878 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV878 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6409]) ).
thf(7619,plain,
! [SV879: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV879 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV879 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6410]) ).
thf(7620,plain,
! [SV880: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV880 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV880 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6411]) ).
thf(7621,plain,
! [SV881: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV881 )
= $false )
| ( ( class_HOL_Oplus @ SV881 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6412]) ).
thf(7622,plain,
! [SV882: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV882 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV882 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6413]) ).
thf(7623,plain,
! [SV883: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV883 )
= $false )
| ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV883 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6414]) ).
thf(7624,plain,
! [SV884: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV884 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV884 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6415]) ).
thf(7625,plain,
! [SV885: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV885 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV885 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6416]) ).
thf(7626,plain,
! [SV886: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV886 )
= $false )
| ( ( class_Orderings_Oorder @ SV886 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6417]) ).
thf(7627,plain,
! [SV887: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV887 )
= $false )
| ( ( class_Orderings_Oord @ SV887 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6418]) ).
thf(7628,plain,
! [SV888: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV888 )
= $false )
| ( ( class_HOL_Ominus @ SV888 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6419]) ).
thf(7629,plain,
! [SV889: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV889 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ SV889 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6420]) ).
thf(7630,plain,
! [SV890: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV890 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV890 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6421]) ).
thf(7631,plain,
! [SV891: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV891 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV891 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6422]) ).
thf(7632,plain,
! [SV892: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV892 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV892 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6423]) ).
thf(7633,plain,
! [SV893: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV893 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV893 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6424]) ).
thf(7634,plain,
! [SV894: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__ring @ SV894 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV894 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6425]) ).
thf(7635,plain,
! [SV895: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV895 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__0 @ SV895 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6426]) ).
thf(7636,plain,
! [SV896: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV896 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring @ SV896 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6427]) ).
thf(7637,plain,
! [SV897: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV897 )
= $false )
| ( ( class_HOL_Oplus @ SV897 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6428]) ).
thf(7638,plain,
! [SV898: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV898 )
= $false )
| ( ( class_HOL_Ozero @ SV898 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6429]) ).
thf(7639,plain,
! [SV899: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV899 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV899 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6430]) ).
thf(7640,plain,
! [SV900: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV900 )
= $false )
| ( ( class_Orderings_Oorder @ SV900 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6431]) ).
thf(7641,plain,
! [SV901: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV901 )
= $false )
| ( ( class_Orderings_Oord @ SV901 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6432]) ).
thf(7642,plain,
! [SV902: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV902 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV902 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6433]) ).
thf(7643,plain,
! [SV903: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV903 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__mult @ SV903 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6434]) ).
thf(7644,plain,
! [SV904: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV904 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV904 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6435]) ).
thf(7645,plain,
! [SV905: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV905 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV905 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6436]) ).
thf(7646,plain,
! [SV906: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV906 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6437]) ).
thf(7647,plain,
! [SV907: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV907 )
= $false )
| ( ( class_HOL_Otimes @ SV907 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6438]) ).
thf(7648,plain,
! [SV908: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV908 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV908 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6439]) ).
thf(7649,plain,
! [SV909: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV909 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV909 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6440]) ).
thf(7650,plain,
! [SV910: $i] :
( ( ( class_Ring__and__Field_Opordered__comm__semiring @ SV910 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV910 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6441]) ).
thf(7651,plain,
! [SV911: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV911 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV911 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6442]) ).
thf(7652,plain,
! [SV912: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV912 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6443]) ).
thf(7653,plain,
! [SV913: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV913 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6444]) ).
thf(7654,plain,
! [SV914: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV914 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV914 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6445]) ).
thf(7655,plain,
! [SV915: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV915 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV915 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6446]) ).
thf(7656,plain,
! [SV916: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV916 )
= $false )
| ( ( class_HOL_Oplus @ SV916 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6447]) ).
thf(7657,plain,
! [SV917: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV917 )
= $false )
| ( ( class_HOL_Ozero @ SV917 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6448]) ).
thf(7658,plain,
! [SV918: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV918 )
= $false )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV918 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6449]) ).
thf(7659,plain,
! [SV919: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV919 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV919 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6450]) ).
thf(7660,plain,
! [SV920: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV920 )
= $false )
| ( ( class_Orderings_Oorder @ SV920 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6451]) ).
thf(7661,plain,
! [SV921: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV921 )
= $false )
| ( ( class_Orderings_Oord @ SV921 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6452]) ).
thf(7662,plain,
! [SV922: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV922 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV922 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6453]) ).
thf(7663,plain,
! [SV923: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV923 )
= $false )
| ( ( class_HOL_Ominus @ SV923 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6454]) ).
thf(7664,plain,
! [SV924: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV924 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV924 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6455]) ).
thf(7665,plain,
! [SV925: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV925 )
= $false )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV925 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6456]) ).
thf(7666,plain,
! [SV926: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV926 )
= $false )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV926 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6457]) ).
thf(7667,plain,
! [SV927: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV927 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV927 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6458]) ).
thf(7668,plain,
! [SV928: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV928 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV928 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6459]) ).
thf(7669,plain,
! [SV929: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV929 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV929 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6460]) ).
thf(7670,plain,
! [SV930: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV930 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV930 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6461]) ).
thf(7671,plain,
! [SV931: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV931 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV931 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6462]) ).
thf(7672,plain,
! [SV932: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV932 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV932 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6463]) ).
thf(7673,plain,
! [SV933: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV933 )
= $false )
| ( ( class_HOL_Otimes @ SV933 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6464]) ).
thf(7674,plain,
! [SV934: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV934 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV934 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6465]) ).
thf(7675,plain,
! [SV935: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV935 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV935 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6466]) ).
thf(7676,plain,
! [SV936: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV936 )
= $false )
| ( ( class_Orderings_Oorder @ SV936 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6467]) ).
thf(7677,plain,
! [SV937: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV937 )
= $false )
| ( ( class_Orderings_Oord @ SV937 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6468]) ).
thf(7678,plain,
! [SV938: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV938 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV938 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6469]) ).
thf(7679,plain,
! [SV939: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV939 )
= $false )
| ( ( class_HOL_Otimes @ SV939 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6470]) ).
thf(7680,plain,
! [SV940: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV940 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV940 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6471]) ).
thf(7681,plain,
! [SV941: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV941 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV941 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6472]) ).
thf(7682,plain,
! [SV942: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV942 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV942 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6473]) ).
thf(7683,plain,
! [SV943: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV943 )
= $false )
| ( ( class_HOL_Oplus @ SV943 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6474]) ).
thf(7684,plain,
! [SV944: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV944 )
= $false )
| ( ( class_HOL_Ozero @ SV944 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6475]) ).
thf(7685,plain,
! [SV945: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV945 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV945 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6476]) ).
thf(7686,plain,
! [SV946: $i] :
( ( ( class_Ring__and__Field_Oring @ SV946 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6477]) ).
thf(7687,plain,
! [SV947: $i] :
( ( ( class_Ring__and__Field_Oring @ SV947 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV947 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6478]) ).
thf(7688,plain,
! [SV948: $i] :
( ( ( class_Ring__and__Field_Oring @ SV948 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV948 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6479]) ).
thf(7689,plain,
! [SV949: $i] :
( ( ( class_Ring__and__Field_Oring @ SV949 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV949 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6480]) ).
thf(7690,plain,
! [SV950: $i] :
( ( ( class_Ring__and__Field_Oring @ SV950 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV950 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6481]) ).
thf(7691,plain,
! [SV951: $i] :
( ( ( class_Ring__and__Field_Oring @ SV951 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV951 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6482]) ).
thf(7692,plain,
! [SV952: $i] :
( ( ( class_Ring__and__Field_Oring @ SV952 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV952 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6483]) ).
thf(7693,plain,
! [SV953: $i] :
( ( ( class_Ring__and__Field_Oring @ SV953 )
= $false )
| ( ( class_HOL_Oplus @ SV953 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6484]) ).
thf(7694,plain,
! [SV954: $i] :
( ( ( class_Ring__and__Field_Oring @ SV954 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV954 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6485]) ).
thf(7695,plain,
! [SV955: $i] :
( ( ( class_Ring__and__Field_Oring @ SV955 )
= $false )
| ( ( class_HOL_Otimes @ SV955 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6486]) ).
thf(7696,plain,
! [SV956: $i] :
( ( ( class_Ring__and__Field_Oring @ SV956 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV956 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6487]) ).
thf(7697,plain,
! [SV957: $i] :
( ( ( class_Ring__and__Field_Oring @ SV957 )
= $false )
| ( ( class_HOL_Ominus @ SV957 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6488]) ).
thf(7698,plain,
! [SV958: $i] :
( ( ( class_Ring__and__Field_Oring @ SV958 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV958 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6489]) ).
thf(7699,plain,
! [SV959: $i] :
( ( ( class_Ring__and__Field_Oring @ SV959 )
= $false )
| ( ( class_HOL_Ozero @ SV959 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6490]) ).
thf(7700,plain,
! [SV960: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV960 )
= $false )
| ( ( class_Ring__and__Field_Oring @ SV960 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6491]) ).
thf(7701,plain,
! [SV961: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV961 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV961 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6492]) ).
thf(7702,plain,
! [SV962: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV962 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV962 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6493]) ).
thf(7703,plain,
! [SV963: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV963 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6494]) ).
thf(7704,plain,
! [SV964: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV964 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV964 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6495]) ).
thf(7705,plain,
! [SV965: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV965 )
= $false )
| ( ( class_HOL_Oplus @ SV965 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6496]) ).
thf(7706,plain,
! [SV966: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV966 )
= $false )
| ( ( class_HOL_Ozero @ SV966 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6497]) ).
thf(7707,plain,
! [SV967: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV967 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV967 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6498]) ).
thf(7708,plain,
! [SV968: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV968 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV968 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6499]) ).
thf(7709,plain,
! [SV969: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV969 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV969 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6500]) ).
thf(7710,plain,
! [SV970: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV970 )
= $false )
| ( ( class_HOL_Oone @ SV970 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6501]) ).
thf(7711,plain,
! [SV971: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV971 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV971 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6502]) ).
thf(7712,plain,
! [SV972: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV972 )
= $false )
| ( ( class_HOL_Ominus @ SV972 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6503]) ).
thf(7713,plain,
! [SV973: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV973 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6504]) ).
thf(7714,plain,
! [SV974: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV974 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV974 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6505]) ).
thf(7715,plain,
! [SV975: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV975 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV975 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6506]) ).
thf(7716,plain,
! [SV976: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV976 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV976 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6507]) ).
thf(7717,plain,
! [SV977: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV977 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6508]) ).
thf(7718,plain,
! [SV978: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV978 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6509]) ).
thf(7719,plain,
! [SV979: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV979 )
= $false )
| ( ( class_HOL_Otimes @ SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6510]) ).
thf(7720,plain,
! [SV980: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV980 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV980 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6511]) ).
thf(7721,plain,
! [SV981: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV981 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV981 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6512]) ).
thf(7722,plain,
! [SV982: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV982 )
= $false )
| ( ( class_HOL_Oplus @ SV982 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6513]) ).
thf(7723,plain,
! [SV983: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV983 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV983 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6514]) ).
thf(7724,plain,
! [SV984: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV984 )
= $false )
| ( ( class_HOL_Otimes @ SV984 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6515]) ).
thf(7725,plain,
! [SV985: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV985 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV985 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6516]) ).
thf(7726,plain,
! [SV986: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV986 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV986 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6517]) ).
thf(7727,plain,
! [SV987: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV987 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV987 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6518]) ).
thf(7728,plain,
! [SV988: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV988 )
= $false )
| ( ( class_HOL_Oplus @ SV988 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6519]) ).
thf(7729,plain,
! [SV989: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV989 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV989 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6520]) ).
thf(7730,plain,
! [SV990: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV990 )
= $false )
| ( ( class_HOL_Otimes @ SV990 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6521]) ).
thf(7731,plain,
! [SV991: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV991 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV991 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6522]) ).
thf(7732,plain,
! [SV992: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV992 )
= $false )
| ( ( class_HOL_Ozero @ SV992 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6523]) ).
thf(7733,plain,
! [SV993: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV993 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV993 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6524]) ).
thf(7734,plain,
! [SV994: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV994 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV994 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6525]) ).
thf(7735,plain,
! [SV995: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV995 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV995 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6526]) ).
thf(7736,plain,
! [SV996: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV996 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV996 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6527]) ).
thf(7737,plain,
! [SV997: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV997 )
= $false )
| ( ( class_HOL_Otimes @ SV997 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6528]) ).
thf(7738,plain,
! [SV998: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV998 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV998 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6529]) ).
thf(7739,plain,
! [SV999: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV999 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV999 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6530]) ).
thf(7740,plain,
! [SV1000: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1000 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV1000 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6531]) ).
thf(7741,plain,
! [SV1001: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1001 )
= $false )
| ( ( class_HOL_Oplus @ SV1001 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6532]) ).
thf(7742,plain,
! [SV1002: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1002 )
= $false )
| ( ( class_HOL_Ozero @ SV1002 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6533]) ).
thf(7743,plain,
! [SV1003: $i] :
( ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1003 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1003 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6534]) ).
thf(7744,plain,
! [SV1004: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1004 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1004 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6535]) ).
thf(7745,plain,
! [SV1005: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1005 )
= $false )
| ( ( class_HOL_Ozero @ SV1005 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6536]) ).
thf(7746,plain,
! [SV1006: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1006 )
= $false )
| ( ( class_HOL_Oplus @ SV1006 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6537]) ).
thf(7747,plain,
! [SV1007: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1007 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV1007 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6538]) ).
thf(7748,plain,
! [SV1008: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1008 )
= $false )
| ( ( class_HOL_Oone @ SV1008 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6539]) ).
thf(7749,plain,
! [SV1009: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1009 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV1009 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6540]) ).
thf(7750,plain,
! [SV1010: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1010 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV1010 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6541]) ).
thf(7751,plain,
! [SV1011: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1011 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV1011 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6542]) ).
thf(7752,plain,
! [SV1012: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1012 )
= $false )
| ( ( class_HOL_Otimes @ SV1012 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6543]) ).
thf(7753,plain,
! [SV1013: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1013 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1013 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6544]) ).
thf(7754,plain,
! [SV1014: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1014 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV1014 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6545]) ).
thf(7755,plain,
! [SV1015: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV1015 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV1015 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6546]) ).
thf(7756,plain,
! [SV1016: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1016 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV1016 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6547]) ).
thf(7757,plain,
! [SV1017: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1017 )
= $false )
| ( ( class_Ring__and__Field_Oaxclass__0__neq__1 @ SV1017 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6548]) ).
thf(7758,plain,
! [SV1018: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1018 )
= $false )
| ( ( class_HOL_Oone @ SV1018 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6549]) ).
thf(7759,plain,
! [SV1019: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1019 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__mult @ SV1019 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6550]) ).
thf(7760,plain,
! [SV1020: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1020 )
= $false )
| ( ( class_HOL_Otimes @ SV1020 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6551]) ).
thf(7761,plain,
! [SV1021: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1021 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV1021 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6552]) ).
thf(7762,plain,
! [SV1022: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1022 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV1022 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6553]) ).
thf(7763,plain,
! [SV1023: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1023 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0__cancel @ SV1023 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6554]) ).
thf(7764,plain,
! [SV1024: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1024 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV1024 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6555]) ).
thf(7765,plain,
! [SV1025: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1025 )
= $false )
| ( ( class_Ring__and__Field_Osemiring @ SV1025 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6556]) ).
thf(7766,plain,
! [SV1026: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1026 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1026 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6557]) ).
thf(7767,plain,
! [SV1027: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1027 )
= $false )
| ( ( class_HOL_Ozero @ SV1027 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6558]) ).
thf(7768,plain,
! [SV1028: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1028 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV1028 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6559]) ).
thf(7769,plain,
! [SV1029: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1029 )
= $false )
| ( ( class_OrderedGroup_Osemigroup__add @ SV1029 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6560]) ).
thf(7770,plain,
! [SV1030: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1030 )
= $false )
| ( ( class_HOL_Oplus @ SV1030 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6561]) ).
thf(7771,plain,
! [SV1031: $i] :
( ( ( class_Ring__and__Field_Osemiring__1__cancel @ SV1031 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV1031 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6562]) ).
thf(7772,plain,
! [SV1032: $i] :
( ( ( class_Wellfounded__Recursion_Owellorder @ SV1032 )
= $false )
| ( ( class_Orderings_Oord @ SV1032 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6563]) ).
thf(7773,plain,
! [SV1033: $i] :
( ( ( class_Wellfounded__Recursion_Owellorder @ SV1033 )
= $false )
| ( ( class_Orderings_Oorder @ SV1033 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6564]) ).
thf(7774,plain,
! [SV1034: $i] :
( ( ( class_Wellfounded__Recursion_Owellorder @ SV1034 )
= $false )
| ( ( class_LOrder_Omeet__semilorder @ SV1034 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6565]) ).
thf(7775,plain,
! [SV1035: $i] :
( ( ( class_Wellfounded__Recursion_Owellorder @ SV1035 )
= $false )
| ( ( class_LOrder_Ojoin__semilorder @ SV1035 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6566]) ).
thf(7776,plain,
! [SV1036: $i] :
( ( ( class_Wellfounded__Recursion_Owellorder @ SV1036 )
= $false )
| ( ( class_LOrder_Olorder @ SV1036 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6567]) ).
thf(7777,plain,
! [SV1037: $i] :
( ( ( class_Wellfounded__Recursion_Owellorder @ SV1037 )
= $false )
| ( ( class_Orderings_Olinorder @ SV1037 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6568]) ).
thf(7778,plain,
! [SV1645: $i,SV1370: $i,SV1038: $i] :
( ( ~ ( c_in @ SV1038 @ ( c_Datatype_Oo2s @ SV1370 @ SV1645 ) @ SV1645 )
| ( SV1370
= ( c_Datatype_Ooption_OSome @ SV1038 @ SV1645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6569]) ).
thf(7779,plain,
! [SV1372: $i,SV1040: $i] :
( ( ( SV1040 = c_Datatype_Ooption_ONone )
= $true )
| ( ( SV1040
= ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__None__eq__iff1__1 @ SV1040 @ SV1372 ) @ SV1372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6571]) ).
thf(7780,plain,
! [SV1373: $i,SV1041: $i] :
( ( ( SV1041 = c_Datatype_Ooption_ONone )
= $true )
| ( ( SV1041
= ( c_Datatype_Ooption_OSome @ ( c_Main_Onot__Some__eq__iff1__1 @ SV1041 @ SV1373 ) @ SV1373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6572]) ).
thf(7781,plain,
! [SV1042: $i] :
( ( ( c_Divides_Oop_Advd @ c_0 @ SV1042 @ tc_nat )
= $false )
| ( ( SV1042 = c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6573]) ).
thf(7782,plain,
! [SV1646: $i,SV1376: $i,SV1045: $i] :
( ( ! [SY3232: $i] :
( ~ ( c_in @ ( c_minus @ SV1045 @ ( c_insert @ SV1376 @ SV1646 @ SY3232 ) @ ( tc_set @ SY3232 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY3232 ) )
| ( c_in @ ( c_minus @ SV1045 @ SV1646 @ ( tc_set @ SY3232 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SY3232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6576]) ).
thf(7783,plain,
! [SV1647: $i,SV1377: $i,SV1046: $i] :
( ( ! [SY3233: $i] :
( ~ ( c_in @ ( c_minus @ SV1046 @ SV1377 @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) )
| ( c_in @ ( c_minus @ SV1046 @ ( c_insert @ SY3233 @ SV1377 @ SV1647 ) @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6577]) ).
thf(7784,plain,
! [SV1378: $i,SV1047: $i] :
( ( ( ~ ( c_in @ ( c_Pow @ SV1047 @ SV1378 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1378 ) ) ) )
= $true )
| ( ( c_in @ SV1047 @ c_Finite__Set_OFinites @ ( tc_set @ SV1378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6578]) ).
thf(7785,plain,
! [SV1379: $i,SV1048: $i] :
( ( ( ~ ( c_in @ SV1048 @ c_Finite__Set_OFinites @ ( tc_set @ SV1379 ) ) )
= $true )
| ( ( c_in @ ( c_Pow @ SV1048 @ SV1379 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6579]) ).
thf(7786,plain,
! [SV1648: $i,SV1380: $i,SV1049: $i] :
( ( ~ ( c_in @ ( c_union @ SV1049 @ SV1380 @ SV1648 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1648 ) )
| ( c_in @ SV1049 @ c_Finite__Set_OFinites @ ( tc_set @ SV1648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6580]) ).
thf(7787,plain,
! [SV1649: $i,SV1381: $i,SV1050: $i] :
( ( ~ ( c_in @ ( c_union @ SV1050 @ SV1381 @ SV1649 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1649 ) )
| ( c_in @ SV1381 @ c_Finite__Set_OFinites @ ( tc_set @ SV1649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6581]) ).
thf(7788,plain,
! [SV1650: $i,SV1382: $i,SV1051: $i] :
( ( ~ ( c_in @ SV1051 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
| ~ ( c_in @ SV1650 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
| ( c_in @ ( c_union @ SV1650 @ SV1051 @ SV1382 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6582]) ).
thf(7789,plain,
! [SV1651: $i,SV1383: $i,SV1052: $i] :
( ( ~ ( c_in @ ( c_Relation_Oconverse @ SV1052 @ SV1383 @ SV1651 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1651 @ SV1383 ) ) )
| ( c_in @ SV1052 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1383 @ SV1651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6583]) ).
thf(7790,plain,
! [SV1652: $i,SV1384: $i,SV1053: $i] :
( ( ~ ( c_in @ SV1053 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1384 @ SV1652 ) ) )
| ( c_in @ ( c_Relation_Oconverse @ SV1053 @ SV1384 @ SV1652 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1652 @ SV1384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6584]) ).
thf(7791,plain,
! [SV1653: $i,SV1385: $i,SV1054: $i] :
( ( ~ ( c_Divides_Oop_Advd @ SV1054 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1385 @ SV1653 @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1054 @ SV1385 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6585]) ).
thf(7792,plain,
! [SV1654: $i,SV1386: $i,SV1055: $i] :
( ( ~ ( c_Divides_Oop_Advd @ SV1055 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1386 @ SV1654 @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1055 @ SV1654 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6586]) ).
thf(7793,plain,
! [SV1655: $i,SV1387: $i,SV1056: $i] :
( ( ~ ( c_Divides_Oop_Advd @ SV1056 @ SV1387 @ tc_nat )
| ~ ( c_Divides_Oop_Advd @ SV1056 @ SV1655 @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1056 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1655 @ SV1387 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6587]) ).
thf(7794,plain,
! [SV1388: $i,SV1057: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ SV1057 @ ( c_uminus @ SV1388 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1057 @ SV1388 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6588]) ).
thf(7795,plain,
! [SV1389: $i,SV1058: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ SV1058 @ SV1389 @ tc_IntDef_Oint ) )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1058 @ ( c_uminus @ SV1389 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6589]) ).
thf(7796,plain,
! [SV1059: $i] :
( ( ( c_Divides_Oop_Advd @ c_0 @ SV1059 @ tc_IntDef_Oint )
= $false )
| ( ( SV1059 = c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6590]) ).
thf(7797,plain,
! [SV1390: $i,SV1060: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ SV1060 @ tc_IntDef_Oint ) @ SV1390 @ tc_IntDef_Oint ) )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1060 @ SV1390 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6591]) ).
thf(7798,plain,
! [SV1391: $i,SV1061: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ SV1061 @ SV1391 @ tc_IntDef_Oint ) )
= $true )
| ( ( c_Divides_Oop_Advd @ ( c_uminus @ SV1061 @ tc_IntDef_Oint ) @ SV1391 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6592]) ).
thf(7799,plain,
! [SV1656: $i,SV1392: $i,SV1062: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV1062 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1392 ) @ ( tc_List_Olist @ SV1392 ) ) @ ( c_List_Olex @ SV1656 @ SV1392 ) @ ( tc_prod @ ( tc_List_Olist @ SV1392 ) @ ( tc_List_Olist @ SV1392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6593]) ).
thf(7800,plain,
! [SV1657: $i,SV1393: $i,SV1065: $i] :
( ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1065 @ ( tc_List_Olist @ SV1393 ) @ ( tc_List_Olist @ SV1393 ) ) @ ( c_List_Olex @ SV1657 @ SV1393 ) @ ( tc_prod @ ( tc_List_Olist @ SV1393 ) @ ( tc_List_Olist @ SV1393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6594]) ).
thf(7801,plain,
! [SV1658: $i,SV1394: $i,SV1066: $i] :
( ( ! [SY3234: $i] :
( ~ ( c_in @ ( c_append @ SV1066 @ SV1394 @ SV1658 ) @ ( c_List_Olists @ SY3234 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) )
| ( c_in @ SV1066 @ ( c_List_Olists @ SY3234 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6595]) ).
thf(7802,plain,
! [SV1659: $i,SV1395: $i,SV1067: $i] :
( ( ! [SY3235: $i] :
( ~ ( c_in @ ( c_append @ SV1067 @ SV1395 @ SV1659 ) @ ( c_List_Olists @ SY3235 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) )
| ( c_in @ SV1395 @ ( c_List_Olists @ SY3235 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6596]) ).
thf(7803,plain,
! [SV1660: $i,SV1396: $i,SV1068: $i] :
( ( ! [SY3236: $i] :
( ~ ( c_in @ SV1068 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
| ~ ( c_in @ SY3236 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
| ( c_in @ ( c_append @ SY3236 @ SV1068 @ SV1660 ) @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6597]) ).
thf(7804,plain,
! [SV1399: $i,SV1074: $i] :
( ( ( c_less @ c_0 @ ( c_Nat_Osize @ SV1074 @ ( tc_List_Olist @ SV1399 ) ) @ tc_nat )
= $true )
| ( ( SV1074 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6601]) ).
thf(7805,plain,
! [SV1661: $i,SV1400: $i,SV1075: $i] :
( ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ SV1075 @ SV1400 ) @ ( c_List_Olist_OCons @ SV1661 @ c_List_Olist_ONil @ SV1400 ) @ SV1400 ) @ SV1400 )
= ( c_List_Olist_OCons @ SV1661 @ SV1075 @ SV1400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6602]) ).
thf(7806,plain,
! [SV1403: $i,SV1081: $i] :
( ( ( ~ ( c_lessequals @ ( c_Suc @ SV1081 ) @ ( c_Suc @ SV1403 ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1081 @ SV1403 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6605]) ).
thf(7807,plain,
! [SV1404: $i,SV1082: $i] :
( ( ( ~ ( c_lessequals @ SV1082 @ SV1404 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Suc @ SV1082 ) @ ( c_Suc @ SV1404 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6606]) ).
thf(7808,plain,
! [SV1405: $i,SV1083: $i] :
( ( ( ~ ( c_less @ ( c_Suc @ SV1083 ) @ ( c_Suc @ SV1405 ) @ tc_nat ) )
= $true )
| ( ( c_less @ SV1083 @ SV1405 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6607]) ).
thf(7809,plain,
! [SV1406: $i,SV1084: $i] :
( ( ( ~ ( c_less @ SV1084 @ SV1406 @ tc_nat ) )
= $true )
| ( ( c_less @ ( c_Suc @ SV1084 ) @ ( c_Suc @ SV1406 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6608]) ).
thf(7810,plain,
! [SV1407: $i,SV1085: $i] :
( ( ( ~ ( c_less @ c_0 @ ( c_plus @ SV1085 @ SV1407 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_less @ c_0 @ SV1407 @ tc_nat )
| ( c_less @ c_0 @ SV1085 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6609]) ).
thf(7811,plain,
! [SV1408: $i,SV1086: $i] :
( ( ( ~ ( c_less @ c_0 @ SV1086 @ tc_nat ) )
= $true )
| ( ( c_less @ c_0 @ ( c_plus @ SV1086 @ SV1408 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6610]) ).
thf(7812,plain,
! [SV1409: $i,SV1087: $i] :
( ( ( ~ ( c_less @ c_0 @ SV1087 @ tc_nat ) )
= $true )
| ( ( c_less @ c_0 @ ( c_plus @ SV1409 @ SV1087 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6611]) ).
thf(7813,plain,
! [SV1088: $i] :
( ( ( c_lessequals @ SV1088 @ c_0 @ tc_nat )
= $false )
| ( ( SV1088 = c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6612]) ).
thf(7814,plain,
! [SV1089: $i] :
( ( ( c_less @ SV1089 @ ( c_Suc @ c_0 ) @ tc_nat )
= $false )
| ( ( SV1089 = c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6613]) ).
thf(7815,plain,
! [SV1090: $i] :
( ( ( c_less @ SV1090 @ c_1 @ tc_nat )
= $false )
| ( ( SV1090 = c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6614]) ).
thf(7816,plain,
! [SV1410: $i,SV1092: $i] :
( ( c_less @ ( c_plus @ SV1092 @ SV1410 @ tc_nat ) @ SV1092 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6616]) ).
thf(7817,plain,
! [SV1411: $i,SV1093: $i] :
( ( c_less @ ( c_plus @ SV1093 @ SV1411 @ tc_nat ) @ SV1411 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6617]) ).
thf(7818,plain,
! [SV1412: $i,SV1095: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV1095 ) )
= $true )
| ( ( ~ ( c_less @ SV1412 @ SV1412 @ SV1095 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6619]) ).
thf(7819,plain,
! [SV1662: $i,SV1414: $i,SV1097: $i] :
( ( ! [SY3237: $i,SY3238: $i] :
( ~ ( c_in @ SV1097 @ ( c_Relation_OImage @ SV1414 @ ( c_insert @ SV1662 @ c_emptyset @ SY3237 ) @ SY3237 @ SY3238 ) @ SY3238 )
| ( c_in @ ( c_Pair @ SV1662 @ SV1097 @ SY3237 @ SY3238 ) @ SV1414 @ ( tc_prod @ SY3237 @ SY3238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6621]) ).
thf(7820,plain,
! [SV1663: $i,SV1415: $i,SV1098: $i] :
( ( ! [SY3239: $i,SY3240: $i] :
( ~ ( c_in @ ( c_Pair @ SV1098 @ SV1415 @ SV1663 @ SY3239 ) @ SY3240 @ ( tc_prod @ SV1663 @ SY3239 ) )
| ( c_in @ SV1415 @ ( c_Relation_OImage @ SY3240 @ ( c_insert @ SV1098 @ c_emptyset @ SV1663 ) @ SV1663 @ SY3239 ) @ SY3239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6622]) ).
thf(7821,plain,
! [SV1664: $i,SV1416: $i,SV1099: $i] :
( ( ! [SY3241: $i,SY3242: $i] :
( ~ ( c_in @ ( c_Pair @ SV1099 @ SV1416 @ SV1664 @ SY3241 ) @ ( c_Relation_Oconverse @ SY3242 @ SY3241 @ SV1664 ) @ ( tc_prod @ SV1664 @ SY3241 ) )
| ( c_in @ ( c_Pair @ SV1416 @ SV1099 @ SY3241 @ SV1664 ) @ SY3242 @ ( tc_prod @ SY3241 @ SV1664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6623]) ).
thf(7822,plain,
! [SV1665: $i,SV1417: $i,SV1100: $i] :
( ( ! [SY3243: $i,SY3244: $i] :
( ~ ( c_in @ ( c_Pair @ SV1100 @ SV1417 @ SV1665 @ SY3243 ) @ SY3244 @ ( tc_prod @ SV1665 @ SY3243 ) )
| ( c_in @ ( c_Pair @ SV1417 @ SV1100 @ SY3243 @ SV1665 ) @ ( c_Relation_Oconverse @ SY3244 @ SV1665 @ SY3243 ) @ ( tc_prod @ SY3243 @ SV1665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6624]) ).
thf(7823,plain,
! [SV1666: $i,SV1418: $i,SV1101: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV1101 @ SV1418 @ SV1666 @ SV1666 ) @ c_Relation_OId @ ( tc_prod @ SV1666 @ SV1666 ) )
| ( SV1101 = SV1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6625]) ).
thf(7824,plain,
! [SV1667: $i,SV1419: $i,SV1102: $i] :
( ( ~ ( class_Orderings_Oord @ SV1102 )
| ~ ( c_in @ SV1419 @ ( c_SetInterval_OatLeast @ SV1667 @ SV1102 ) @ SV1102 )
| ( c_lessequals @ SV1667 @ SV1419 @ SV1102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6626]) ).
thf(7825,plain,
! [SV1668: $i,SV1420: $i,SV1103: $i] :
( ( ~ ( class_Orderings_Oord @ SV1103 )
| ~ ( c_lessequals @ SV1420 @ SV1668 @ SV1103 )
| ( c_in @ SV1668 @ ( c_SetInterval_OatLeast @ SV1420 @ SV1103 ) @ SV1103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6627]) ).
thf(7826,plain,
! [SV1669: $i,SV1421: $i,SV1104: $i] :
( ( ~ ( class_Orderings_Oorder @ SV1104 )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1421 @ SV1104 ) @ ( c_SetInterval_OatLeast @ SV1669 @ SV1104 ) @ ( tc_set @ SV1104 ) )
| ( c_lessequals @ SV1669 @ SV1421 @ SV1104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6628]) ).
thf(7827,plain,
! [SV1670: $i,SV1422: $i,SV1105: $i] :
( ( ~ ( class_Orderings_Oorder @ SV1105 )
| ~ ( c_lessequals @ SV1422 @ SV1670 @ SV1105 )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1670 @ SV1105 ) @ ( c_SetInterval_OatLeast @ SV1422 @ SV1105 ) @ ( tc_set @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6629]) ).
thf(7828,plain,
! [SV1671: $i,SV1423: $i,SV1106: $i] :
( ( ~ ( class_Orderings_Oord @ SV1106 )
| ~ ( c_in @ SV1423 @ ( c_SetInterval_OatMost @ SV1671 @ SV1106 ) @ SV1106 )
| ( c_lessequals @ SV1423 @ SV1671 @ SV1106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6630]) ).
thf(7829,plain,
! [SV1672: $i,SV1424: $i,SV1107: $i] :
( ( ~ ( class_Orderings_Oord @ SV1107 )
| ~ ( c_lessequals @ SV1424 @ SV1672 @ SV1107 )
| ( c_in @ SV1424 @ ( c_SetInterval_OatMost @ SV1672 @ SV1107 ) @ SV1107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6631]) ).
thf(7830,plain,
! [SV1673: $i,SV1425: $i,SV1108: $i] :
( ( ~ ( class_Orderings_Oorder @ SV1108 )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1425 @ SV1108 ) @ ( c_SetInterval_OatMost @ SV1673 @ SV1108 ) @ ( tc_set @ SV1108 ) )
| ( c_lessequals @ SV1425 @ SV1673 @ SV1108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6632]) ).
thf(7831,plain,
! [SV1674: $i,SV1426: $i,SV1109: $i] :
( ( ~ ( class_Orderings_Oorder @ SV1109 )
| ~ ( c_lessequals @ SV1426 @ SV1674 @ SV1109 )
| ( c_lessequals @ ( c_SetInterval_OatMost @ SV1426 @ SV1109 ) @ ( c_SetInterval_OatMost @ SV1674 @ SV1109 ) @ ( tc_set @ SV1109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6633]) ).
thf(7832,plain,
! [SV1675: $i,SV1427: $i,SV1110: $i] :
( ( ~ ( class_Orderings_Oord @ SV1110 )
| ~ ( c_in @ SV1427 @ ( c_SetInterval_OgreaterThan @ SV1675 @ SV1110 ) @ SV1110 )
| ( c_less @ SV1675 @ SV1427 @ SV1110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6634]) ).
thf(7833,plain,
! [SV1676: $i,SV1428: $i,SV1111: $i] :
( ( ~ ( class_Orderings_Oord @ SV1111 )
| ~ ( c_less @ SV1428 @ SV1676 @ SV1111 )
| ( c_in @ SV1676 @ ( c_SetInterval_OgreaterThan @ SV1428 @ SV1111 ) @ SV1111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6635]) ).
thf(7834,plain,
! [SV1677: $i,SV1429: $i,SV1112: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1112 )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1429 @ SV1112 ) @ ( c_SetInterval_OgreaterThan @ SV1677 @ SV1112 ) @ ( tc_set @ SV1112 ) )
| ( c_lessequals @ SV1677 @ SV1429 @ SV1112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6636]) ).
thf(7835,plain,
! [SV1678: $i,SV1430: $i,SV1113: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1113 )
| ~ ( c_lessequals @ SV1430 @ SV1678 @ SV1113 )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1678 @ SV1113 ) @ ( c_SetInterval_OgreaterThan @ SV1430 @ SV1113 ) @ ( tc_set @ SV1113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6637]) ).
thf(7836,plain,
! [SV1679: $i,SV1431: $i,SV1114: $i] :
( ( ~ ( class_Orderings_Oord @ SV1114 )
| ~ ( c_in @ SV1431 @ ( c_SetInterval_OlessThan @ SV1679 @ SV1114 ) @ SV1114 )
| ( c_less @ SV1431 @ SV1679 @ SV1114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6638]) ).
thf(7837,plain,
! [SV1680: $i,SV1432: $i,SV1115: $i] :
( ( ~ ( class_Orderings_Oord @ SV1115 )
| ~ ( c_less @ SV1432 @ SV1680 @ SV1115 )
| ( c_in @ SV1432 @ ( c_SetInterval_OlessThan @ SV1680 @ SV1115 ) @ SV1115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6639]) ).
thf(7838,plain,
! [SV1681: $i,SV1433: $i,SV1116: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1116 )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1433 @ SV1116 ) @ ( c_SetInterval_OlessThan @ SV1681 @ SV1116 ) @ ( tc_set @ SV1116 ) )
| ( c_lessequals @ SV1433 @ SV1681 @ SV1116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6640]) ).
thf(7839,plain,
! [SV1682: $i,SV1434: $i,SV1117: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1117 )
| ~ ( c_lessequals @ SV1434 @ SV1682 @ SV1117 )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1434 @ SV1117 ) @ ( c_SetInterval_OlessThan @ SV1682 @ SV1117 ) @ ( tc_set @ SV1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6641]) ).
thf(7840,plain,
! [SV1683: $i,SV1435: $i,SV1118: $i] :
( ( ~ ( c_in @ SV1118 @ SV1435 @ SV1683 )
| ~ ( c_in @ SV1118 @ ( c_uminus @ SV1435 @ ( tc_set @ SV1683 ) ) @ SV1683 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6642]) ).
thf(7841,plain,
! [SV1684: $i,SV1436: $i,SV1119: $i] :
( ( ( c_in @ SV1119 @ SV1436 @ SV1684 )
| ( c_in @ SV1119 @ ( c_uminus @ SV1436 @ ( tc_set @ SV1684 ) ) @ SV1684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6643]) ).
thf(7842,plain,
! [SV1685: $i,SV1437: $i,SV1120: $i] :
( ( ~ ( c_lessequals @ ( c_uminus @ SV1120 @ ( tc_set @ SV1437 ) ) @ ( c_uminus @ SV1685 @ ( tc_set @ SV1437 ) ) @ ( tc_set @ SV1437 ) )
| ( c_lessequals @ SV1685 @ SV1120 @ ( tc_set @ SV1437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6644]) ).
thf(7843,plain,
! [SV1686: $i,SV1438: $i,SV1121: $i] :
( ( ~ ( c_lessequals @ SV1121 @ SV1438 @ ( tc_set @ SV1686 ) )
| ( c_lessequals @ ( c_uminus @ SV1438 @ ( tc_set @ SV1686 ) ) @ ( c_uminus @ SV1121 @ ( tc_set @ SV1686 ) ) @ ( tc_set @ SV1686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6645]) ).
thf(7844,plain,
! [SV1687: $i,SV1439: $i,SV1122: $i] :
( ( ! [SY3245: $i] :
( ~ ( c_in @ SV1122 @ SV1439 @ SV1687 )
| ~ ( c_in @ SV1122 @ ( c_minus @ SY3245 @ SV1439 @ ( tc_set @ SV1687 ) ) @ SV1687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6646]) ).
thf(7845,plain,
! [SV1688: $i,SV1440: $i,SV1123: $i] :
( ( ! [SY3246: $i] :
( ~ ( c_in @ SV1123 @ ( c_minus @ SV1440 @ SV1688 @ ( tc_set @ SY3246 ) ) @ SY3246 )
| ( c_in @ SV1123 @ SV1440 @ SY3246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6647]) ).
thf(7846,plain,
! [SV1689: $i,SV1441: $i,SV1124: $i] :
( ( ! [SY3247: $i] :
( ~ ( c_in @ SV1124 @ SV1441 @ SV1689 )
| ( c_in @ SV1124 @ SY3247 @ SV1689 )
| ( c_in @ SV1124 @ ( c_minus @ SV1441 @ SY3247 @ ( tc_set @ SV1689 ) ) @ SV1689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6648]) ).
thf(7847,plain,
! [SV1690: $i,SV1442: $i,SV1125: $i] :
( ( ! [SY3248: $i] :
( ~ ( c_in @ SV1125 @ ( c_inter @ SV1442 @ SV1690 @ SY3248 ) @ SY3248 )
| ( c_in @ SV1125 @ SV1690 @ SY3248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6649]) ).
thf(7848,plain,
! [SV1691: $i,SV1443: $i,SV1126: $i] :
( ( ! [SY3249: $i] :
( ~ ( c_in @ SV1126 @ ( c_inter @ SV1443 @ SV1691 @ SY3249 ) @ SY3249 )
| ( c_in @ SV1126 @ SV1443 @ SY3249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6650]) ).
thf(7849,plain,
! [SV1692: $i,SV1444: $i,SV1127: $i] :
( ( ! [SY3250: $i] :
( ~ ( c_in @ SV1127 @ SV1444 @ SV1692 )
| ~ ( c_in @ SV1127 @ SY3250 @ SV1692 )
| ( c_in @ SV1127 @ ( c_inter @ SY3250 @ SV1444 @ SV1692 ) @ SV1692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6651]) ).
thf(7850,plain,
! [SV1693: $i,SV1445: $i,SV1128: $i] :
( ( ! [SY3251: $i] :
( ~ ( c_in @ SV1128 @ SV1445 @ ( tc_set @ SV1693 ) )
| ~ ( c_in @ SY3251 @ ( c_Inter @ SV1445 @ SV1693 ) @ SV1693 )
| ( c_in @ SY3251 @ SV1128 @ SV1693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6652]) ).
thf(7851,plain,
! [SV1694: $i,SV1446: $i,SV1129: $i] :
( ( ~ ( c_in @ SV1129 @ ( c_Pow @ SV1446 @ SV1694 ) @ ( tc_set @ SV1694 ) )
| ( c_lessequals @ SV1129 @ SV1446 @ ( tc_set @ SV1694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6653]) ).
thf(7852,plain,
! [SV1695: $i,SV1447: $i,SV1130: $i] :
( ( ~ ( c_lessequals @ SV1130 @ SV1447 @ ( tc_set @ SV1695 ) )
| ( c_in @ SV1130 @ ( c_Pow @ SV1447 @ SV1695 ) @ ( tc_set @ SV1695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6654]) ).
thf(7853,plain,
! [SV1696: $i,SV1448: $i,SV1131: $i] :
( ( ! [SY3252: $i] :
( ~ ( c_in @ SV1131 @ SV1448 @ SV1696 )
| ( c_in @ SV1131 @ ( c_union @ SY3252 @ SV1448 @ SV1696 ) @ SV1696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6655]) ).
thf(7854,plain,
! [SV1697: $i,SV1449: $i,SV1132: $i] :
( ( ! [SY3253: $i] :
( ~ ( c_in @ SV1132 @ SV1449 @ SV1697 )
| ( c_in @ SV1132 @ ( c_union @ SV1449 @ SY3253 @ SV1697 ) @ SV1697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6656]) ).
thf(7855,plain,
! [SV1698: $i,SV1450: $i,SV1133: $i] :
( ( ! [SY3254: $i] :
( ~ ( c_in @ SV1133 @ ( c_union @ SV1450 @ SV1698 @ SY3254 ) @ SY3254 )
| ( c_in @ SV1133 @ SV1698 @ SY3254 )
| ( c_in @ SV1133 @ SV1450 @ SY3254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6657]) ).
thf(7856,plain,
! [SV1699: $i,SV1451: $i,SV1135: $i] :
( ( ! [SY3255: $i] :
( ~ ( c_in @ SV1135 @ SV1451 @ SV1699 )
| ~ ( c_in @ SV1451 @ SY3255 @ ( tc_set @ SV1699 ) )
| ( c_in @ SV1135 @ ( c_Union @ SY3255 @ SV1699 ) @ SV1699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6658]) ).
thf(7857,plain,
! [SV1452: $i,SV1136: $i] :
( ( c_in @ SV1136 @ c_emptyset @ SV1452 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6659]) ).
thf(7858,plain,
! [SV1700: $i,SV1453: $i,SV1137: $i] :
( ( ! [SY3256: $i] :
( ~ ( c_in @ SV1137 @ SV1453 @ SV1700 )
| ( c_in @ SV1137 @ ( c_insert @ SY3256 @ SV1453 @ SV1700 ) @ SV1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6660]) ).
thf(7859,plain,
! [SV1701: $i,SV1454: $i,SV1138: $i] :
( ( c_in @ SV1138 @ ( c_insert @ SV1138 @ SV1454 @ SV1701 ) @ SV1701 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6661]) ).
thf(7860,plain,
! [SV1702: $i,SV1455: $i,SV1139: $i] :
( ( ! [SY3257: $i] :
( ~ ( c_in @ SV1139 @ ( c_insert @ SV1455 @ SV1702 @ SY3257 ) @ SY3257 )
| ( c_in @ SV1139 @ SV1702 @ SY3257 )
| ( SV1139 = SV1455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6662]) ).
thf(7861,plain,
! [SV1456: $i,SV1140: $i] :
( ( c_less @ SV1140 @ c_emptyset @ ( tc_set @ SV1456 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6663]) ).
thf(7862,plain,
! [SV1703: $i,SV1457: $i,SV1141: $i] :
( ( ~ ( c_lessequals @ SV1141 @ ( c_insert @ SV1457 @ c_emptyset @ SV1703 ) @ ( tc_set @ SV1703 ) )
| ( ( c_insert @ SV1457 @ SV1141 @ SV1703 )
= ( c_insert @ SV1457 @ c_emptyset @ SV1703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6664]) ).
thf(7863,plain,
! [SV1704: $i,SV1458: $i,SV1142: $i] :
( ( ~ ( c_lessequals @ SV1142 @ ( c_insert @ SV1458 @ c_emptyset @ SV1704 ) @ ( tc_set @ SV1704 ) )
| ( ( c_insert @ SV1458 @ c_emptyset @ SV1704 )
= ( c_insert @ SV1458 @ SV1142 @ SV1704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6665]) ).
thf(7864,plain,
! [SV1459: $i,SV1143: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1143 @ SV1459 @ SV1459 ) @ SV1459 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Oacyclic @ SV1143 @ SV1459 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6666]) ).
thf(7865,plain,
! [SV1460: $i,SV1144: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1144 @ SV1460 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1144 @ SV1460 @ SV1460 ) @ SV1460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6667]) ).
thf(7866,plain,
! [SV1705: $i,SV1461: $i,SV1145: $i] :
( ( ! [SY3258: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1145 @ SV1461 @ SV1705 @ SV1705 ) @ SY3258 @ ( tc_prod @ SV1705 @ SV1705 ) ) @ SV1705 )
| ( c_Wellfounded__Recursion_Oacyclic @ SY3258 @ SV1705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6668]) ).
thf(7867,plain,
! [SV1706: $i,SV1462: $i,SV1146: $i] :
( ( ! [SY3259: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1146 @ SV1462 @ SV1706 @ SV1706 ) @ SY3259 @ ( tc_prod @ SV1706 @ SV1706 ) ) @ SV1706 )
| ~ ( c_in @ ( c_Pair @ SV1462 @ SV1146 @ SV1706 @ SV1706 ) @ ( c_Transitive__Closure_Ortrancl @ SY3259 @ SV1706 ) @ ( tc_prod @ SV1706 @ SV1706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6669]) ).
thf(7868,plain,
! [SV1707: $i,SV1463: $i,SV1147: $i] :
( ( ! [SY3260: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1147 @ SV1463 )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1707 @ SY3260 @ SV1463 @ SV1463 ) @ SV1147 @ ( tc_prod @ SV1463 @ SV1463 ) ) @ SV1463 )
| ( c_in @ ( c_Pair @ SY3260 @ SV1707 @ SV1463 @ SV1463 ) @ ( c_Transitive__Closure_Ortrancl @ SV1147 @ SV1463 ) @ ( tc_prod @ SV1463 @ SV1463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6670]) ).
thf(7869,plain,
! [SV1708: $i,SV1464: $i,SV1148: $i] :
( ( ! [SY3261: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1148 @ SV1464 @ SV1708 @ SV1708 ) @ SY3261 @ ( tc_prod @ SV1708 @ SV1708 ) ) @ SV1708 )
| ( c_Wellfounded__Recursion_Owf @ SY3261 @ SV1708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6671]) ).
thf(7870,plain,
! [SV1709: $i,SV1465: $i,SV1149: $i] :
( ( ! [SY3262: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1149 @ SV1465 @ SV1709 @ SV1709 ) @ SY3262 @ ( tc_prod @ SV1709 @ SV1709 ) ) @ SV1709 )
| ~ ( c_in @ ( c_Pair @ SV1465 @ SV1149 @ SV1709 @ SV1709 ) @ ( c_Transitive__Closure_Ortrancl @ SY3262 @ SV1709 ) @ ( tc_prod @ SV1709 @ SV1709 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6672]) ).
thf(7871,plain,
! [SV1710: $i,SV1466: $i,SV1150: $i] :
( ( ! [SY3263: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ SV1150 @ SV1466 )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1710 @ SY3263 @ SV1466 @ SV1466 ) @ SV1150 @ ( tc_prod @ SV1466 @ SV1466 ) ) @ SV1466 )
| ( c_in @ ( c_Pair @ SY3263 @ SV1710 @ SV1466 @ SV1466 ) @ ( c_Transitive__Closure_Ortrancl @ SV1150 @ SV1466 ) @ ( tc_prod @ SV1466 @ SV1466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6673]) ).
thf(7872,plain,
! [SV1467: $i,SV1151: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1151 @ SV1467 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) )
= $true )
| ( ( c_less @ SV1151 @ SV1467 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6674]) ).
thf(7873,plain,
! [SV1468: $i,SV1152: $i] :
( ( ( ~ ( c_less @ SV1152 @ SV1468 @ tc_nat ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1152 @ SV1468 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6675]) ).
thf(7874,plain,
! [SV1711: $i,SV1469: $i,SV1153: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1153 @ SV1469 ) @ ( c_Message_Oanalz @ SV1711 ) @ tc_Message_Omsg )
| ( c_in @ SV1469 @ ( c_Message_Oanalz @ SV1711 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6676]) ).
thf(7875,plain,
! [SV1712: $i,SV1470: $i,SV1154: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1154 @ SV1470 ) @ ( c_Message_Oanalz @ SV1712 ) @ tc_Message_Omsg )
| ( c_in @ SV1154 @ ( c_Message_Oanalz @ SV1712 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6677]) ).
thf(7876,plain,
! [SV1713: $i,SV1471: $i,SV1155: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1155 @ SV1471 ) @ ( c_Message_Oparts @ SV1713 ) @ tc_Message_Omsg )
| ( c_in @ SV1471 @ ( c_Message_Oparts @ SV1713 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6678]) ).
thf(7877,plain,
! [SV1714: $i,SV1472: $i,SV1156: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1156 @ SV1472 ) @ ( c_Message_Oparts @ SV1714 ) @ tc_Message_Omsg )
| ( c_in @ SV1156 @ ( c_Message_Oparts @ SV1714 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6679]) ).
thf(7878,plain,
! [SV1715: $i,SV1473: $i,SV1157: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1157 @ SV1473 ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1157 ) ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
| ( c_in @ SV1473 @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6680]) ).
thf(7879,plain,
! [SV1474: $i,SV1158: $i] :
( ( ( ~ ( c_in @ SV1158 @ SV1474 @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1158 @ ( c_Message_Oanalz @ SV1474 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6681]) ).
thf(7880,plain,
! [SV1475: $i,SV1159: $i] :
( ( ( ~ ( c_in @ SV1159 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SV1475 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1159 @ ( c_Message_Oanalz @ SV1475 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6682]) ).
thf(7881,plain,
! [SV1476: $i,SV1160: $i] :
( ( ( ~ ( c_lessequals @ SV1160 @ SV1476 @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( c_lessequals @ ( c_Message_Oanalz @ SV1160 ) @ ( c_Message_Oanalz @ SV1476 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6683]) ).
thf(7882,plain,
! [SV1716: $i,SV1477: $i,SV1161: $i] :
( ( ~ ( c_in @ SV1161 @ ( c_Message_Oparts @ ( c_union @ SV1477 @ SV1716 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1716 ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1477 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6684]) ).
thf(7883,plain,
! [SV1717: $i,SV1478: $i,SV1162: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1162 @ SV1478 ) @ ( c_Message_Oparts @ SV1717 ) @ tc_Message_Omsg )
| ( c_in @ SV1478 @ ( c_Message_Oparts @ SV1717 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6685]) ).
thf(7884,plain,
! [SV1479: $i,SV1163: $i] :
( ( ( ~ ( c_in @ SV1163 @ SV1479 @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1163 @ ( c_Message_Oparts @ SV1479 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6686]) ).
thf(7885,plain,
! [SV1480: $i,SV1165: $i] :
( ( ( ~ ( c_in @ SV1165 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SV1480 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1165 @ ( c_Message_Oparts @ SV1480 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6688]) ).
thf(7886,plain,
! [SV1718: $i,SV1481: $i,SV1166: $i] :
( ( c_lessequals @ SV1166 @ ( c_union @ SV1166 @ SV1481 @ SV1718 ) @ ( tc_set @ SV1718 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6689]) ).
thf(7887,plain,
! [SV1719: $i,SV1482: $i,SV1167: $i] :
( ( c_lessequals @ SV1167 @ ( c_union @ SV1482 @ SV1167 @ SV1719 ) @ ( tc_set @ SV1719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6690]) ).
thf(7888,plain,
! [SV1720: $i,SV1483: $i,SV1168: $i] :
( ( ! [SY3264: $i] :
( ~ ( c_lessequals @ SV1168 @ SV1483 @ ( tc_set @ SV1720 ) )
| ~ ( c_lessequals @ SY3264 @ SV1168 @ ( tc_set @ SV1720 ) )
| ( c_lessequals @ SY3264 @ SV1483 @ ( tc_set @ SV1720 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6691]) ).
thf(7889,plain,
! [SV1721: $i,SV1484: $i,SV1169: $i] :
( ( ! [SY3265: $i] :
( ( c_Datatype__Universe_OIn0 @ SV1169 @ SV1484 @ SV1721 )
!= ( c_Datatype__Universe_OIn1 @ SY3265 @ SV1484 @ SV1721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6692]) ).
thf(7890,plain,
! [SV1722: $i,SV1485: $i,SV1170: $i] :
( ( ! [SY3266: $i] :
( ( ( c_Message_Omsg_OCrypt @ SV1170 @ SV1485 )
!= ( c_Message_Omsg_OCrypt @ SV1722 @ SY3266 ) )
| ( SV1170 = SV1722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6693]) ).
thf(7891,plain,
! [SV1486: $i,SV1171: $i] :
( ( ( ( c_List_Orev @ SV1171 @ SV1486 )
!= c_List_Olist_ONil )
= $true )
| ( ( SV1171 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6694]) ).
thf(7892,plain,
! [SV1723: $i,SV1487: $i,SV1172: $i] :
( ( ! [SY3267: $i,SY3268: $i] :
( ( ( c_append @ SV1172 @ ( c_List_Olist_OCons @ SV1487 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 )
!= ( c_append @ SY3267 @ ( c_List_Olist_OCons @ SY3268 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 ) )
| ( SV1487 = SY3268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6695]) ).
thf(7893,plain,
! [SV1724: $i,SV1488: $i,SV1173: $i] :
( ( ! [SY3269: $i,SY3270: $i] :
( ( c_Datatype__Universe_OScons @ SV1173 @ SV1488 @ SV1724 @ SY3269 )
!= ( c_Datatype__Universe_ONumb @ SY3270 @ SV1724 @ SY3269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6696]) ).
thf(7894,plain,
! [SV1489: $i,SV1174: $i] :
( ( ( ( c_List_Oset @ SV1174 @ SV1489 )
!= c_emptyset )
= $true )
| ( ( SV1174 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6697]) ).
thf(7895,plain,
! [SV1490: $i,SV1175: $i] :
( ( c_Datatype_Ooption_ONone
= ( c_Datatype_Ooption_OSome @ SV1175 @ SV1490 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6698]) ).
thf(7896,plain,
! [SV1725: $i,SV1491: $i,SV1176: $i] :
( ( ! [SY3271: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SV1176 @ SV1491 @ SV1725 )
!= ( c_Datatype__Universe_OLeaf @ SY3271 @ SV1491 @ SV1725 ) )
| ( SV1176 = SY3271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6699]) ).
thf(7897,plain,
! [SV1726: $i,SV1492: $i,SV1177: $i] :
( ( ! [SY3272: $i] :
( ( c_Datatype__Universe_OIn1 @ SV1177 @ SV1492 @ SV1726 )
!= ( c_Datatype__Universe_OIn0 @ SY3272 @ SV1492 @ SV1726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6700]) ).
thf(7898,plain,
! [SV1493: $i,SV1178: $i] :
( ( ( ( c_List_Oremdups @ SV1178 @ SV1493 )
!= SV1178 )
= $true )
| ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1178 @ SV1493 ) @ ( tc_List_Olist @ SV1493 ) )
= ( c_Nat_Osize @ SV1178 @ ( tc_List_Olist @ SV1493 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6701]) ).
thf(7899,plain,
! [SV1727: $i,SV1494: $i,SV1180: $i] :
( ( ! [SY3273: $i] :
( ( ( c_Datatype__Universe_ONumb @ SV1180 @ SV1494 @ SV1727 )
!= ( c_Datatype__Universe_ONumb @ SY3273 @ SV1494 @ SV1727 ) )
| ( SV1180 = SY3273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6703]) ).
thf(7900,plain,
! [SV1728: $i,SV1495: $i,SV1182: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ SV1182 @ SV1495 @ SV1728 )
!= c_emptyset )
| ( SV1182 = c_emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6705]) ).
thf(7901,plain,
! [SV1496: $i,SV1183: $i] :
( ( ( ( c_Nat_Osize @ SV1183 @ ( tc_List_Olist @ SV1496 ) )
!= c_0 )
= $true )
| ( ( SV1183 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6706]) ).
thf(7902,plain,
! [SV1729: $i,SV1497: $i,SV1184: $i] :
( ( ! [SY3274: $i] :
( ( ( c_Message_Omsg_OMPair @ SV1184 @ SV1497 )
!= ( c_Message_Omsg_OMPair @ SV1729 @ SY3274 ) )
| ( SV1184 = SV1729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6707]) ).
thf(7903,plain,
! [SV1730: $i,SV1498: $i,SV1185: $i] :
( ( ! [SY3275: $i,SY3276: $i] :
( ( ( c_List_Olist_OCons @ SV1185 @ SV1498 @ SV1730 )
!= ( c_List_Olist_OCons @ SY3275 @ SY3276 @ SV1730 ) )
| ( SV1498 = SY3276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6708]) ).
thf(7904,plain,
! [SV1731: $i,SV1499: $i,SV1186: $i] :
( ( ! [SY3277: $i] :
( ( c_Sum__Type_OInr @ SV1186 @ SV1499 @ SV1731 )
!= ( c_Sum__Type_OInl @ SY3277 @ SV1731 @ SV1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6709]) ).
thf(7905,plain,
! [SV1500: $i,SV1187: $i] :
( ( ( ( c_Message_Omsg_OHash @ SV1187 )
!= ( c_Message_Omsg_OHash @ SV1500 ) )
= $true )
| ( ( SV1187 = SV1500 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6710]) ).
thf(7906,plain,
! [SV1732: $i,SV1501: $i,SV1188: $i] :
( ( ! [SY3278: $i,SY3279: $i] :
( ( ( c_append @ SV1188 @ ( c_List_Olist_OCons @ SV1501 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 )
!= ( c_append @ SY3278 @ ( c_List_Olist_OCons @ SY3279 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 ) )
| ( SV1188 = SY3278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6711]) ).
thf(7907,plain,
! [SV1733: $i,SV1502: $i,SV1189: $i] :
( ( ! [SY3280: $i] :
( ( ( c_Datatype__Universe_OAtom @ SV1189 @ SV1502 @ SV1733 )
!= ( c_Datatype__Universe_OAtom @ SY3280 @ SV1502 @ SV1733 ) )
| ( SV1189 = SY3280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6712]) ).
thf(7908,plain,
! [SV1734: $i,SV1503: $i,SV1191: $i] :
( ( ( ( c_append @ SV1191 @ SV1503 @ SV1734 )
!= c_List_Olist_ONil )
| ( SV1503 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6714]) ).
thf(7909,plain,
! [SV1735: $i,SV1504: $i,SV1192: $i] :
( ( ! [SY3281: $i] :
( ( ( c_Datatype__Universe_OIn1 @ SV1192 @ SV1504 @ SV1735 )
!= ( c_Datatype__Universe_OIn1 @ SY3281 @ SV1504 @ SV1735 ) )
| ( SV1192 = SY3281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6715]) ).
thf(7910,plain,
! [SV1736: $i,SV1505: $i,SV1193: $i] :
( ( ( ( c_union @ SV1193 @ SV1505 @ SV1736 )
!= c_emptyset )
| ( SV1505 = c_emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6716]) ).
thf(7911,plain,
! [SV1737: $i,SV1506: $i,SV1194: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1194 )
| ( ( c_SetInterval_OlessThan @ SV1506 @ SV1194 )
!= ( c_SetInterval_OlessThan @ SV1737 @ SV1194 ) )
| ( SV1506 = SV1737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6717]) ).
thf(7912,plain,
! [SV1738: $i,SV1507: $i,SV1195: $i] :
( ( ! [SY3282: $i,SY3283: $i,SY3284: $i] :
( ( ( c_Pair @ SV1195 @ SV1507 @ SV1738 @ SY3282 )
!= ( c_Pair @ SY3283 @ SY3284 @ SV1738 @ SY3282 ) )
| ( SV1195 = SY3283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6718]) ).
thf(7913,plain,
! [SV1739: $i,SV1508: $i,SV1196: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SV1196 @ SV1508 @ SV1739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6719]) ).
thf(7914,plain,
! [SV1509: $i,SV1197: $i] :
( ( ( ( c_Message_Omsg_OKey @ SV1197 )
!= ( c_Message_Omsg_OKey @ SV1509 ) )
= $true )
| ( ( SV1197 = SV1509 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6720]) ).
thf(7915,plain,
! [SV1740: $i,SV1510: $i,SV1198: $i] :
( ( ! [SY3285: $i] :
( ( ( c_List_Ochar_OChar @ SV1198 @ SV1510 )
!= ( c_List_Ochar_OChar @ SV1740 @ SY3285 ) )
| ( SV1510 = SY3285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6721]) ).
thf(7916,plain,
! [SV1511: $i,SV1199: $i] :
( ( ( ( c_plus @ SV1199 @ SV1511 @ tc_nat )
!= c_0 )
= $true )
| ( ( SV1511 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6722]) ).
thf(7917,plain,
! [SV1741: $i,SV1512: $i,SV1200: $i] :
( ( ! [SY3286: $i,SY3287: $i] :
( ( c_Datatype__Universe_OLeaf @ SV1200 @ SV1512 @ SV1741 )
!= ( c_Datatype__Universe_OScons @ SY3286 @ SY3287 @ SV1512 @ SV1741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6723]) ).
thf(7918,plain,
! [SV1742: $i,SV1513: $i,SV1201: $i] :
( ( ( c_List_Olist_ONil
!= ( c_append @ SV1201 @ SV1513 @ SV1742 ) )
| ( SV1513 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6724]) ).
thf(7919,plain,
! [SV1743: $i,SV1514: $i,SV1202: $i] :
( ( ! [SY3288: $i] :
( ( ( c_append @ SV1202 @ SV1514 @ SV1743 )
!= ( c_append @ SV1202 @ SY3288 @ SV1743 ) )
| ( SV1514 = SY3288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6725]) ).
thf(7920,plain,
! [SV1744: $i,SV1515: $i,SV1203: $i] :
( ( ( ( c_union @ SV1203 @ SV1515 @ SV1744 )
!= c_emptyset )
| ( SV1203 = c_emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6726]) ).
thf(7921,plain,
! [SV1745: $i,SV1516: $i,SV1205: $i] :
( ( ! [SY3289: $i] :
( ( ( c_Datatype__Universe_OIn0 @ SV1205 @ SV1516 @ SV1745 )
!= ( c_Datatype__Universe_OIn0 @ SY3289 @ SV1516 @ SV1745 ) )
| ( SV1205 = SY3289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6728]) ).
thf(7922,plain,
! [SV1746: $i,SV1517: $i,SV1206: $i] :
( ( ! [SY3290: $i,SY3291: $i,SY3292: $i] :
( ( ( c_Pair @ SV1206 @ SV1517 @ SV1746 @ SY3290 )
!= ( c_Pair @ SY3291 @ SY3292 @ SV1746 @ SY3290 ) )
| ( SV1517 = SY3292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6729]) ).
thf(7923,plain,
! [SV1747: $i,SV1518: $i,SV1207: $i] :
( ( ! [SY3293: $i,SY3294: $i] :
( ( c_Datatype__Universe_OAtom @ SV1207 @ SV1518 @ SV1747 )
!= ( c_Datatype__Universe_OScons @ SY3293 @ SY3294 @ SV1518 @ SV1747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6730]) ).
thf(7924,plain,
! [SV1748: $i,SV1519: $i,SV1209: $i] :
( ( ! [SY3295: $i] :
( ( ( c_List_Orev @ SV1209 @ SV1519 )
!= ( c_List_Olist_OCons @ SV1748 @ SY3295 @ SV1519 ) )
| ( SV1209
= ( c_append @ ( c_List_Orev @ SY3295 @ SV1519 ) @ ( c_List_Olist_OCons @ SV1748 @ c_List_Olist_ONil @ SV1519 ) @ SV1519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6732]) ).
thf(7925,plain,
! [SV1749: $i,SV1520: $i,SV1210: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1210 )
| ( ( c_SetInterval_OatLeast @ SV1520 @ SV1210 )
!= ( c_SetInterval_OatLeast @ SV1749 @ SV1210 ) )
| ( SV1520 = SV1749 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6733]) ).
thf(7926,plain,
! [SV1750: $i,SV1521: $i,SV1211: $i] :
( ( ( ( c_uminus @ SV1211 @ ( tc_set @ SV1521 ) )
!= ( c_uminus @ SV1750 @ ( tc_set @ SV1521 ) ) )
| ( SV1211 = SV1750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6734]) ).
thf(7927,plain,
! [SV1751: $i,SV1522: $i,SV1212: $i] :
( ( ! [SY3296: $i,SY3297: $i] :
( ( c_Datatype__Universe_ONumb @ SV1212 @ SV1522 @ SV1751 )
!= ( c_Datatype__Universe_OScons @ SY3296 @ SY3297 @ SV1522 @ SV1751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6735]) ).
thf(7928,plain,
! [SV1752: $i,SV1523: $i,SV1213: $i] :
( ( ! [SY3298: $i] :
( ( ( c_insert @ SV1213 @ c_emptyset @ SV1523 )
!= ( c_insert @ SV1752 @ SY3298 @ SV1523 ) )
| ( SV1752 = SV1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6736]) ).
thf(7929,plain,
! [SV1753: $i,SV1524: $i,SV1214: $i] :
( ( ( SV1214
!= ( c_append @ SV1524 @ SV1214 @ SV1753 ) )
| ( SV1524 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6737]) ).
thf(7930,plain,
! [SV1525: $i,SV1215: $i] :
( ( ( ( c_Message_Oagent_OFriend @ SV1215 )
!= ( c_Message_Oagent_OFriend @ SV1525 ) )
= $true )
| ( ( SV1215 = SV1525 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6738]) ).
thf(7931,plain,
! [SV1754: $i,SV1526: $i,SV1217: $i] :
( ( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ SV1217 @ SV1526 @ SV1754 ) )
| ( SV1217 = c_emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6740]) ).
thf(7932,plain,
! [SV1755: $i,SV1527: $i,SV1218: $i] :
( ( ( c_List_Olist_ONil
!= ( c_append @ SV1218 @ SV1527 @ SV1755 ) )
| ( SV1218 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6741]) ).
thf(7933,plain,
! [SV1528: $i,SV1219: $i] :
( ( ( c_Datatype_Ooption_OSome @ SV1219 @ SV1528 )
= c_Datatype_Ooption_ONone )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6742]) ).
thf(7934,plain,
! [SV1756: $i,SV1529: $i,SV1220: $i] :
( ( ( ( c_append @ SV1220 @ SV1529 @ SV1756 )
!= SV1220 )
| ( SV1529 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6743]) ).
thf(7935,plain,
! [SV1757: $i,SV1530: $i,SV1221: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1221 )
| ( ( c_SetInterval_OgreaterThan @ SV1530 @ SV1221 )
!= ( c_SetInterval_OgreaterThan @ SV1757 @ SV1221 ) )
| ( SV1530 = SV1757 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6744]) ).
thf(7936,plain,
! [SV1758: $i,SV1531: $i,SV1222: $i] :
( ( ! [SY3299: $i] :
( ( ( c_Message_Omsg_OCrypt @ SV1222 @ SV1531 )
!= ( c_Message_Omsg_OCrypt @ SV1758 @ SY3299 ) )
| ( SV1531 = SY3299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6745]) ).
thf(7937,plain,
! [SV1532: $i,SV1223: $i] :
( ( ( ( c_Message_Omsg_OAgent @ SV1223 )
!= ( c_Message_Omsg_OAgent @ SV1532 ) )
= $true )
| ( ( SV1223 = SV1532 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6746]) ).
thf(7938,plain,
! [SV1759: $i,SV1533: $i,SV1224: $i] :
( ( ( ( c_Datatype_Ooption_OSome @ SV1224 @ SV1533 )
!= ( c_Datatype_Ooption_OSome @ SV1759 @ SV1533 ) )
| ( SV1224 = SV1759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6747]) ).
thf(7939,plain,
! [SV1534: $i,SV1225: $i] :
( ( ( ( c_Message_Omsg_ONonce @ SV1225 )
!= ( c_Message_Omsg_ONonce @ SV1534 ) )
= $true )
| ( ( SV1225 = SV1534 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6748]) ).
thf(7940,plain,
! [SV1760: $i,SV1535: $i,SV1226: $i] :
( ( ( ( c_append @ SV1226 @ SV1535 @ SV1760 )
!= SV1535 )
| ( SV1226 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6749]) ).
thf(7941,plain,
! [SV1761: $i,SV1536: $i,SV1227: $i] :
( ( ( SV1227
!= ( c_append @ SV1227 @ SV1536 @ SV1761 ) )
| ( SV1536 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6750]) ).
thf(7942,plain,
! [SV1537: $i,SV1228: $i] :
( ( ( ( c_Message_Omsg_ONumber @ SV1228 )
!= ( c_Message_Omsg_ONumber @ SV1537 ) )
= $true )
| ( ( SV1228 = SV1537 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6751]) ).
thf(7943,plain,
! [SV1538: $i,SV1229: $i] :
( ( ( c_emptyset
!= ( c_List_Oset @ SV1229 @ SV1538 ) )
= $true )
| ( ( SV1229 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6752]) ).
thf(7944,plain,
! [SV1762: $i,SV1539: $i,SV1230: $i] :
( ( ( ( c_insert @ SV1230 @ c_emptyset @ SV1539 )
!= ( c_insert @ SV1762 @ c_emptyset @ SV1539 ) )
| ( SV1230 = SV1762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6753]) ).
thf(7945,plain,
! [SV1540: $i,SV1231: $i] :
( ( ( ( c_Divides_Oop_Amod @ SV1231 @ SV1540 @ tc_nat )
!= c_0 )
= $true )
| ( ( SV1231
= ( c_times @ SV1540 @ ( c_Main_Omod__eq__0D__dest__1 @ SV1540 @ SV1231 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6754]) ).
thf(7946,plain,
! [SV1763: $i,SV1541: $i,SV1232: $i] :
( ( ! [SY3300: $i] :
( ( c_Sum__Type_OInl @ SV1232 @ SV1541 @ SV1763 )
!= ( c_Sum__Type_OInr @ SY3300 @ SV1763 @ SV1541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6755]) ).
thf(7947,plain,
! [SV1542: $i,SV1233: $i] :
( ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1233 @ SV1542 ) @ ( tc_List_Olist @ SV1542 ) )
!= ( c_Nat_Osize @ SV1233 @ ( tc_List_Olist @ SV1542 ) ) )
= $true )
| ( ( ( c_List_Oremdups @ SV1233 @ SV1542 )
= SV1233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6756]) ).
thf(7948,plain,
! [SV1764: $i,SV1543: $i,SV1234: $i] :
( ( ! [SY3301: $i,SY3302: $i] :
( ( c_Datatype__Universe_OScons @ SV1234 @ SV1543 @ SV1764 @ SY3301 )
!= ( c_Datatype__Universe_OLeaf @ SY3302 @ SV1764 @ SY3301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6757]) ).
thf(7949,plain,
! [SV1765: $i,SV1544: $i,SV1235: $i] :
( ( ! [SY3303: $i,SY3304: $i] :
( ( ( c_List_Olist_OCons @ SV1235 @ SV1544 @ SV1765 )
!= ( c_List_Olist_OCons @ SY3303 @ SY3304 @ SV1765 ) )
| ( SV1235 = SY3303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6758]) ).
thf(7950,plain,
! [SV1545: $i,SV1236: $i] :
( ( ( ( c_Suc @ SV1236 )
!= ( c_Suc @ SV1545 ) )
= $true )
| ( ( SV1236 = SV1545 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6759]) ).
thf(7951,plain,
! [SV1766: $i,SV1546: $i,SV1237: $i] :
( ( ! [SY3305: $i] :
( ( c_Datatype__Universe_ONumb @ SV1237 @ SV1546 @ SV1766 )
!= ( c_Datatype__Universe_OLeaf @ SY3305 @ SV1546 @ SV1766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6760]) ).
thf(7952,plain,
! [SV1767: $i,SV1547: $i,SV1238: $i] :
( ( ( c_List_Olist_OCons @ SV1238 @ SV1547 @ SV1767 )
!= c_List_Olist_ONil )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6761]) ).
thf(7953,plain,
! [SV1548: $i,SV1239: $i] :
( ( ( ( c_plus @ SV1239 @ SV1548 @ tc_nat )
!= c_0 )
= $true )
| ( ( SV1239 = c_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6762]) ).
thf(7954,plain,
! [SV1768: $i,SV1549: $i,SV1240: $i] :
( ( ! [SY3306: $i] :
( ( ( c_Sum__Type_OInl @ SV1240 @ SV1549 @ SV1768 )
!= ( c_Sum__Type_OInl @ SY3306 @ SV1549 @ SV1768 ) )
| ( SV1240 = SY3306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6763]) ).
thf(7955,plain,
! [SV1769: $i,SV1550: $i,SV1241: $i] :
( ( ! [SY3307: $i,SY3308: $i,SY3309: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1241 @ SV1550 @ SV1769 @ SY3307 )
!= ( c_Datatype__Universe_OScons @ SY3308 @ SY3309 @ SV1769 @ SY3307 ) )
| ( SV1241 = SY3308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6764]) ).
thf(7956,plain,
! [SV1770: $i,SV1551: $i,SV1242: $i] :
( ( ! [SY3310: $i] :
( ( ( c_append @ SV1242 @ SV1551 @ SV1770 )
!= ( c_append @ SY3310 @ SV1551 @ SV1770 ) )
| ( SV1242 = SY3310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6765]) ).
thf(7957,plain,
! [SV1552: $i,SV1243: $i] :
( ( ( c_List_Olist_ONil
!= ( c_List_Orev @ SV1243 @ SV1552 ) )
= $true )
| ( ( SV1243 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6766]) ).
thf(7958,plain,
! [SV1771: $i,SV1553: $i,SV1244: $i] :
( ( ! [SY3311: $i,SY3312: $i] :
( ( c_Datatype__Universe_OScons @ SV1244 @ SV1553 @ SV1771 @ SY3311 )
!= ( c_Datatype__Universe_OAtom @ SY3312 @ SV1771 @ SY3311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6767]) ).
thf(7959,plain,
! [SV1772: $i,SV1554: $i,SV1245: $i] :
( ( ! [SY3313: $i] :
( ( c_Datatype__Universe_OLeaf @ SV1245 @ SV1554 @ SV1772 )
!= ( c_Datatype__Universe_ONumb @ SY3313 @ SV1554 @ SV1772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6768]) ).
thf(7960,plain,
! [SV1773: $i,SV1555: $i,SV1246: $i] :
( ( ! [SY3314: $i] :
( ( ( c_List_Ochar_OChar @ SV1246 @ SV1555 )
!= ( c_List_Ochar_OChar @ SV1773 @ SY3314 ) )
| ( SV1246 = SV1773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6769]) ).
thf(7961,plain,
! [SV1774: $i,SV1556: $i,SV1247: $i] :
( ( ( ( c_append @ SV1247 @ SV1556 @ SV1774 )
!= c_List_Olist_ONil )
| ( SV1247 = c_List_Olist_ONil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6770]) ).
thf(7962,plain,
! [SV1775: $i,SV1557: $i,SV1248: $i] :
( ( ! [SY3315: $i,SY3316: $i,SY3317: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1248 @ SV1557 @ SV1775 @ SY3315 )
!= ( c_Datatype__Universe_OScons @ SY3316 @ SY3317 @ SV1775 @ SY3315 ) )
| ( SV1557 = SY3317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6771]) ).
thf(7963,plain,
! [SV1776: $i,SV1558: $i,SV1249: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV1249 )
| ( ( c_SetInterval_OatMost @ SV1558 @ SV1249 )
!= ( c_SetInterval_OatMost @ SV1776 @ SV1249 ) )
| ( SV1558 = SV1776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6772]) ).
thf(7964,plain,
! [SV1559: $i,SV1250: $i] :
( ( ( ( c_Divides_Oop_Amod @ SV1250 @ SV1559 @ tc_IntDef_Oint )
!= c_0 )
= $true )
| ( ( SV1250
= ( c_times @ SV1559 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SV1559 @ SV1250 ) @ tc_IntDef_Oint ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6773]) ).
thf(7965,plain,
! [SV1777: $i,SV1560: $i,SV1251: $i] :
( ( ( ( c_List_Orev @ SV1251 @ SV1560 )
!= ( c_List_Orev @ SV1777 @ SV1560 ) )
| ( SV1251 = SV1777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6774]) ).
thf(7966,plain,
! [SV1778: $i,SV1561: $i,SV1252: $i] :
( ( ! [SY3318: $i] :
( ( ( c_Message_Omsg_OMPair @ SV1252 @ SV1561 )
!= ( c_Message_Omsg_OMPair @ SV1778 @ SY3318 ) )
| ( SV1561 = SY3318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6775]) ).
thf(7967,plain,
! [SV1779: $i,SV1562: $i,SV1253: $i] :
( ( ! [SY3319: $i] :
( ( ( c_insert @ SV1253 @ c_emptyset @ SV1562 )
!= ( c_insert @ SV1779 @ SY3319 @ SV1562 ) )
| ( c_lessequals @ SY3319 @ ( c_insert @ SV1253 @ c_emptyset @ SV1562 ) @ ( tc_set @ SV1562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6776]) ).
thf(7968,plain,
! [SV1563: $i,SV1254: $i] :
( ( ( ( c_IntDef_Oint @ SV1254 )
!= ( c_IntDef_Oint @ SV1563 ) )
= $true )
| ( ( SV1254 = SV1563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6777]) ).
thf(7969,plain,
! [SV1780: $i,SV1564: $i,SV1255: $i] :
( ( ! [SY3320: $i] :
( ( ( c_Sum__Type_OInr @ SV1255 @ SV1564 @ SV1780 )
!= ( c_Sum__Type_OInr @ SY3320 @ SV1564 @ SV1780 ) )
| ( SV1255 = SY3320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6778]) ).
thf(7970,plain,
! [SV1781: $i,SV1565: $i,SV1256: $i] :
( ( ! [SY3321: $i] :
( ( ( c_insert @ SV1256 @ SV1565 @ SV1781 )
!= ( c_insert @ SY3321 @ c_emptyset @ SV1781 ) )
| ( c_lessequals @ SV1565 @ ( c_insert @ SY3321 @ c_emptyset @ SV1781 ) @ ( tc_set @ SV1781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6779]) ).
thf(7971,plain,
! [SV1782: $i,SV1566: $i,SV1257: $i] :
( ( ! [SY3322: $i] :
( ( ( c_insert @ SV1257 @ SV1566 @ SV1782 )
!= ( c_insert @ SY3322 @ c_emptyset @ SV1782 ) )
| ( SV1257 = SY3322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6780]) ).
thf(7972,plain,
! [SV1783: $i,SV1567: $i,SV1258: $i,SV1: $i] :
( ( ! [SY3323: $i] :
( ~ ( c_in @ SV1 @ ( c_Datatype__Universe_Odprod @ SV1258 @ SV1567 @ SV1783 @ SY3323 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SY3323 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SY3323 ) ) ) )
| ( SV1
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SY3323 ) @ ( c_Main_OdprodE__2 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SY3323 ) @ SV1783 @ SY3323 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SY3323 ) @ ( c_Main_OdprodE__4 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SY3323 ) @ SV1783 @ SY3323 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SY3323 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SY3323 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6782]) ).
thf(7973,plain,
! [SV1784: $i,SV1568: $i,SV1259: $i,SV2: $i] :
( ( ! [SY3324: $i] :
( ~ ( c_in @ SV2 @ ( c_Datatype__Universe_Odprod @ SV1259 @ SV1568 @ SV1784 @ SY3324 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SY3324 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SY3324 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SY3324 ) @ ( c_Main_OdprodE__4 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SY3324 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SY3324 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SY3324 ) ) ) @ SV1568 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SY3324 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SY3324 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6783]) ).
thf(7974,plain,
! [SV1785: $i,SV1569: $i,SV1260: $i,SV3: $i] :
( ( ! [SY3325: $i] :
( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1260 @ SV1569 @ SV1785 @ SY3325 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SY3325 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SY3325 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SY3325 ) @ ( c_Main_OdprodE__3 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SY3325 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SY3325 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SY3325 ) ) ) @ SV1260 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SY3325 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SY3325 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6784]) ).
thf(7975,plain,
! [SV1786: $i,SV1570: $i,SV1261: $i,SV4: $i] :
( ( ! [SY3326: $i,SY3327: $i,SY3328: $i,SY3329: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SY3326 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SY3327 @ SY3328 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SY3329 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY3327 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SY3328 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3329 @ SY3326 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6785]) ).
thf(7976,plain,
! [SV1787: $i,SV1571: $i,SV1262: $i,SV5: $i] :
( ( ! [SY3330: $i] :
( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SV1262 @ SV1571 @ SV1787 @ SY3330 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SY3330 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SY3330 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1262 @ SV5 @ SV1787 @ SY3330 ) @ SV1787 @ SY3330 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1262 @ SV5 @ SV1787 @ SY3330 ) @ SV1787 @ SY3330 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SY3330 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SY3330 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1571 @ SV5 @ SV1787 @ SY3330 ) @ SV1787 @ SY3330 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1571 @ SV5 @ SV1787 @ SY3330 ) @ SV1787 @ SY3330 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SY3330 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SY3330 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6786]) ).
thf(7977,plain,
! [SV1788: $i,SV1572: $i,SV1263: $i,SV6: $i] :
( ( ! [SY3331: $i] :
( ~ ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SV1263 @ SV1572 @ SV1788 @ SY3331 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1572 @ SV6 @ SV1788 @ SY3331 ) @ ( c_Main_OdsumE__4 @ SV1572 @ SV6 @ SV1788 @ SY3331 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) ) @ SV1572 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) ) )
| ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1263 @ SV6 @ SV1788 @ SY3331 ) @ SV1788 @ SY3331 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1263 @ SV6 @ SV1788 @ SY3331 ) @ SV1788 @ SY3331 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SY3331 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6787]) ).
thf(7978,plain,
! [SV1789: $i,SV1573: $i,SV1264: $i,SV7: $i] :
( ( ! [SY3332: $i] :
( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1264 @ SV1573 @ SV1789 @ SY3332 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1264 @ SV7 @ SV1789 @ SY3332 ) @ ( c_Main_OdsumE__2 @ SV1264 @ SV7 @ SV1789 @ SY3332 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) ) @ SV1264 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) ) )
| ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1573 @ SV7 @ SV1789 @ SY3332 ) @ SV1789 @ SY3332 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1573 @ SV7 @ SV1789 @ SY3332 ) @ SV1789 @ SY3332 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SY3332 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6788]) ).
thf(7979,plain,
! [SV1790: $i,SV1574: $i,SV1265: $i,SV8: $i] :
( ( ! [SY3333: $i] :
( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1265 @ SV1574 @ SV1790 @ SY3333 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1265 @ SV8 @ SV1790 @ SY3333 ) @ ( c_Main_OdsumE__2 @ SV1265 @ SV8 @ SV1790 @ SY3333 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) ) @ SV1265 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1574 @ SV8 @ SV1790 @ SY3333 ) @ ( c_Main_OdsumE__4 @ SV1574 @ SV8 @ SV1790 @ SY3333 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) ) @ SV1574 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SY3333 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6789]) ).
thf(7980,plain,
! [SV1791: $i,SV1575: $i,SV1266: $i,SV9: $i] :
( ( ! [SY3334: $i,SY3335: $i] :
( ~ ( c_in @ ( c_Pair @ SV9 @ SV1266 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ SY3334 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SV1575 @ SV1791 ) @ ( c_Datatype__Universe_OIn0 @ SV1266 @ SV1575 @ SV1791 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3334 @ SY3335 @ SV1575 @ SV1791 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6790]) ).
thf(7981,plain,
! [SV1792: $i,SV1576: $i,SV1267: $i,SV10: $i] :
( ( ! [SY3336: $i,SY3337: $i] :
( ~ ( c_in @ ( c_Pair @ SV10 @ SV1267 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ SY3336 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SV1576 @ SV1792 ) @ ( c_Datatype__Universe_OIn1 @ SV1267 @ SV1576 @ SV1792 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3337 @ SY3336 @ SV1576 @ SV1792 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6791]) ).
thf(7982,plain,
! [SV1793: $i,SV1577: $i,SV1268: $i,SV11: $i] :
( ( ! [SY3338: $i] :
( ~ ( c_in @ SV11 @ ( c_Datatype__Universe_Ouprod @ SV1268 @ SV1577 @ SV1793 @ SY3338 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1793 @ SY3338 ) ) )
| ( SV11
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SY3338 ) @ ( c_Main_OuprodE__2 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SY3338 ) @ SV1793 @ SY3338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6792]) ).
thf(7983,plain,
! [SV1794: $i,SV1578: $i,SV1269: $i,SV12: $i] :
( ( ! [SY3339: $i] :
( ~ ( c_in @ SV12 @ ( c_Datatype__Universe_Ouprod @ SV1269 @ SV1578 @ SV1794 @ SY3339 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SY3339 ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ SV1269 @ SV1578 @ SV12 @ SV1794 @ SY3339 ) @ SV1578 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SY3339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6793]) ).
thf(7984,plain,
! [SV1795: $i,SV1579: $i,SV1270: $i,SV13: $i] :
( ( ! [SY3340: $i] :
( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1270 @ SV1579 @ SV1795 @ SY3340 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SY3340 ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ SV1270 @ SV1579 @ SV13 @ SV1795 @ SY3340 ) @ SV1270 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SY3340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6794]) ).
thf(7985,plain,
! [SV1796: $i,SV1580: $i,SV1271: $i,SV14: $i] :
( ( ! [SY3341: $i,SY3342: $i] :
( ~ ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ~ ( c_in @ SY3341 @ SY3342 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SY3341 @ SV14 @ SV1580 @ SV1796 ) @ ( c_Datatype__Universe_Ouprod @ SY3342 @ SV1271 @ SV1580 @ SV1796 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6795]) ).
thf(7986,plain,
! [SV1797: $i,SV1581: $i,SV1272: $i,SV15: $i] :
( ( ! [SY3343: $i] :
( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SV1272 @ SV1581 @ SV1797 @ SY3343 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1797 @ SY3343 ) ) )
| ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1272 @ SV15 @ SV1797 @ SY3343 ) @ SV1797 @ SY3343 ) )
| ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1581 @ SV15 @ SV1797 @ SY3343 ) @ SV1797 @ SY3343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6796]) ).
thf(7987,plain,
! [SV1798: $i,SV1582: $i,SV1273: $i,SV16: $i] :
( ( ! [SY3344: $i] :
( ~ ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SV1273 @ SV1582 @ SV1798 @ SY3344 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SY3344 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1582 @ SV16 @ SV1798 @ SY3344 ) @ SV1582 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SY3344 ) ) )
| ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1273 @ SV16 @ SV1798 @ SY3344 ) @ SV1798 @ SY3344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6797]) ).
thf(7988,plain,
! [SV1799: $i,SV1583: $i,SV1274: $i,SV17: $i] :
( ( ! [SY3345: $i] :
( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1274 @ SV1583 @ SV1799 @ SY3345 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SY3345 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1274 @ SV17 @ SV1799 @ SY3345 ) @ SV1274 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SY3345 ) ) )
| ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1583 @ SV17 @ SV1799 @ SY3345 ) @ SV1799 @ SY3345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6798]) ).
thf(7989,plain,
! [SV1800: $i,SV1584: $i,SV1275: $i,SV18: $i] :
( ( ! [SY3346: $i] :
( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1275 @ SV1584 @ SV1800 @ SY3346 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SY3346 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1275 @ SV18 @ SV1800 @ SY3346 ) @ SV1275 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SY3346 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1584 @ SV18 @ SV1800 @ SY3346 ) @ SV1584 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SY3346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6799]) ).
thf(7990,plain,
! [SV1801: $i,SV1585: $i,SV1276: $i,SV19: $i] :
( ( ! [SY3347: $i] :
( ~ ( c_in @ SV19 @ SV1276 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn0 @ SV19 @ SV1585 @ SV1801 ) @ ( c_Datatype__Universe_Ousum @ SV1276 @ SY3347 @ SV1585 @ SV1801 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6800]) ).
thf(7991,plain,
! [SV1802: $i,SV1586: $i,SV1277: $i,SV20: $i] :
( ( ! [SY3348: $i] :
( ~ ( c_in @ SV20 @ SV1277 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn1 @ SV20 @ SV1586 @ SV1802 ) @ ( c_Datatype__Universe_Ousum @ SY3348 @ SV1277 @ SV1586 @ SV1802 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6801]) ).
thf(7992,plain,
! [SV1587: $i,SV1280: $i,SV26: $i] :
( ( ( ~ ( c_in @ SV26 @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) ) )
= $true )
| ( ( c_in @ ( c_insert @ SV1587 @ SV26 @ SV1280 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6802]) ).
thf(7993,plain,
! [SV1588: $i,SV1281: $i,SV27: $i] :
( ( ( ~ ( c_in @ SV27 @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) ) )
= $true )
| ( ( c_in @ ( c_inter @ SV27 @ SV1588 @ SV1281 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6803]) ).
thf(7994,plain,
! [SV1589: $i,SV1282: $i,SV28: $i] :
( ( ( ~ ( c_in @ SV28 @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) ) )
= $true )
| ( ( c_in @ ( c_inter @ SV1589 @ SV28 @ SV1282 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6804]) ).
thf(7995,plain,
! [SV1283: $i,SV29: $i] :
( ( ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1283 ) ) )
= $false )
| ( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV29 @ SV1283 ) @ SV29 @ ( tc_set @ SV1283 ) )
| ( c_in @ ( c_Union @ SV29 @ SV1283 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6805]) ).
thf(7996,plain,
! [SV1284: $i,SV30: $i] :
( ( ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1284 ) ) )
= $false )
| ( ( ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) )
| ( c_in @ ( c_Union @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6806]) ).
thf(7997,plain,
! [SV1803: $i,SV1590: $i,SV1287: $i,SV33: $i] :
( ( ~ ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
| ~ ( c_in @ SV1590 @ SV33 @ SV1287 )
| ~ ( c_in @ SV1803 @ SV33 @ SV1287 )
| ( SV1590 = SV1803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6807]) ).
thf(7998,plain,
! [SV1804: $i,SV1591: $i,SV1294: $i,SV42: $i] :
( ( ~ ( c_in @ SV42 @ ( c_List_Olists @ SV1294 @ SV1591 ) @ ( tc_List_Olist @ SV1591 ) )
| ~ ( c_in @ SV1804 @ ( c_List_Oset @ SV42 @ SV1591 ) @ SV1591 )
| ( c_in @ SV1804 @ SV1294 @ SV1591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6808]) ).
thf(7999,plain,
! [SV1592: $i,SV1295: $i,SV43: $i] :
( ( ( c_in @ SV43 @ ( c_List_Olists @ SV1295 @ SV1592 ) @ ( tc_List_Olist @ SV1592 ) )
= $true )
| ( ( c_in @ ( c_Main_Oin__listsI__1 @ SV1295 @ SV43 @ SV1592 ) @ ( c_List_Oset @ SV43 @ SV1592 ) @ SV1592 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6809]) ).
thf(8000,plain,
! [SV1593: $i,SV1296: $i,SV44: $i] :
( ( ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ SV44 @ SV1296 @ SV1593 ) @ SV44 @ SV1593 ) )
= $true )
| ( ( c_in @ SV1296 @ ( c_List_Olists @ SV44 @ SV1593 ) @ ( tc_List_Olist @ SV1593 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6810]) ).
thf(8001,plain,
! [SV1805: $i,SV1594: $i,SV1298: $i,SV46: $i] :
( ( ! [SY3349: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV46 @ SV1298 @ SV1594 ) @ SV1805 @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) @ ( c_List_Olistrel @ SY3349 @ SV1594 ) @ ( tc_prod @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) )
| ( SV1805
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SY3349 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ ( c_Main_Olistrel__Cons1__2 @ SY3349 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ SV1594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6811]) ).
thf(8002,plain,
! [SV1806: $i,SV1595: $i,SV1299: $i,SV47: $i] :
( ( ! [SY3350: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV47 @ SV1299 @ SV1595 ) @ SV1806 @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SY3350 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) )
| ( c_in @ ( c_Pair @ SV1299 @ ( c_Main_Olistrel__Cons1__2 @ SY3350 @ SV1806 @ SV47 @ SV1299 @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SY3350 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6812]) ).
thf(8003,plain,
! [SV1807: $i,SV1596: $i,SV1300: $i,SV48: $i] :
( ( ! [SY3351: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV48 @ SV1300 @ SV1596 ) @ SV1807 @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) @ ( c_List_Olistrel @ SY3351 @ SV1596 ) @ ( tc_prod @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) )
| ( c_in @ ( c_Pair @ SV48 @ ( c_Main_Olistrel__Cons1__1 @ SY3351 @ SV1807 @ SV48 @ SV1300 @ SV1596 ) @ SV1596 @ SV1596 ) @ SY3351 @ ( tc_prod @ SV1596 @ SV1596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6813]) ).
thf(8004,plain,
! [SV1808: $i,SV1597: $i,SV1301: $i,SV49: $i] :
( ( ! [SY3352: $i] :
( ~ ( c_in @ ( c_Pair @ SV49 @ ( c_List_Olist_OCons @ SV1301 @ SV1597 @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) @ ( c_List_Olistrel @ SY3352 @ SV1808 ) @ ( tc_prod @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) )
| ( SV49
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SY3352 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ ( c_Main_Olistrel__Cons2__2 @ SY3352 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ SV1808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6814]) ).
thf(8005,plain,
! [SV1809: $i,SV1598: $i,SV1302: $i,SV50: $i] :
( ( ! [SY3353: $i] :
( ~ ( c_in @ ( c_Pair @ SV50 @ ( c_List_Olist_OCons @ SV1302 @ SV1598 @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SY3353 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SY3353 @ SV50 @ SV1302 @ SV1598 @ SV1809 ) @ SV1598 @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SY3353 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6815]) ).
thf(8006,plain,
! [SV1810: $i,SV1599: $i,SV1303: $i,SV51: $i] :
( ( ! [SY3354: $i] :
( ~ ( c_in @ ( c_Pair @ SV51 @ ( c_List_Olist_OCons @ SV1303 @ SV1599 @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) @ ( c_List_Olistrel @ SY3354 @ SV1810 ) @ ( tc_prod @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SY3354 @ SV51 @ SV1303 @ SV1599 @ SV1810 ) @ SV1303 @ SV1810 @ SV1810 ) @ SY3354 @ ( tc_prod @ SV1810 @ SV1810 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6816]) ).
thf(8007,plain,
! [SV1600: $i,SV1304: $i,SV52: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV52 @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) @ ( c_List_Olistrel @ SV1600 @ SV1304 ) @ ( tc_prod @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) ) )
= $true )
| ( ( SV52 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6817]) ).
thf(8008,plain,
! [SV1601: $i,SV1305: $i,SV53: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV53 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) @ ( c_List_Olistrel @ SV1601 @ SV1305 ) @ ( tc_prod @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) ) )
= $true )
| ( ( SV53 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6818]) ).
thf(8009,plain,
! [SV1811: $i,SV1602: $i,SV1306: $i,SV54: $i] :
( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV54 @ SV1306 @ SV1602 ) @ ( c_List_Olists @ SV1811 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) )
| ( c_in @ SV1306 @ ( c_List_Olists @ SV1811 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6819]) ).
thf(8010,plain,
! [SV1812: $i,SV1603: $i,SV1307: $i,SV55: $i] :
( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV55 @ SV1307 @ SV1603 ) @ ( c_List_Olists @ SV1812 @ SV1603 ) @ ( tc_List_Olist @ SV1603 ) )
| ( c_in @ SV55 @ SV1812 @ SV1603 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6820]) ).
thf(8011,plain,
! [SV1813: $i,SV1604: $i,SV1308: $i,SV56: $i] :
( ( ~ ( c_in @ SV56 @ SV1308 @ SV1604 )
| ~ ( c_in @ SV1813 @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) )
| ( c_in @ ( c_List_Olist_OCons @ SV56 @ SV1813 @ SV1604 ) @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6821]) ).
thf(8012,plain,
! [SV1310: $i,SV58: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ SV58 @ SV1310 )
= $false )
| ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ SV58 @ SV1310 ) @ ( tc_List_Olist @ SV1310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6822]) ).
thf(8013,plain,
! [SV1311: $i,SV59: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ SV59 @ SV1311 )
= $false )
| ( ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ SV59 @ SV1311 ) @ ( tc_List_Olist @ SV1311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6823]) ).
thf(8014,plain,
! [SV1312: $i,SV64: $i] :
( ( ( class_Orderings_Oorder @ SV64 )
= $false )
| ( ( c_lessequals @ SV1312 @ SV1312 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6824]) ).
thf(8015,plain,
! [SV1814: $i,SV1605: $i,SV1313: $i,SV65: $i] :
( ( ~ ( c_in @ SV65 @ ( c_Relation_ODomain @ SV1313 @ SV1605 @ SV1814 ) @ SV1605 )
| ( c_in @ ( c_Pair @ SV65 @ ( c_Main_ODomainE__1 @ SV65 @ SV1313 @ SV1605 @ SV1814 ) @ SV1605 @ SV1814 ) @ SV1313 @ ( tc_prod @ SV1605 @ SV1814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6825]) ).
thf(8016,plain,
! [SV1815: $i,SV1606: $i,SV1314: $i,SV66: $i] :
( ( ! [SY3355: $i] :
( ~ ( c_in @ ( c_Pair @ SV66 @ SV1314 @ SV1606 @ SV1815 ) @ SY3355 @ ( tc_prod @ SV1606 @ SV1815 ) )
| ( c_in @ SV66 @ ( c_Relation_ODomain @ SY3355 @ SV1606 @ SV1815 ) @ SV1606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6826]) ).
thf(8017,plain,
! [SV1315: $i,SV67: $i] :
( ( ( c_in @ SV67 @ c_Relation_OId @ ( tc_prod @ SV1315 @ SV1315 ) )
= $false )
| ( ( SV67
= ( c_Pair @ ( c_Main_OIdE__1 @ SV67 @ SV1315 ) @ ( c_Main_OIdE__1 @ SV67 @ SV1315 ) @ SV1315 @ SV1315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6827]) ).
thf(8018,plain,
! [SV1816: $i,SV1607: $i,SV1316: $i,SV68: $i] :
( ( ! [SY3356: $i] :
( ~ ( c_in @ SV68 @ ( c_Relation_OImage @ SV1316 @ SV1607 @ SV1816 @ SY3356 ) @ SY3356 )
| ( c_in @ ( c_Main_OImageE__1 @ SV1607 @ SV68 @ SV1316 @ SV1816 @ SY3356 ) @ SV1607 @ SV1816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6828]) ).
thf(8019,plain,
! [SV1817: $i,SV1608: $i,SV1317: $i,SV69: $i] :
( ( ! [SY3357: $i] :
( ~ ( c_in @ SV69 @ ( c_Relation_OImage @ SV1317 @ SV1608 @ SV1817 @ SY3357 ) @ SY3357 )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1608 @ SV69 @ SV1317 @ SV1817 @ SY3357 ) @ SV69 @ SV1817 @ SY3357 ) @ SV1317 @ ( tc_prod @ SV1817 @ SY3357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6829]) ).
thf(8020,plain,
! [SV1818: $i,SV1609: $i,SV1318: $i,SV70: $i] :
( ( ! [SY3358: $i,SY3359: $i] :
( ~ ( c_in @ SV70 @ SV1318 @ SV1609 )
| ~ ( c_in @ ( c_Pair @ SV70 @ SV1818 @ SV1609 @ SY3358 ) @ SY3359 @ ( tc_prod @ SV1609 @ SY3358 ) )
| ( c_in @ SV1818 @ ( c_Relation_OImage @ SY3359 @ SV1318 @ SV1609 @ SY3358 ) @ SY3358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6830]) ).
thf(8021,plain,
! [SV1819: $i,SV1610: $i,SV1319: $i,SV71: $i] :
( ( ~ ( c_in @ SV71 @ ( c_Relation_ORange @ SV1319 @ SV1610 @ SV1819 ) @ SV1819 )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV71 @ SV1319 @ SV1819 @ SV1610 ) @ SV71 @ SV1610 @ SV1819 ) @ SV1319 @ ( tc_prod @ SV1610 @ SV1819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6831]) ).
thf(8022,plain,
! [SV1820: $i,SV1611: $i,SV1320: $i,SV72: $i] :
( ( ! [SY3360: $i] :
( ~ ( c_in @ ( c_Pair @ SV72 @ SV1320 @ SV1611 @ SV1820 ) @ SY3360 @ ( tc_prod @ SV1611 @ SV1820 ) )
| ( c_in @ SV1320 @ ( c_Relation_ORange @ SY3360 @ SV1611 @ SV1820 ) @ SV1820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6832]) ).
thf(8023,plain,
! [SV1821: $i,SV1612: $i,SV1321: $i,SV73: $i] :
( ( ~ ( c_in @ SV73 @ ( c_Relation_Oconverse @ SV1321 @ SV1612 @ SV1821 ) @ ( tc_prod @ SV1821 @ SV1612 ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1321 @ SV73 @ SV1612 @ SV1821 ) @ ( c_Main_OconverseE__2 @ SV1321 @ SV73 @ SV1612 @ SV1821 ) @ SV1612 @ SV1821 ) @ SV1321 @ ( tc_prod @ SV1612 @ SV1821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6833]) ).
thf(8024,plain,
! [SV1822: $i,SV1613: $i,SV1322: $i,SV74: $i] :
( ( ~ ( c_in @ SV74 @ ( c_Relation_Oconverse @ SV1322 @ SV1613 @ SV1822 ) @ ( tc_prod @ SV1822 @ SV1613 ) )
| ( SV74
= ( c_Pair @ ( c_Main_OconverseE__2 @ SV1322 @ SV74 @ SV1613 @ SV1822 ) @ ( c_Main_OconverseE__1 @ SV1322 @ SV74 @ SV1613 @ SV1822 ) @ SV1822 @ SV1613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6834]) ).
thf(8025,plain,
! [SV1614: $i,SV1323: $i,SV75: $i] :
( ( ( ~ ( c_in @ SV75 @ ( c_Relation_Odiag @ SV1323 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) )
= $true )
| ( ( SV75
= ( c_Pair @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SV1614 ) @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SV1614 ) @ SV1614 @ SV1614 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6835]) ).
thf(8026,plain,
! [SV1615: $i,SV1324: $i,SV76: $i] :
( ( ( ~ ( c_in @ SV76 @ ( c_Relation_Odiag @ SV1324 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) ) )
= $true )
| ( ( c_in @ ( c_Main_OdiagE__1 @ SV1324 @ SV76 @ SV1615 ) @ SV1324 @ SV1615 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6836]) ).
thf(8027,plain,
! [SV1616: $i,SV1325: $i,SV77: $i] :
( ( ( ~ ( c_in @ SV77 @ SV1325 @ SV1616 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV77 @ SV77 @ SV1616 @ SV1616 ) @ ( c_Relation_Odiag @ SV1325 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6837]) ).
thf(8028,plain,
! [SV1823: $i,SV1617: $i,SV1326: $i,SV78: $i] :
( ( ! [SY3361: $i,SY3362: $i] :
( ~ ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SV1326 @ SV1617 @ SV1823 @ SY3361 @ SY3362 ) @ ( tc_prod @ SY3362 @ SY3361 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SY3361 @ SY3362 ) @ ( c_Main_Orel__compE__3 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SY3361 @ SY3362 ) @ SV1823 @ SY3361 ) @ SV1326 @ ( tc_prod @ SV1823 @ SY3361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6838]) ).
thf(8029,plain,
! [SV1824: $i,SV1618: $i,SV1327: $i,SV79: $i] :
( ( ! [SY3363: $i,SY3364: $i] :
( ~ ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SV1327 @ SV1618 @ SV1824 @ SY3363 @ SY3364 ) @ ( tc_prod @ SY3364 @ SY3363 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SY3363 @ SY3364 ) @ ( c_Main_Orel__compE__2 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SY3363 @ SY3364 ) @ SY3364 @ SV1824 ) @ SV1618 @ ( tc_prod @ SY3364 @ SV1824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6839]) ).
thf(8030,plain,
! [SV1825: $i,SV1619: $i,SV1328: $i,SV80: $i] :
( ( ! [SY3365: $i,SY3366: $i] :
( ~ ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SV1328 @ SV1619 @ SV1825 @ SY3365 @ SY3366 ) @ ( tc_prod @ SY3366 @ SY3365 ) )
| ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SY3365 @ SY3366 ) @ ( c_Main_Orel__compE__3 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SY3365 @ SY3366 ) @ SY3366 @ SY3365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6840]) ).
thf(8031,plain,
! [SV1826: $i,SV1620: $i,SV1329: $i,SV81: $i] :
( ( ! [SY3367: $i,SY3368: $i,SY3369: $i,SY3370: $i] :
( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SY3367 @ ( tc_prod @ SV1620 @ SV1826 ) )
| ~ ( c_in @ ( c_Pair @ SY3368 @ SV81 @ SY3369 @ SV1620 ) @ SY3370 @ ( tc_prod @ SY3369 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SY3368 @ SV1329 @ SY3369 @ SV1826 ) @ ( c_Relation_Orel__comp @ SY3367 @ SY3370 @ SV1620 @ SV1826 @ SY3369 ) @ ( tc_prod @ SY3369 @ SV1826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6841]) ).
thf(8032,plain,
! [SV1621: $i,SV1338: $i,SV92: $i] :
( ( ( c_in @ SV92 @ ( c_Inter @ SV1338 @ SV1621 ) @ SV1621 )
= $true )
| ( ( c_in @ ( c_Main_OInterI__1 @ SV92 @ SV1338 @ SV1621 ) @ SV1338 @ ( tc_set @ SV1621 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6842]) ).
thf(8033,plain,
! [SV1622: $i,SV1339: $i,SV93: $i] :
( ( ( ~ ( c_in @ SV93 @ ( c_Main_OInterI__1 @ SV93 @ SV1339 @ SV1622 ) @ SV1622 ) )
= $true )
| ( ( c_in @ SV93 @ ( c_Inter @ SV1339 @ SV1622 ) @ SV1622 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6843]) ).
thf(8034,plain,
! [SV1623: $i,SV1341: $i,SV95: $i] :
( ( ( ~ ( c_in @ SV95 @ ( c_Union @ SV1341 @ SV1623 ) @ SV1623 ) )
= $true )
| ( ( c_in @ ( c_Main_OUnionE__1 @ SV95 @ SV1341 @ SV1623 ) @ SV1341 @ ( tc_set @ SV1623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6844]) ).
thf(8035,plain,
! [SV1624: $i,SV1342: $i,SV96: $i] :
( ( ( ~ ( c_in @ SV96 @ ( c_Union @ SV1342 @ SV1624 ) @ SV1624 ) )
= $true )
| ( ( c_in @ SV96 @ ( c_Main_OUnionE__1 @ SV96 @ SV1342 @ SV1624 ) @ SV1624 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6845]) ).
thf(8036,plain,
! [SV1625: $i,SV1344: $i,SV98: $i] :
( ( ( ~ ( c_less @ SV98 @ SV1344 @ ( tc_set @ SV1625 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1344 @ SV98 @ ( tc_set @ SV1625 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6846]) ).
thf(8037,plain,
! [SV1626: $i,SV1345: $i,SV99: $i] :
( ( ( ~ ( c_less @ SV99 @ SV1345 @ ( tc_set @ SV1626 ) ) )
= $true )
| ( ( c_lessequals @ SV99 @ SV1345 @ ( tc_set @ SV1626 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6847]) ).
thf(8038,plain,
! [SV1627: $i,SV1346: $i,SV100: $i] :
( ( ( ~ ( c_lessequals @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) ) )
= $true )
| ( ( ( c_less @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) )
| ( SV100 = SV1346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6848]) ).
thf(8039,plain,
! [SV1628: $i,SV1347: $i,SV101: $i] :
( ( ( ~ ( c_in @ SV101 @ ( c_insert @ SV1347 @ c_emptyset @ SV1628 ) @ SV1628 ) )
= $true )
| ( ( SV101 = SV1347 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6849]) ).
thf(8040,plain,
! [SV1827: $i,SV1629: $i,SV1349: $i,SV103: $i] :
( ( ~ ( c_in @ SV103 @ SV1349 @ SV1629 )
| ~ ( c_lessequals @ SV1349 @ SV1827 @ ( tc_set @ SV1629 ) )
| ( c_in @ SV103 @ SV1827 @ SV1629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6850]) ).
thf(8041,plain,
! [SV1630: $i,SV1350: $i,SV104: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV104 @ SV1350 @ SV1630 ) @ SV104 @ SV1630 )
= $true )
| ( ( c_lessequals @ SV104 @ SV1350 @ ( tc_set @ SV1630 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6851]) ).
thf(8042,plain,
! [SV1631: $i,SV1351: $i,SV105: $i] :
( ( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV105 @ SV1351 @ SV1631 ) @ SV1351 @ SV1631 ) )
= $true )
| ( ( c_lessequals @ SV105 @ SV1351 @ ( tc_set @ SV1631 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6852]) ).
thf(8043,plain,
! [SV1632: $i,SV1352: $i,SV106: $i] :
( ( ( ~ ( c_lessequals @ SV106 @ SV1352 @ ( tc_set @ SV1632 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1352 @ SV106 @ ( tc_set @ SV1632 ) )
| ( SV1352 = SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6853]) ).
thf(8044,plain,
! [SV1828: $i,SV1633: $i,SV1354: $i,SV108: $i] :
( ( ! [SY3371: $i] :
( ~ ( c_in @ SV108 @ SV1354 @ SV1633 )
| ( c_in @ ( c_Sum__Type_OInl @ SV108 @ SV1633 @ SV1828 ) @ ( c_Sum__Type_OPlus @ SV1354 @ SY3371 @ SV1633 @ SV1828 ) @ ( tc_sum @ SV1633 @ SV1828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6854]) ).
thf(8045,plain,
! [SV1829: $i,SV1634: $i,SV1355: $i,SV109: $i] :
( ( ! [SY3372: $i] :
( ~ ( c_in @ SV109 @ SV1355 @ SV1634 )
| ( c_in @ ( c_Sum__Type_OInr @ SV109 @ SV1634 @ SV1829 ) @ ( c_Sum__Type_OPlus @ SY3372 @ SV1355 @ SV1829 @ SV1634 ) @ ( tc_sum @ SV1829 @ SV1634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6855]) ).
thf(8046,plain,
! [SV1830: $i,SV1635: $i,SV1356: $i,SV110: $i] :
( ( ! [SY3373: $i] :
( ~ ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SV1356 @ SV1635 @ SV1830 @ SY3373 ) @ ( tc_sum @ SV1830 @ SY3373 ) )
| ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1356 @ SV110 @ SV1830 @ SY3373 ) @ SV1830 @ SY3373 ) )
| ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1635 @ SV110 @ SY3373 @ SV1830 ) @ SY3373 @ SV1830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6856]) ).
thf(8047,plain,
! [SV1831: $i,SV1636: $i,SV1357: $i,SV111: $i] :
( ( ! [SY3374: $i] :
( ~ ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SV1357 @ SV1636 @ SV1831 @ SY3374 ) @ ( tc_sum @ SV1831 @ SY3374 ) )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1636 @ SV111 @ SY3374 @ SV1831 ) @ SV1636 @ SY3374 )
| ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1357 @ SV111 @ SV1831 @ SY3374 ) @ SV1831 @ SY3374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6857]) ).
thf(8048,plain,
! [SV1832: $i,SV1637: $i,SV1358: $i,SV112: $i] :
( ( ! [SY3375: $i] :
( ~ ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SV1358 @ SV1637 @ SV1832 @ SY3375 ) @ ( tc_sum @ SV1832 @ SY3375 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1358 @ SV112 @ SV1832 @ SY3375 ) @ SV1358 @ SV1832 )
| ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1637 @ SV112 @ SY3375 @ SV1832 ) @ SY3375 @ SV1832 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6858]) ).
thf(8049,plain,
! [SV1833: $i,SV1638: $i,SV1359: $i,SV113: $i] :
( ( ! [SY3376: $i] :
( ~ ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SV1359 @ SV1638 @ SV1833 @ SY3376 ) @ ( tc_sum @ SV1833 @ SY3376 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1359 @ SV113 @ SV1833 @ SY3376 ) @ SV1359 @ SV1833 )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1638 @ SV113 @ SY3376 @ SV1833 ) @ SV1638 @ SY3376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6859]) ).
thf(8050,plain,
! [SV1639: $i,SV1360: $i,SV114: $i] :
( ( ( ~ ( c_in @ SV114 @ SV1360 @ ( tc_prod @ SV1639 @ SV1639 ) ) )
= $true )
| ( ( c_in @ SV114 @ ( c_Transitive__Closure_Ortrancl @ SV1360 @ SV1639 ) @ ( tc_prod @ SV1639 @ SV1639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6860]) ).
thf(8051,plain,
! [SV1834: $i,SV1641: $i,SV1362: $i,SV116: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ SV1834 @ ( tc_prod @ SV1641 @ SV1641 ) )
| ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ ( c_Transitive__Closure_Otrancl @ SV1834 @ SV1641 ) @ ( tc_prod @ SV1641 @ SV1641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6862]) ).
thf(8052,plain,
! [SV1835: $i,SV1642: $i,SV1363: $i,SV117: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Otrancl @ SV1835 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
| ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Ortrancl @ SV1835 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6863]) ).
thf(8053,plain,
! [SV1836: $i,SV1643: $i,SV1364: $i,SV119: $i] :
( ( ~ ( c_Relation_Otrans @ SV119 @ SV1364 )
| ~ ( c_Relation_Otrans @ SV1643 @ SV1836 )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1643 @ SV119 @ SV1836 @ SV1364 ) @ ( tc_prod @ SV1836 @ SV1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6864]) ).
thf(8054,plain,
! [SV1837: $i,SV1644: $i,SV1365: $i,SV120: $i] :
( ( ~ ( c_Wellfounded__Recursion_Owf @ SV120 @ SV1365 )
| ~ ( c_Wellfounded__Recursion_Owf @ SV1644 @ SV1837 )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1644 @ SV120 @ SV1837 @ SV1365 ) @ ( tc_prod @ SV1837 @ SV1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6865]) ).
thf(8055,plain,
! [SV122: $i,SV1366: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite @ SV1366 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV122 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV122 @ SV1366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6867]) ).
thf(8056,plain,
! [SV124: $i,SV1368: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite @ SV1368 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV124 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV124 @ SV1368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6868]) ).
thf(8057,plain,
! [SV130: $i,SV1369: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite @ SV1369 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV130 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV130 @ SV1369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6870]) ).
thf(8058,plain,
! [SV1645: $i,SV1370: $i,SV1038: $i] :
( ( ( ~ ( c_in @ SV1038 @ ( c_Datatype_Oo2s @ SV1370 @ SV1645 ) @ SV1645 ) )
= $true )
| ( ( SV1370
= ( c_Datatype_Ooption_OSome @ SV1038 @ SV1645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7778]) ).
thf(8059,plain,
! [SV1838: $i,SV1646: $i,SV1376: $i,SV1045: $i] :
( ( ~ ( c_in @ ( c_minus @ SV1045 @ ( c_insert @ SV1376 @ SV1646 @ SV1838 ) @ ( tc_set @ SV1838 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1838 ) )
| ( c_in @ ( c_minus @ SV1045 @ SV1646 @ ( tc_set @ SV1838 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7782]) ).
thf(8060,plain,
! [SV1839: $i,SV1647: $i,SV1377: $i,SV1046: $i] :
( ( ~ ( c_in @ ( c_minus @ SV1046 @ SV1377 @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) )
| ( c_in @ ( c_minus @ SV1046 @ ( c_insert @ SV1839 @ SV1377 @ SV1647 ) @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7783]) ).
thf(8061,plain,
! [SV1378: $i,SV1047: $i] :
( ( ( c_in @ ( c_Pow @ SV1047 @ SV1378 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1378 ) ) )
= $false )
| ( ( c_in @ SV1047 @ c_Finite__Set_OFinites @ ( tc_set @ SV1378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7784]) ).
thf(8062,plain,
! [SV1379: $i,SV1048: $i] :
( ( ( c_in @ SV1048 @ c_Finite__Set_OFinites @ ( tc_set @ SV1379 ) )
= $false )
| ( ( c_in @ ( c_Pow @ SV1048 @ SV1379 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1379 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7785]) ).
thf(8063,plain,
! [SV1648: $i,SV1380: $i,SV1049: $i] :
( ( ( ~ ( c_in @ ( c_union @ SV1049 @ SV1380 @ SV1648 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1648 ) ) )
= $true )
| ( ( c_in @ SV1049 @ c_Finite__Set_OFinites @ ( tc_set @ SV1648 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7786]) ).
thf(8064,plain,
! [SV1649: $i,SV1381: $i,SV1050: $i] :
( ( ( ~ ( c_in @ ( c_union @ SV1050 @ SV1381 @ SV1649 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1649 ) ) )
= $true )
| ( ( c_in @ SV1381 @ c_Finite__Set_OFinites @ ( tc_set @ SV1649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7787]) ).
thf(8065,plain,
! [SV1650: $i,SV1382: $i,SV1051: $i] :
( ( ( ~ ( c_in @ SV1051 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1650 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
| ( c_in @ ( c_union @ SV1650 @ SV1051 @ SV1382 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7788]) ).
thf(8066,plain,
! [SV1651: $i,SV1383: $i,SV1052: $i] :
( ( ( ~ ( c_in @ ( c_Relation_Oconverse @ SV1052 @ SV1383 @ SV1651 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1651 @ SV1383 ) ) ) )
= $true )
| ( ( c_in @ SV1052 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1383 @ SV1651 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7789]) ).
thf(8067,plain,
! [SV1652: $i,SV1384: $i,SV1053: $i] :
( ( ( ~ ( c_in @ SV1053 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1384 @ SV1652 ) ) ) )
= $true )
| ( ( c_in @ ( c_Relation_Oconverse @ SV1053 @ SV1384 @ SV1652 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1652 @ SV1384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7790]) ).
thf(8068,plain,
! [SV1653: $i,SV1385: $i,SV1054: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ SV1054 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1385 @ SV1653 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1054 @ SV1385 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7791]) ).
thf(8069,plain,
! [SV1654: $i,SV1386: $i,SV1055: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ SV1055 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1386 @ SV1654 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1055 @ SV1654 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7792]) ).
thf(8070,plain,
! [SV1655: $i,SV1387: $i,SV1056: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ SV1056 @ SV1387 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Divides_Oop_Advd @ SV1056 @ SV1655 @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1056 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1655 @ SV1387 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7793]) ).
thf(8071,plain,
! [SV1388: $i,SV1057: $i] :
( ( ( c_Divides_Oop_Advd @ SV1057 @ ( c_uminus @ SV1388 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= $false )
| ( ( c_Divides_Oop_Advd @ SV1057 @ SV1388 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7794]) ).
thf(8072,plain,
! [SV1389: $i,SV1058: $i] :
( ( ( c_Divides_Oop_Advd @ SV1058 @ SV1389 @ tc_IntDef_Oint )
= $false )
| ( ( c_Divides_Oop_Advd @ SV1058 @ ( c_uminus @ SV1389 @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7795]) ).
thf(8073,plain,
! [SV1390: $i,SV1060: $i] :
( ( ( c_Divides_Oop_Advd @ ( c_uminus @ SV1060 @ tc_IntDef_Oint ) @ SV1390 @ tc_IntDef_Oint )
= $false )
| ( ( c_Divides_Oop_Advd @ SV1060 @ SV1390 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7797]) ).
thf(8074,plain,
! [SV1391: $i,SV1061: $i] :
( ( ( c_Divides_Oop_Advd @ SV1061 @ SV1391 @ tc_IntDef_Oint )
= $false )
| ( ( c_Divides_Oop_Advd @ ( c_uminus @ SV1061 @ tc_IntDef_Oint ) @ SV1391 @ tc_IntDef_Oint )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7798]) ).
thf(8075,plain,
! [SV1656: $i,SV1392: $i,SV1062: $i] :
( ( c_in @ ( c_Pair @ SV1062 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1392 ) @ ( tc_List_Olist @ SV1392 ) ) @ ( c_List_Olex @ SV1656 @ SV1392 ) @ ( tc_prod @ ( tc_List_Olist @ SV1392 ) @ ( tc_List_Olist @ SV1392 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7799]) ).
thf(8076,plain,
! [SV1657: $i,SV1393: $i,SV1065: $i] :
( ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV1065 @ ( tc_List_Olist @ SV1393 ) @ ( tc_List_Olist @ SV1393 ) ) @ ( c_List_Olex @ SV1657 @ SV1393 ) @ ( tc_prod @ ( tc_List_Olist @ SV1393 ) @ ( tc_List_Olist @ SV1393 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7800]) ).
thf(8077,plain,
! [SV1840: $i,SV1658: $i,SV1394: $i,SV1066: $i] :
( ( ~ ( c_in @ ( c_append @ SV1066 @ SV1394 @ SV1658 ) @ ( c_List_Olists @ SV1840 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) )
| ( c_in @ SV1066 @ ( c_List_Olists @ SV1840 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7801]) ).
thf(8078,plain,
! [SV1841: $i,SV1659: $i,SV1395: $i,SV1067: $i] :
( ( ~ ( c_in @ ( c_append @ SV1067 @ SV1395 @ SV1659 ) @ ( c_List_Olists @ SV1841 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) )
| ( c_in @ SV1395 @ ( c_List_Olists @ SV1841 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7802]) ).
thf(8079,plain,
! [SV1842: $i,SV1660: $i,SV1396: $i,SV1068: $i] :
( ( ~ ( c_in @ SV1068 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
| ~ ( c_in @ SV1842 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
| ( c_in @ ( c_append @ SV1842 @ SV1068 @ SV1660 ) @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7803]) ).
thf(8080,plain,
! [SV1403: $i,SV1081: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV1081 ) @ ( c_Suc @ SV1403 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1081 @ SV1403 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7806]) ).
thf(8081,plain,
! [SV1404: $i,SV1082: $i] :
( ( ( c_lessequals @ SV1082 @ SV1404 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV1082 ) @ ( c_Suc @ SV1404 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7807]) ).
thf(8082,plain,
! [SV1405: $i,SV1083: $i] :
( ( ( c_less @ ( c_Suc @ SV1083 ) @ ( c_Suc @ SV1405 ) @ tc_nat )
= $false )
| ( ( c_less @ SV1083 @ SV1405 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7808]) ).
thf(8083,plain,
! [SV1406: $i,SV1084: $i] :
( ( ( c_less @ SV1084 @ SV1406 @ tc_nat )
= $false )
| ( ( c_less @ ( c_Suc @ SV1084 ) @ ( c_Suc @ SV1406 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7809]) ).
thf(8084,plain,
! [SV1407: $i,SV1085: $i] :
( ( ( c_less @ c_0 @ ( c_plus @ SV1085 @ SV1407 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_less @ c_0 @ SV1407 @ tc_nat )
| ( c_less @ c_0 @ SV1085 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7810]) ).
thf(8085,plain,
! [SV1408: $i,SV1086: $i] :
( ( ( c_less @ c_0 @ SV1086 @ tc_nat )
= $false )
| ( ( c_less @ c_0 @ ( c_plus @ SV1086 @ SV1408 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7811]) ).
thf(8086,plain,
! [SV1409: $i,SV1087: $i] :
( ( ( c_less @ c_0 @ SV1087 @ tc_nat )
= $false )
| ( ( c_less @ c_0 @ ( c_plus @ SV1409 @ SV1087 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7812]) ).
thf(8087,plain,
! [SV1412: $i,SV1095: $i] :
( ( ( class_Orderings_Oorder @ SV1095 )
= $false )
| ( ( ~ ( c_less @ SV1412 @ SV1412 @ SV1095 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7818]) ).
thf(8088,plain,
! [SV1843: $i,SV1662: $i,SV1414: $i,SV1097: $i] :
( ( ! [SY3377: $i] :
( ~ ( c_in @ SV1097 @ ( c_Relation_OImage @ SV1414 @ ( c_insert @ SV1662 @ c_emptyset @ SV1843 ) @ SV1843 @ SY3377 ) @ SY3377 )
| ( c_in @ ( c_Pair @ SV1662 @ SV1097 @ SV1843 @ SY3377 ) @ SV1414 @ ( tc_prod @ SV1843 @ SY3377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7819]) ).
thf(8089,plain,
! [SV1844: $i,SV1663: $i,SV1415: $i,SV1098: $i] :
( ( ! [SY3378: $i] :
( ~ ( c_in @ ( c_Pair @ SV1098 @ SV1415 @ SV1663 @ SV1844 ) @ SY3378 @ ( tc_prod @ SV1663 @ SV1844 ) )
| ( c_in @ SV1415 @ ( c_Relation_OImage @ SY3378 @ ( c_insert @ SV1098 @ c_emptyset @ SV1663 ) @ SV1663 @ SV1844 ) @ SV1844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7820]) ).
thf(8090,plain,
! [SV1845: $i,SV1664: $i,SV1416: $i,SV1099: $i] :
( ( ! [SY3379: $i] :
( ~ ( c_in @ ( c_Pair @ SV1099 @ SV1416 @ SV1664 @ SV1845 ) @ ( c_Relation_Oconverse @ SY3379 @ SV1845 @ SV1664 ) @ ( tc_prod @ SV1664 @ SV1845 ) )
| ( c_in @ ( c_Pair @ SV1416 @ SV1099 @ SV1845 @ SV1664 ) @ SY3379 @ ( tc_prod @ SV1845 @ SV1664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7821]) ).
thf(8091,plain,
! [SV1846: $i,SV1665: $i,SV1417: $i,SV1100: $i] :
( ( ! [SY3380: $i] :
( ~ ( c_in @ ( c_Pair @ SV1100 @ SV1417 @ SV1665 @ SV1846 ) @ SY3380 @ ( tc_prod @ SV1665 @ SV1846 ) )
| ( c_in @ ( c_Pair @ SV1417 @ SV1100 @ SV1846 @ SV1665 ) @ ( c_Relation_Oconverse @ SY3380 @ SV1665 @ SV1846 ) @ ( tc_prod @ SV1846 @ SV1665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7822]) ).
thf(8092,plain,
! [SV1666: $i,SV1418: $i,SV1101: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1101 @ SV1418 @ SV1666 @ SV1666 ) @ c_Relation_OId @ ( tc_prod @ SV1666 @ SV1666 ) ) )
= $true )
| ( ( SV1101 = SV1418 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7823]) ).
thf(8093,plain,
! [SV1667: $i,SV1419: $i,SV1102: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1102 ) )
= $true )
| ( ( ~ ( c_in @ SV1419 @ ( c_SetInterval_OatLeast @ SV1667 @ SV1102 ) @ SV1102 )
| ( c_lessequals @ SV1667 @ SV1419 @ SV1102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7824]) ).
thf(8094,plain,
! [SV1668: $i,SV1420: $i,SV1103: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1103 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1420 @ SV1668 @ SV1103 )
| ( c_in @ SV1668 @ ( c_SetInterval_OatLeast @ SV1420 @ SV1103 ) @ SV1103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7825]) ).
thf(8095,plain,
! [SV1669: $i,SV1421: $i,SV1104: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV1104 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1421 @ SV1104 ) @ ( c_SetInterval_OatLeast @ SV1669 @ SV1104 ) @ ( tc_set @ SV1104 ) )
| ( c_lessequals @ SV1669 @ SV1421 @ SV1104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7826]) ).
thf(8096,plain,
! [SV1670: $i,SV1422: $i,SV1105: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV1105 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1422 @ SV1670 @ SV1105 )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1670 @ SV1105 ) @ ( c_SetInterval_OatLeast @ SV1422 @ SV1105 ) @ ( tc_set @ SV1105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7827]) ).
thf(8097,plain,
! [SV1671: $i,SV1423: $i,SV1106: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1106 ) )
= $true )
| ( ( ~ ( c_in @ SV1423 @ ( c_SetInterval_OatMost @ SV1671 @ SV1106 ) @ SV1106 )
| ( c_lessequals @ SV1423 @ SV1671 @ SV1106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7828]) ).
thf(8098,plain,
! [SV1672: $i,SV1424: $i,SV1107: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1107 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1424 @ SV1672 @ SV1107 )
| ( c_in @ SV1424 @ ( c_SetInterval_OatMost @ SV1672 @ SV1107 ) @ SV1107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7829]) ).
thf(8099,plain,
! [SV1673: $i,SV1425: $i,SV1108: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV1108 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1425 @ SV1108 ) @ ( c_SetInterval_OatMost @ SV1673 @ SV1108 ) @ ( tc_set @ SV1108 ) )
| ( c_lessequals @ SV1425 @ SV1673 @ SV1108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7830]) ).
thf(8100,plain,
! [SV1674: $i,SV1426: $i,SV1109: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV1109 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1426 @ SV1674 @ SV1109 )
| ( c_lessequals @ ( c_SetInterval_OatMost @ SV1426 @ SV1109 ) @ ( c_SetInterval_OatMost @ SV1674 @ SV1109 ) @ ( tc_set @ SV1109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7831]) ).
thf(8101,plain,
! [SV1675: $i,SV1427: $i,SV1110: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1110 ) )
= $true )
| ( ( ~ ( c_in @ SV1427 @ ( c_SetInterval_OgreaterThan @ SV1675 @ SV1110 ) @ SV1110 )
| ( c_less @ SV1675 @ SV1427 @ SV1110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7832]) ).
thf(8102,plain,
! [SV1676: $i,SV1428: $i,SV1111: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1111 ) )
= $true )
| ( ( ~ ( c_less @ SV1428 @ SV1676 @ SV1111 )
| ( c_in @ SV1676 @ ( c_SetInterval_OgreaterThan @ SV1428 @ SV1111 ) @ SV1111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7833]) ).
thf(8103,plain,
! [SV1677: $i,SV1429: $i,SV1112: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1112 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1429 @ SV1112 ) @ ( c_SetInterval_OgreaterThan @ SV1677 @ SV1112 ) @ ( tc_set @ SV1112 ) )
| ( c_lessequals @ SV1677 @ SV1429 @ SV1112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7834]) ).
thf(8104,plain,
! [SV1678: $i,SV1430: $i,SV1113: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1113 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1430 @ SV1678 @ SV1113 )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1678 @ SV1113 ) @ ( c_SetInterval_OgreaterThan @ SV1430 @ SV1113 ) @ ( tc_set @ SV1113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7835]) ).
thf(8105,plain,
! [SV1679: $i,SV1431: $i,SV1114: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1114 ) )
= $true )
| ( ( ~ ( c_in @ SV1431 @ ( c_SetInterval_OlessThan @ SV1679 @ SV1114 ) @ SV1114 )
| ( c_less @ SV1431 @ SV1679 @ SV1114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7836]) ).
thf(8106,plain,
! [SV1680: $i,SV1432: $i,SV1115: $i] :
( ( ( ~ ( class_Orderings_Oord @ SV1115 ) )
= $true )
| ( ( ~ ( c_less @ SV1432 @ SV1680 @ SV1115 )
| ( c_in @ SV1432 @ ( c_SetInterval_OlessThan @ SV1680 @ SV1115 ) @ SV1115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7837]) ).
thf(8107,plain,
! [SV1681: $i,SV1433: $i,SV1116: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1116 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1433 @ SV1116 ) @ ( c_SetInterval_OlessThan @ SV1681 @ SV1116 ) @ ( tc_set @ SV1116 ) )
| ( c_lessequals @ SV1433 @ SV1681 @ SV1116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7838]) ).
thf(8108,plain,
! [SV1682: $i,SV1434: $i,SV1117: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1117 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1434 @ SV1682 @ SV1117 )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1434 @ SV1117 ) @ ( c_SetInterval_OlessThan @ SV1682 @ SV1117 ) @ ( tc_set @ SV1117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7839]) ).
thf(8109,plain,
! [SV1683: $i,SV1435: $i,SV1118: $i] :
( ( ( ~ ( c_in @ SV1118 @ SV1435 @ SV1683 ) )
= $true )
| ( ( ~ ( c_in @ SV1118 @ ( c_uminus @ SV1435 @ ( tc_set @ SV1683 ) ) @ SV1683 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7840]) ).
thf(8110,plain,
! [SV1684: $i,SV1436: $i,SV1119: $i] :
( ( ( c_in @ SV1119 @ SV1436 @ SV1684 )
= $true )
| ( ( c_in @ SV1119 @ ( c_uminus @ SV1436 @ ( tc_set @ SV1684 ) ) @ SV1684 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7841]) ).
thf(8111,plain,
! [SV1685: $i,SV1437: $i,SV1120: $i] :
( ( ( ~ ( c_lessequals @ ( c_uminus @ SV1120 @ ( tc_set @ SV1437 ) ) @ ( c_uminus @ SV1685 @ ( tc_set @ SV1437 ) ) @ ( tc_set @ SV1437 ) ) )
= $true )
| ( ( c_lessequals @ SV1685 @ SV1120 @ ( tc_set @ SV1437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7842]) ).
thf(8112,plain,
! [SV1686: $i,SV1438: $i,SV1121: $i] :
( ( ( ~ ( c_lessequals @ SV1121 @ SV1438 @ ( tc_set @ SV1686 ) ) )
= $true )
| ( ( c_lessequals @ ( c_uminus @ SV1438 @ ( tc_set @ SV1686 ) ) @ ( c_uminus @ SV1121 @ ( tc_set @ SV1686 ) ) @ ( tc_set @ SV1686 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7843]) ).
thf(8113,plain,
! [SV1847: $i,SV1687: $i,SV1439: $i,SV1122: $i] :
( ( ~ ( c_in @ SV1122 @ SV1439 @ SV1687 )
| ~ ( c_in @ SV1122 @ ( c_minus @ SV1847 @ SV1439 @ ( tc_set @ SV1687 ) ) @ SV1687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7844]) ).
thf(8114,plain,
! [SV1848: $i,SV1688: $i,SV1440: $i,SV1123: $i] :
( ( ~ ( c_in @ SV1123 @ ( c_minus @ SV1440 @ SV1688 @ ( tc_set @ SV1848 ) ) @ SV1848 )
| ( c_in @ SV1123 @ SV1440 @ SV1848 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7845]) ).
thf(8115,plain,
! [SV1849: $i,SV1689: $i,SV1441: $i,SV1124: $i] :
( ( ~ ( c_in @ SV1124 @ SV1441 @ SV1689 )
| ( c_in @ SV1124 @ SV1849 @ SV1689 )
| ( c_in @ SV1124 @ ( c_minus @ SV1441 @ SV1849 @ ( tc_set @ SV1689 ) ) @ SV1689 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7846]) ).
thf(8116,plain,
! [SV1850: $i,SV1690: $i,SV1442: $i,SV1125: $i] :
( ( ~ ( c_in @ SV1125 @ ( c_inter @ SV1442 @ SV1690 @ SV1850 ) @ SV1850 )
| ( c_in @ SV1125 @ SV1690 @ SV1850 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7847]) ).
thf(8117,plain,
! [SV1851: $i,SV1691: $i,SV1443: $i,SV1126: $i] :
( ( ~ ( c_in @ SV1126 @ ( c_inter @ SV1443 @ SV1691 @ SV1851 ) @ SV1851 )
| ( c_in @ SV1126 @ SV1443 @ SV1851 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7848]) ).
thf(8118,plain,
! [SV1852: $i,SV1692: $i,SV1444: $i,SV1127: $i] :
( ( ~ ( c_in @ SV1127 @ SV1444 @ SV1692 )
| ~ ( c_in @ SV1127 @ SV1852 @ SV1692 )
| ( c_in @ SV1127 @ ( c_inter @ SV1852 @ SV1444 @ SV1692 ) @ SV1692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7849]) ).
thf(8119,plain,
! [SV1853: $i,SV1693: $i,SV1445: $i,SV1128: $i] :
( ( ~ ( c_in @ SV1128 @ SV1445 @ ( tc_set @ SV1693 ) )
| ~ ( c_in @ SV1853 @ ( c_Inter @ SV1445 @ SV1693 ) @ SV1693 )
| ( c_in @ SV1853 @ SV1128 @ SV1693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7850]) ).
thf(8120,plain,
! [SV1694: $i,SV1446: $i,SV1129: $i] :
( ( ( ~ ( c_in @ SV1129 @ ( c_Pow @ SV1446 @ SV1694 ) @ ( tc_set @ SV1694 ) ) )
= $true )
| ( ( c_lessequals @ SV1129 @ SV1446 @ ( tc_set @ SV1694 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7851]) ).
thf(8121,plain,
! [SV1695: $i,SV1447: $i,SV1130: $i] :
( ( ( ~ ( c_lessequals @ SV1130 @ SV1447 @ ( tc_set @ SV1695 ) ) )
= $true )
| ( ( c_in @ SV1130 @ ( c_Pow @ SV1447 @ SV1695 ) @ ( tc_set @ SV1695 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7852]) ).
thf(8122,plain,
! [SV1854: $i,SV1696: $i,SV1448: $i,SV1131: $i] :
( ( ~ ( c_in @ SV1131 @ SV1448 @ SV1696 )
| ( c_in @ SV1131 @ ( c_union @ SV1854 @ SV1448 @ SV1696 ) @ SV1696 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7853]) ).
thf(8123,plain,
! [SV1855: $i,SV1697: $i,SV1449: $i,SV1132: $i] :
( ( ~ ( c_in @ SV1132 @ SV1449 @ SV1697 )
| ( c_in @ SV1132 @ ( c_union @ SV1449 @ SV1855 @ SV1697 ) @ SV1697 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7854]) ).
thf(8124,plain,
! [SV1856: $i,SV1698: $i,SV1450: $i,SV1133: $i] :
( ( ~ ( c_in @ SV1133 @ ( c_union @ SV1450 @ SV1698 @ SV1856 ) @ SV1856 )
| ( c_in @ SV1133 @ SV1698 @ SV1856 )
| ( c_in @ SV1133 @ SV1450 @ SV1856 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7855]) ).
thf(8125,plain,
! [SV1857: $i,SV1699: $i,SV1451: $i,SV1135: $i] :
( ( ~ ( c_in @ SV1135 @ SV1451 @ SV1699 )
| ~ ( c_in @ SV1451 @ SV1857 @ ( tc_set @ SV1699 ) )
| ( c_in @ SV1135 @ ( c_Union @ SV1857 @ SV1699 ) @ SV1699 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7856]) ).
thf(8126,plain,
! [SV1858: $i,SV1700: $i,SV1453: $i,SV1137: $i] :
( ( ~ ( c_in @ SV1137 @ SV1453 @ SV1700 )
| ( c_in @ SV1137 @ ( c_insert @ SV1858 @ SV1453 @ SV1700 ) @ SV1700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7858]) ).
thf(8127,plain,
! [SV1859: $i,SV1702: $i,SV1455: $i,SV1139: $i] :
( ( ~ ( c_in @ SV1139 @ ( c_insert @ SV1455 @ SV1702 @ SV1859 ) @ SV1859 )
| ( c_in @ SV1139 @ SV1702 @ SV1859 )
| ( SV1139 = SV1455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7860]) ).
thf(8128,plain,
! [SV1703: $i,SV1457: $i,SV1141: $i] :
( ( ( ~ ( c_lessequals @ SV1141 @ ( c_insert @ SV1457 @ c_emptyset @ SV1703 ) @ ( tc_set @ SV1703 ) ) )
= $true )
| ( ( ( c_insert @ SV1457 @ SV1141 @ SV1703 )
= ( c_insert @ SV1457 @ c_emptyset @ SV1703 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7862]) ).
thf(8129,plain,
! [SV1704: $i,SV1458: $i,SV1142: $i] :
( ( ( ~ ( c_lessequals @ SV1142 @ ( c_insert @ SV1458 @ c_emptyset @ SV1704 ) @ ( tc_set @ SV1704 ) ) )
= $true )
| ( ( ( c_insert @ SV1458 @ c_emptyset @ SV1704 )
= ( c_insert @ SV1458 @ SV1142 @ SV1704 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7863]) ).
thf(8130,plain,
! [SV1459: $i,SV1143: $i] :
( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1143 @ SV1459 @ SV1459 ) @ SV1459 )
= $false )
| ( ( c_Wellfounded__Recursion_Oacyclic @ SV1143 @ SV1459 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7864]) ).
thf(8131,plain,
! [SV1460: $i,SV1144: $i] :
( ( ( c_Wellfounded__Recursion_Oacyclic @ SV1144 @ SV1460 )
= $false )
| ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ SV1144 @ SV1460 @ SV1460 ) @ SV1460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7865]) ).
thf(8132,plain,
! [SV1860: $i,SV1705: $i,SV1461: $i,SV1145: $i] :
( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1145 @ SV1461 @ SV1705 @ SV1705 ) @ SV1860 @ ( tc_prod @ SV1705 @ SV1705 ) ) @ SV1705 )
| ( c_Wellfounded__Recursion_Oacyclic @ SV1860 @ SV1705 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7866]) ).
thf(8133,plain,
! [SV1861: $i,SV1706: $i,SV1462: $i,SV1146: $i] :
( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1146 @ SV1462 @ SV1706 @ SV1706 ) @ SV1861 @ ( tc_prod @ SV1706 @ SV1706 ) ) @ SV1706 )
| ~ ( c_in @ ( c_Pair @ SV1462 @ SV1146 @ SV1706 @ SV1706 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1706 ) @ ( tc_prod @ SV1706 @ SV1706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7867]) ).
thf(8134,plain,
! [SV1862: $i,SV1707: $i,SV1463: $i,SV1147: $i] :
( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1147 @ SV1463 )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1707 @ SV1862 @ SV1463 @ SV1463 ) @ SV1147 @ ( tc_prod @ SV1463 @ SV1463 ) ) @ SV1463 )
| ( c_in @ ( c_Pair @ SV1862 @ SV1707 @ SV1463 @ SV1463 ) @ ( c_Transitive__Closure_Ortrancl @ SV1147 @ SV1463 ) @ ( tc_prod @ SV1463 @ SV1463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7868]) ).
thf(8135,plain,
! [SV1863: $i,SV1708: $i,SV1464: $i,SV1148: $i] :
( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1148 @ SV1464 @ SV1708 @ SV1708 ) @ SV1863 @ ( tc_prod @ SV1708 @ SV1708 ) ) @ SV1708 )
| ( c_Wellfounded__Recursion_Owf @ SV1863 @ SV1708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7869]) ).
thf(8136,plain,
! [SV1864: $i,SV1709: $i,SV1465: $i,SV1149: $i] :
( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1149 @ SV1465 @ SV1709 @ SV1709 ) @ SV1864 @ ( tc_prod @ SV1709 @ SV1709 ) ) @ SV1709 )
| ~ ( c_in @ ( c_Pair @ SV1465 @ SV1149 @ SV1709 @ SV1709 ) @ ( c_Transitive__Closure_Ortrancl @ SV1864 @ SV1709 ) @ ( tc_prod @ SV1709 @ SV1709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7870]) ).
thf(8137,plain,
! [SV1865: $i,SV1710: $i,SV1466: $i,SV1150: $i] :
( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1150 @ SV1466 )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1710 @ SV1865 @ SV1466 @ SV1466 ) @ SV1150 @ ( tc_prod @ SV1466 @ SV1466 ) ) @ SV1466 )
| ( c_in @ ( c_Pair @ SV1865 @ SV1710 @ SV1466 @ SV1466 ) @ ( c_Transitive__Closure_Ortrancl @ SV1150 @ SV1466 ) @ ( tc_prod @ SV1466 @ SV1466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7871]) ).
thf(8138,plain,
! [SV1467: $i,SV1151: $i] :
( ( ( c_in @ ( c_Pair @ SV1151 @ SV1467 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
= $false )
| ( ( c_less @ SV1151 @ SV1467 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7872]) ).
thf(8139,plain,
! [SV1468: $i,SV1152: $i] :
( ( ( c_less @ SV1152 @ SV1468 @ tc_nat )
= $false )
| ( ( c_in @ ( c_Pair @ SV1152 @ SV1468 @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7873]) ).
thf(8140,plain,
! [SV1711: $i,SV1469: $i,SV1153: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1153 @ SV1469 ) @ ( c_Message_Oanalz @ SV1711 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1469 @ ( c_Message_Oanalz @ SV1711 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7874]) ).
thf(8141,plain,
! [SV1712: $i,SV1470: $i,SV1154: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1154 @ SV1470 ) @ ( c_Message_Oanalz @ SV1712 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1154 @ ( c_Message_Oanalz @ SV1712 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7875]) ).
thf(8142,plain,
! [SV1713: $i,SV1471: $i,SV1155: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1155 @ SV1471 ) @ ( c_Message_Oparts @ SV1713 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1471 @ ( c_Message_Oparts @ SV1713 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7876]) ).
thf(8143,plain,
! [SV1714: $i,SV1472: $i,SV1156: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1156 @ SV1472 ) @ ( c_Message_Oparts @ SV1714 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1156 @ ( c_Message_Oparts @ SV1714 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7877]) ).
thf(8144,plain,
! [SV1715: $i,SV1473: $i,SV1157: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1157 @ SV1473 ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1157 ) ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
| ( c_in @ SV1473 @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7878]) ).
thf(8145,plain,
! [SV1474: $i,SV1158: $i] :
( ( ( c_in @ SV1158 @ SV1474 @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1158 @ ( c_Message_Oanalz @ SV1474 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7879]) ).
thf(8146,plain,
! [SV1475: $i,SV1159: $i] :
( ( ( c_in @ SV1159 @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ SV1475 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1159 @ ( c_Message_Oanalz @ SV1475 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7880]) ).
thf(8147,plain,
! [SV1476: $i,SV1160: $i] :
( ( ( c_lessequals @ SV1160 @ SV1476 @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ ( c_Message_Oanalz @ SV1160 ) @ ( c_Message_Oanalz @ SV1476 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7881]) ).
thf(8148,plain,
! [SV1716: $i,SV1477: $i,SV1161: $i] :
( ( ( ~ ( c_in @ SV1161 @ ( c_Message_Oparts @ ( c_union @ SV1477 @ SV1716 @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1716 ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1477 ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7882]) ).
thf(8149,plain,
! [SV1717: $i,SV1478: $i,SV1162: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1162 @ SV1478 ) @ ( c_Message_Oparts @ SV1717 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1478 @ ( c_Message_Oparts @ SV1717 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7883]) ).
thf(8150,plain,
! [SV1479: $i,SV1163: $i] :
( ( ( c_in @ SV1163 @ SV1479 @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1163 @ ( c_Message_Oparts @ SV1479 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7884]) ).
thf(8151,plain,
! [SV1480: $i,SV1165: $i] :
( ( ( c_in @ SV1165 @ ( c_Message_Oparts @ ( c_Message_Oparts @ SV1480 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1165 @ ( c_Message_Oparts @ SV1480 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7885]) ).
thf(8152,plain,
! [SV1866: $i,SV1720: $i,SV1483: $i,SV1168: $i] :
( ( ~ ( c_lessequals @ SV1168 @ SV1483 @ ( tc_set @ SV1720 ) )
| ~ ( c_lessequals @ SV1866 @ SV1168 @ ( tc_set @ SV1720 ) )
| ( c_lessequals @ SV1866 @ SV1483 @ ( tc_set @ SV1720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7888]) ).
thf(8153,plain,
! [SV1867: $i,SV1721: $i,SV1484: $i,SV1169: $i] :
( ( ( c_Datatype__Universe_OIn0 @ SV1169 @ SV1484 @ SV1721 )
!= ( c_Datatype__Universe_OIn1 @ SV1867 @ SV1484 @ SV1721 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7889]) ).
thf(8154,plain,
! [SV1868: $i,SV1722: $i,SV1485: $i,SV1170: $i] :
( ( ( ( c_Message_Omsg_OCrypt @ SV1170 @ SV1485 )
!= ( c_Message_Omsg_OCrypt @ SV1722 @ SV1868 ) )
| ( SV1170 = SV1722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7890]) ).
thf(8155,plain,
! [SV1486: $i,SV1171: $i] :
( ( ( ( c_List_Orev @ SV1171 @ SV1486 )
= c_List_Olist_ONil )
= $false )
| ( ( SV1171 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7891]) ).
thf(8156,plain,
! [SV1869: $i,SV1723: $i,SV1487: $i,SV1172: $i] :
( ( ! [SY3381: $i] :
( ( ( c_append @ SV1172 @ ( c_List_Olist_OCons @ SV1487 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 )
!= ( c_append @ SV1869 @ ( c_List_Olist_OCons @ SY3381 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 ) )
| ( SV1487 = SY3381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7892]) ).
thf(8157,plain,
! [SV1870: $i,SV1724: $i,SV1488: $i,SV1173: $i] :
( ( ! [SY3382: $i] :
( ( c_Datatype__Universe_OScons @ SV1173 @ SV1488 @ SV1724 @ SV1870 )
!= ( c_Datatype__Universe_ONumb @ SY3382 @ SV1724 @ SV1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7893]) ).
thf(8158,plain,
! [SV1489: $i,SV1174: $i] :
( ( ( ( c_List_Oset @ SV1174 @ SV1489 )
= c_emptyset )
= $false )
| ( ( SV1174 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7894]) ).
thf(8159,plain,
! [SV1871: $i,SV1725: $i,SV1491: $i,SV1176: $i] :
( ( ( ( c_Datatype__Universe_OLeaf @ SV1176 @ SV1491 @ SV1725 )
!= ( c_Datatype__Universe_OLeaf @ SV1871 @ SV1491 @ SV1725 ) )
| ( SV1176 = SV1871 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7896]) ).
thf(8160,plain,
! [SV1872: $i,SV1726: $i,SV1492: $i,SV1177: $i] :
( ( ( c_Datatype__Universe_OIn1 @ SV1177 @ SV1492 @ SV1726 )
!= ( c_Datatype__Universe_OIn0 @ SV1872 @ SV1492 @ SV1726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7897]) ).
thf(8161,plain,
! [SV1493: $i,SV1178: $i] :
( ( ( ( c_List_Oremdups @ SV1178 @ SV1493 )
= SV1178 )
= $false )
| ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1178 @ SV1493 ) @ ( tc_List_Olist @ SV1493 ) )
= ( c_Nat_Osize @ SV1178 @ ( tc_List_Olist @ SV1493 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7898]) ).
thf(8162,plain,
! [SV1873: $i,SV1727: $i,SV1494: $i,SV1180: $i] :
( ( ( ( c_Datatype__Universe_ONumb @ SV1180 @ SV1494 @ SV1727 )
!= ( c_Datatype__Universe_ONumb @ SV1873 @ SV1494 @ SV1727 ) )
| ( SV1180 = SV1873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7899]) ).
thf(8163,plain,
! [SV1728: $i,SV1495: $i,SV1182: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ SV1182 @ SV1495 @ SV1728 )
!= c_emptyset )
= $true )
| ( ( SV1182 = c_emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7900]) ).
thf(8164,plain,
! [SV1496: $i,SV1183: $i] :
( ( ( ( c_Nat_Osize @ SV1183 @ ( tc_List_Olist @ SV1496 ) )
= c_0 )
= $false )
| ( ( SV1183 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7901]) ).
thf(8165,plain,
! [SV1874: $i,SV1729: $i,SV1497: $i,SV1184: $i] :
( ( ( ( c_Message_Omsg_OMPair @ SV1184 @ SV1497 )
!= ( c_Message_Omsg_OMPair @ SV1729 @ SV1874 ) )
| ( SV1184 = SV1729 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7902]) ).
thf(8166,plain,
! [SV1875: $i,SV1730: $i,SV1498: $i,SV1185: $i] :
( ( ! [SY3383: $i] :
( ( ( c_List_Olist_OCons @ SV1185 @ SV1498 @ SV1730 )
!= ( c_List_Olist_OCons @ SV1875 @ SY3383 @ SV1730 ) )
| ( SV1498 = SY3383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7903]) ).
thf(8167,plain,
! [SV1876: $i,SV1731: $i,SV1499: $i,SV1186: $i] :
( ( ( c_Sum__Type_OInr @ SV1186 @ SV1499 @ SV1731 )
!= ( c_Sum__Type_OInl @ SV1876 @ SV1731 @ SV1499 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7904]) ).
thf(8168,plain,
! [SV1500: $i,SV1187: $i] :
( ( ( ( c_Message_Omsg_OHash @ SV1187 )
= ( c_Message_Omsg_OHash @ SV1500 ) )
= $false )
| ( ( SV1187 = SV1500 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7905]) ).
thf(8169,plain,
! [SV1877: $i,SV1732: $i,SV1501: $i,SV1188: $i] :
( ( ! [SY3384: $i] :
( ( ( c_append @ SV1188 @ ( c_List_Olist_OCons @ SV1501 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 )
!= ( c_append @ SV1877 @ ( c_List_Olist_OCons @ SY3384 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 ) )
| ( SV1188 = SV1877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7906]) ).
thf(8170,plain,
! [SV1878: $i,SV1733: $i,SV1502: $i,SV1189: $i] :
( ( ( ( c_Datatype__Universe_OAtom @ SV1189 @ SV1502 @ SV1733 )
!= ( c_Datatype__Universe_OAtom @ SV1878 @ SV1502 @ SV1733 ) )
| ( SV1189 = SV1878 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7907]) ).
thf(8171,plain,
! [SV1734: $i,SV1503: $i,SV1191: $i] :
( ( ( ( c_append @ SV1191 @ SV1503 @ SV1734 )
!= c_List_Olist_ONil )
= $true )
| ( ( SV1503 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7908]) ).
thf(8172,plain,
! [SV1879: $i,SV1735: $i,SV1504: $i,SV1192: $i] :
( ( ( ( c_Datatype__Universe_OIn1 @ SV1192 @ SV1504 @ SV1735 )
!= ( c_Datatype__Universe_OIn1 @ SV1879 @ SV1504 @ SV1735 ) )
| ( SV1192 = SV1879 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7909]) ).
thf(8173,plain,
! [SV1736: $i,SV1505: $i,SV1193: $i] :
( ( ( ( c_union @ SV1193 @ SV1505 @ SV1736 )
!= c_emptyset )
= $true )
| ( ( SV1505 = c_emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7910]) ).
thf(8174,plain,
! [SV1737: $i,SV1506: $i,SV1194: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1194 ) )
= $true )
| ( ( ( ( c_SetInterval_OlessThan @ SV1506 @ SV1194 )
!= ( c_SetInterval_OlessThan @ SV1737 @ SV1194 ) )
| ( SV1506 = SV1737 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7911]) ).
thf(8175,plain,
! [SV1880: $i,SV1738: $i,SV1507: $i,SV1195: $i] :
( ( ! [SY3385: $i,SY3386: $i] :
( ( ( c_Pair @ SV1195 @ SV1507 @ SV1738 @ SV1880 )
!= ( c_Pair @ SY3385 @ SY3386 @ SV1738 @ SV1880 ) )
| ( SV1195 = SY3385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7912]) ).
thf(8176,plain,
! [SV1739: $i,SV1508: $i,SV1196: $i] :
( ( c_List_Olist_ONil
= ( c_List_Olist_OCons @ SV1196 @ SV1508 @ SV1739 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7913]) ).
thf(8177,plain,
! [SV1509: $i,SV1197: $i] :
( ( ( ( c_Message_Omsg_OKey @ SV1197 )
= ( c_Message_Omsg_OKey @ SV1509 ) )
= $false )
| ( ( SV1197 = SV1509 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7914]) ).
thf(8178,plain,
! [SV1881: $i,SV1740: $i,SV1510: $i,SV1198: $i] :
( ( ( ( c_List_Ochar_OChar @ SV1198 @ SV1510 )
!= ( c_List_Ochar_OChar @ SV1740 @ SV1881 ) )
| ( SV1510 = SV1881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7915]) ).
thf(8179,plain,
! [SV1511: $i,SV1199: $i] :
( ( ( ( c_plus @ SV1199 @ SV1511 @ tc_nat )
= c_0 )
= $false )
| ( ( SV1511 = c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7916]) ).
thf(8180,plain,
! [SV1882: $i,SV1741: $i,SV1512: $i,SV1200: $i] :
( ( ! [SY3387: $i] :
( ( c_Datatype__Universe_OLeaf @ SV1200 @ SV1512 @ SV1741 )
!= ( c_Datatype__Universe_OScons @ SV1882 @ SY3387 @ SV1512 @ SV1741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7917]) ).
thf(8181,plain,
! [SV1742: $i,SV1513: $i,SV1201: $i] :
( ( ( c_List_Olist_ONil
!= ( c_append @ SV1201 @ SV1513 @ SV1742 ) )
= $true )
| ( ( SV1513 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7918]) ).
thf(8182,plain,
! [SV1883: $i,SV1743: $i,SV1514: $i,SV1202: $i] :
( ( ( ( c_append @ SV1202 @ SV1514 @ SV1743 )
!= ( c_append @ SV1202 @ SV1883 @ SV1743 ) )
| ( SV1514 = SV1883 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7919]) ).
thf(8183,plain,
! [SV1744: $i,SV1515: $i,SV1203: $i] :
( ( ( ( c_union @ SV1203 @ SV1515 @ SV1744 )
!= c_emptyset )
= $true )
| ( ( SV1203 = c_emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7920]) ).
thf(8184,plain,
! [SV1884: $i,SV1745: $i,SV1516: $i,SV1205: $i] :
( ( ( ( c_Datatype__Universe_OIn0 @ SV1205 @ SV1516 @ SV1745 )
!= ( c_Datatype__Universe_OIn0 @ SV1884 @ SV1516 @ SV1745 ) )
| ( SV1205 = SV1884 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7921]) ).
thf(8185,plain,
! [SV1885: $i,SV1746: $i,SV1517: $i,SV1206: $i] :
( ( ! [SY3388: $i,SY3389: $i] :
( ( ( c_Pair @ SV1206 @ SV1517 @ SV1746 @ SV1885 )
!= ( c_Pair @ SY3388 @ SY3389 @ SV1746 @ SV1885 ) )
| ( SV1517 = SY3389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7922]) ).
thf(8186,plain,
! [SV1886: $i,SV1747: $i,SV1518: $i,SV1207: $i] :
( ( ! [SY3390: $i] :
( ( c_Datatype__Universe_OAtom @ SV1207 @ SV1518 @ SV1747 )
!= ( c_Datatype__Universe_OScons @ SV1886 @ SY3390 @ SV1518 @ SV1747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7923]) ).
thf(8187,plain,
! [SV1887: $i,SV1748: $i,SV1519: $i,SV1209: $i] :
( ( ( ( c_List_Orev @ SV1209 @ SV1519 )
!= ( c_List_Olist_OCons @ SV1748 @ SV1887 @ SV1519 ) )
| ( SV1209
= ( c_append @ ( c_List_Orev @ SV1887 @ SV1519 ) @ ( c_List_Olist_OCons @ SV1748 @ c_List_Olist_ONil @ SV1519 ) @ SV1519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7924]) ).
thf(8188,plain,
! [SV1749: $i,SV1520: $i,SV1210: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1210 ) )
= $true )
| ( ( ( ( c_SetInterval_OatLeast @ SV1520 @ SV1210 )
!= ( c_SetInterval_OatLeast @ SV1749 @ SV1210 ) )
| ( SV1520 = SV1749 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7925]) ).
thf(8189,plain,
! [SV1750: $i,SV1521: $i,SV1211: $i] :
( ( ( ( c_uminus @ SV1211 @ ( tc_set @ SV1521 ) )
!= ( c_uminus @ SV1750 @ ( tc_set @ SV1521 ) ) )
= $true )
| ( ( SV1211 = SV1750 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7926]) ).
thf(8190,plain,
! [SV1888: $i,SV1751: $i,SV1522: $i,SV1212: $i] :
( ( ! [SY3391: $i] :
( ( c_Datatype__Universe_ONumb @ SV1212 @ SV1522 @ SV1751 )
!= ( c_Datatype__Universe_OScons @ SV1888 @ SY3391 @ SV1522 @ SV1751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7927]) ).
thf(8191,plain,
! [SV1889: $i,SV1752: $i,SV1523: $i,SV1213: $i] :
( ( ( ( c_insert @ SV1213 @ c_emptyset @ SV1523 )
!= ( c_insert @ SV1752 @ SV1889 @ SV1523 ) )
| ( SV1752 = SV1213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7928]) ).
thf(8192,plain,
! [SV1753: $i,SV1524: $i,SV1214: $i] :
( ( ( SV1214
!= ( c_append @ SV1524 @ SV1214 @ SV1753 ) )
= $true )
| ( ( SV1524 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7929]) ).
thf(8193,plain,
! [SV1525: $i,SV1215: $i] :
( ( ( ( c_Message_Oagent_OFriend @ SV1215 )
= ( c_Message_Oagent_OFriend @ SV1525 ) )
= $false )
| ( ( SV1215 = SV1525 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7930]) ).
thf(8194,plain,
! [SV1754: $i,SV1526: $i,SV1217: $i] :
( ( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ SV1217 @ SV1526 @ SV1754 ) )
= $true )
| ( ( SV1217 = c_emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7931]) ).
thf(8195,plain,
! [SV1755: $i,SV1527: $i,SV1218: $i] :
( ( ( c_List_Olist_ONil
!= ( c_append @ SV1218 @ SV1527 @ SV1755 ) )
= $true )
| ( ( SV1218 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7932]) ).
thf(8196,plain,
! [SV1756: $i,SV1529: $i,SV1220: $i] :
( ( ( ( c_append @ SV1220 @ SV1529 @ SV1756 )
!= SV1220 )
= $true )
| ( ( SV1529 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7934]) ).
thf(8197,plain,
! [SV1757: $i,SV1530: $i,SV1221: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1221 ) )
= $true )
| ( ( ( ( c_SetInterval_OgreaterThan @ SV1530 @ SV1221 )
!= ( c_SetInterval_OgreaterThan @ SV1757 @ SV1221 ) )
| ( SV1530 = SV1757 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7935]) ).
thf(8198,plain,
! [SV1890: $i,SV1758: $i,SV1531: $i,SV1222: $i] :
( ( ( ( c_Message_Omsg_OCrypt @ SV1222 @ SV1531 )
!= ( c_Message_Omsg_OCrypt @ SV1758 @ SV1890 ) )
| ( SV1531 = SV1890 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7936]) ).
thf(8199,plain,
! [SV1532: $i,SV1223: $i] :
( ( ( ( c_Message_Omsg_OAgent @ SV1223 )
= ( c_Message_Omsg_OAgent @ SV1532 ) )
= $false )
| ( ( SV1223 = SV1532 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7937]) ).
thf(8200,plain,
! [SV1759: $i,SV1533: $i,SV1224: $i] :
( ( ( ( c_Datatype_Ooption_OSome @ SV1224 @ SV1533 )
!= ( c_Datatype_Ooption_OSome @ SV1759 @ SV1533 ) )
= $true )
| ( ( SV1224 = SV1759 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7938]) ).
thf(8201,plain,
! [SV1534: $i,SV1225: $i] :
( ( ( ( c_Message_Omsg_ONonce @ SV1225 )
= ( c_Message_Omsg_ONonce @ SV1534 ) )
= $false )
| ( ( SV1225 = SV1534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7939]) ).
thf(8202,plain,
! [SV1760: $i,SV1535: $i,SV1226: $i] :
( ( ( ( c_append @ SV1226 @ SV1535 @ SV1760 )
!= SV1535 )
= $true )
| ( ( SV1226 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7940]) ).
thf(8203,plain,
! [SV1761: $i,SV1536: $i,SV1227: $i] :
( ( ( SV1227
!= ( c_append @ SV1227 @ SV1536 @ SV1761 ) )
= $true )
| ( ( SV1536 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7941]) ).
thf(8204,plain,
! [SV1537: $i,SV1228: $i] :
( ( ( ( c_Message_Omsg_ONumber @ SV1228 )
= ( c_Message_Omsg_ONumber @ SV1537 ) )
= $false )
| ( ( SV1228 = SV1537 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7942]) ).
thf(8205,plain,
! [SV1538: $i,SV1229: $i] :
( ( ( c_emptyset
= ( c_List_Oset @ SV1229 @ SV1538 ) )
= $false )
| ( ( SV1229 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7943]) ).
thf(8206,plain,
! [SV1762: $i,SV1539: $i,SV1230: $i] :
( ( ( ( c_insert @ SV1230 @ c_emptyset @ SV1539 )
!= ( c_insert @ SV1762 @ c_emptyset @ SV1539 ) )
= $true )
| ( ( SV1230 = SV1762 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7944]) ).
thf(8207,plain,
! [SV1540: $i,SV1231: $i] :
( ( ( ( c_Divides_Oop_Amod @ SV1231 @ SV1540 @ tc_nat )
= c_0 )
= $false )
| ( ( SV1231
= ( c_times @ SV1540 @ ( c_Main_Omod__eq__0D__dest__1 @ SV1540 @ SV1231 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7945]) ).
thf(8208,plain,
! [SV1891: $i,SV1763: $i,SV1541: $i,SV1232: $i] :
( ( ( c_Sum__Type_OInl @ SV1232 @ SV1541 @ SV1763 )
!= ( c_Sum__Type_OInr @ SV1891 @ SV1763 @ SV1541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7946]) ).
thf(8209,plain,
! [SV1542: $i,SV1233: $i] :
( ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ SV1233 @ SV1542 ) @ ( tc_List_Olist @ SV1542 ) )
= ( c_Nat_Osize @ SV1233 @ ( tc_List_Olist @ SV1542 ) ) )
= $false )
| ( ( ( c_List_Oremdups @ SV1233 @ SV1542 )
= SV1233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7947]) ).
thf(8210,plain,
! [SV1892: $i,SV1764: $i,SV1543: $i,SV1234: $i] :
( ( ! [SY3392: $i] :
( ( c_Datatype__Universe_OScons @ SV1234 @ SV1543 @ SV1764 @ SV1892 )
!= ( c_Datatype__Universe_OLeaf @ SY3392 @ SV1764 @ SV1892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7948]) ).
thf(8211,plain,
! [SV1893: $i,SV1765: $i,SV1544: $i,SV1235: $i] :
( ( ! [SY3393: $i] :
( ( ( c_List_Olist_OCons @ SV1235 @ SV1544 @ SV1765 )
!= ( c_List_Olist_OCons @ SV1893 @ SY3393 @ SV1765 ) )
| ( SV1235 = SV1893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7949]) ).
thf(8212,plain,
! [SV1545: $i,SV1236: $i] :
( ( ( ( c_Suc @ SV1236 )
= ( c_Suc @ SV1545 ) )
= $false )
| ( ( SV1236 = SV1545 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7950]) ).
thf(8213,plain,
! [SV1894: $i,SV1766: $i,SV1546: $i,SV1237: $i] :
( ( ( c_Datatype__Universe_ONumb @ SV1237 @ SV1546 @ SV1766 )
!= ( c_Datatype__Universe_OLeaf @ SV1894 @ SV1546 @ SV1766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7951]) ).
thf(8214,plain,
! [SV1767: $i,SV1547: $i,SV1238: $i] :
( ( ( c_List_Olist_OCons @ SV1238 @ SV1547 @ SV1767 )
= c_List_Olist_ONil )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7952]) ).
thf(8215,plain,
! [SV1548: $i,SV1239: $i] :
( ( ( ( c_plus @ SV1239 @ SV1548 @ tc_nat )
= c_0 )
= $false )
| ( ( SV1239 = c_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7953]) ).
thf(8216,plain,
! [SV1895: $i,SV1768: $i,SV1549: $i,SV1240: $i] :
( ( ( ( c_Sum__Type_OInl @ SV1240 @ SV1549 @ SV1768 )
!= ( c_Sum__Type_OInl @ SV1895 @ SV1549 @ SV1768 ) )
| ( SV1240 = SV1895 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7954]) ).
thf(8217,plain,
! [SV1896: $i,SV1769: $i,SV1550: $i,SV1241: $i] :
( ( ! [SY3394: $i,SY3395: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1241 @ SV1550 @ SV1769 @ SV1896 )
!= ( c_Datatype__Universe_OScons @ SY3394 @ SY3395 @ SV1769 @ SV1896 ) )
| ( SV1241 = SY3394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7955]) ).
thf(8218,plain,
! [SV1897: $i,SV1770: $i,SV1551: $i,SV1242: $i] :
( ( ( ( c_append @ SV1242 @ SV1551 @ SV1770 )
!= ( c_append @ SV1897 @ SV1551 @ SV1770 ) )
| ( SV1242 = SV1897 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7956]) ).
thf(8219,plain,
! [SV1552: $i,SV1243: $i] :
( ( ( c_List_Olist_ONil
= ( c_List_Orev @ SV1243 @ SV1552 ) )
= $false )
| ( ( SV1243 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7957]) ).
thf(8220,plain,
! [SV1898: $i,SV1771: $i,SV1553: $i,SV1244: $i] :
( ( ! [SY3396: $i] :
( ( c_Datatype__Universe_OScons @ SV1244 @ SV1553 @ SV1771 @ SV1898 )
!= ( c_Datatype__Universe_OAtom @ SY3396 @ SV1771 @ SV1898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7958]) ).
thf(8221,plain,
! [SV1899: $i,SV1772: $i,SV1554: $i,SV1245: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SV1245 @ SV1554 @ SV1772 )
!= ( c_Datatype__Universe_ONumb @ SV1899 @ SV1554 @ SV1772 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7959]) ).
thf(8222,plain,
! [SV1900: $i,SV1773: $i,SV1555: $i,SV1246: $i] :
( ( ( ( c_List_Ochar_OChar @ SV1246 @ SV1555 )
!= ( c_List_Ochar_OChar @ SV1773 @ SV1900 ) )
| ( SV1246 = SV1773 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7960]) ).
thf(8223,plain,
! [SV1774: $i,SV1556: $i,SV1247: $i] :
( ( ( ( c_append @ SV1247 @ SV1556 @ SV1774 )
!= c_List_Olist_ONil )
= $true )
| ( ( SV1247 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7961]) ).
thf(8224,plain,
! [SV1901: $i,SV1775: $i,SV1557: $i,SV1248: $i] :
( ( ! [SY3397: $i,SY3398: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1248 @ SV1557 @ SV1775 @ SV1901 )
!= ( c_Datatype__Universe_OScons @ SY3397 @ SY3398 @ SV1775 @ SV1901 ) )
| ( SV1557 = SY3398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7962]) ).
thf(8225,plain,
! [SV1776: $i,SV1558: $i,SV1249: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV1249 ) )
= $true )
| ( ( ( ( c_SetInterval_OatMost @ SV1558 @ SV1249 )
!= ( c_SetInterval_OatMost @ SV1776 @ SV1249 ) )
| ( SV1558 = SV1776 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7963]) ).
thf(8226,plain,
! [SV1559: $i,SV1250: $i] :
( ( ( ( c_Divides_Oop_Amod @ SV1250 @ SV1559 @ tc_IntDef_Oint )
= c_0 )
= $false )
| ( ( SV1250
= ( c_times @ SV1559 @ ( c_Main_Ozmod__eq__0D__dest__1 @ SV1559 @ SV1250 ) @ tc_IntDef_Oint ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7964]) ).
thf(8227,plain,
! [SV1777: $i,SV1560: $i,SV1251: $i] :
( ( ( ( c_List_Orev @ SV1251 @ SV1560 )
!= ( c_List_Orev @ SV1777 @ SV1560 ) )
= $true )
| ( ( SV1251 = SV1777 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7965]) ).
thf(8228,plain,
! [SV1902: $i,SV1778: $i,SV1561: $i,SV1252: $i] :
( ( ( ( c_Message_Omsg_OMPair @ SV1252 @ SV1561 )
!= ( c_Message_Omsg_OMPair @ SV1778 @ SV1902 ) )
| ( SV1561 = SV1902 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7966]) ).
thf(8229,plain,
! [SV1903: $i,SV1779: $i,SV1562: $i,SV1253: $i] :
( ( ( ( c_insert @ SV1253 @ c_emptyset @ SV1562 )
!= ( c_insert @ SV1779 @ SV1903 @ SV1562 ) )
| ( c_lessequals @ SV1903 @ ( c_insert @ SV1253 @ c_emptyset @ SV1562 ) @ ( tc_set @ SV1562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7967]) ).
thf(8230,plain,
! [SV1563: $i,SV1254: $i] :
( ( ( ( c_IntDef_Oint @ SV1254 )
= ( c_IntDef_Oint @ SV1563 ) )
= $false )
| ( ( SV1254 = SV1563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7968]) ).
thf(8231,plain,
! [SV1904: $i,SV1780: $i,SV1564: $i,SV1255: $i] :
( ( ( ( c_Sum__Type_OInr @ SV1255 @ SV1564 @ SV1780 )
!= ( c_Sum__Type_OInr @ SV1904 @ SV1564 @ SV1780 ) )
| ( SV1255 = SV1904 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7969]) ).
thf(8232,plain,
! [SV1905: $i,SV1781: $i,SV1565: $i,SV1256: $i] :
( ( ( ( c_insert @ SV1256 @ SV1565 @ SV1781 )
!= ( c_insert @ SV1905 @ c_emptyset @ SV1781 ) )
| ( c_lessequals @ SV1565 @ ( c_insert @ SV1905 @ c_emptyset @ SV1781 ) @ ( tc_set @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7970]) ).
thf(8233,plain,
! [SV1906: $i,SV1782: $i,SV1566: $i,SV1257: $i] :
( ( ( ( c_insert @ SV1257 @ SV1566 @ SV1782 )
!= ( c_insert @ SV1906 @ c_emptyset @ SV1782 ) )
| ( SV1257 = SV1906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7971]) ).
thf(8234,plain,
! [SV1907: $i,SV1783: $i,SV1567: $i,SV1258: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ ( c_Datatype__Universe_Odprod @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) ) )
| ( SV1
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( c_Main_OdprodE__2 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ SV1783 @ SV1907 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( c_Main_OdprodE__4 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ SV1783 @ SV1907 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7972]) ).
thf(8235,plain,
! [SV1908: $i,SV1784: $i,SV1568: $i,SV1259: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ ( c_Datatype__Universe_Odprod @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( c_Main_OdprodE__4 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) @ SV1568 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7973]) ).
thf(8236,plain,
! [SV1909: $i,SV1785: $i,SV1569: $i,SV1260: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( c_Main_OdprodE__3 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) @ SV1260 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7974]) ).
thf(8237,plain,
! [SV1910: $i,SV1786: $i,SV1570: $i,SV1261: $i,SV4: $i] :
( ( ! [SY3399: $i,SY3400: $i,SY3401: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SY3399 @ SY3400 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SY3401 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SY3399 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SY3400 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3401 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7975]) ).
thf(8238,plain,
! [SV1911: $i,SV1787: $i,SV1571: $i,SV1262: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SV1262 @ SV1571 @ SV1787 @ SV1911 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7976]) ).
thf(8239,plain,
! [SV1912: $i,SV1788: $i,SV1572: $i,SV1263: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SV1263 @ SV1572 @ SV1788 @ SV1912 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( c_Main_OdsumE__4 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) @ SV1572 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
| ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7977]) ).
thf(8240,plain,
! [SV1913: $i,SV1789: $i,SV1573: $i,SV1264: $i,SV7: $i] :
( ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1264 @ SV1573 @ SV1789 @ SV1913 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( c_Main_OdsumE__2 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) @ SV1264 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
| ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7978]) ).
thf(8241,plain,
! [SV1914: $i,SV1790: $i,SV1574: $i,SV1265: $i,SV8: $i] :
( ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1265 @ SV1574 @ SV1790 @ SV1914 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__2 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1265 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__4 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1574 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7979]) ).
thf(8242,plain,
! [SV1915: $i,SV1791: $i,SV1575: $i,SV1266: $i,SV9: $i] :
( ( ! [SY3402: $i] :
( ~ ( c_in @ ( c_Pair @ SV9 @ SV1266 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ SV1915 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SV1575 @ SV1791 ) @ ( c_Datatype__Universe_OIn0 @ SV1266 @ SV1575 @ SV1791 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1915 @ SY3402 @ SV1575 @ SV1791 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7980]) ).
thf(8243,plain,
! [SV1916: $i,SV1792: $i,SV1576: $i,SV1267: $i,SV10: $i] :
( ( ! [SY3403: $i] :
( ~ ( c_in @ ( c_Pair @ SV10 @ SV1267 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ SV1916 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SV1576 @ SV1792 ) @ ( c_Datatype__Universe_OIn1 @ SV1267 @ SV1576 @ SV1792 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ ( c_Datatype__Universe_Odsum @ SY3403 @ SV1916 @ SV1576 @ SV1792 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7981]) ).
thf(8244,plain,
! [SV1917: $i,SV1793: $i,SV1577: $i,SV1268: $i,SV11: $i] :
( ( ~ ( c_in @ SV11 @ ( c_Datatype__Universe_Ouprod @ SV1268 @ SV1577 @ SV1793 @ SV1917 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1793 @ SV1917 ) ) )
| ( SV11
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SV1917 ) @ ( c_Main_OuprodE__2 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SV1917 ) @ SV1793 @ SV1917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7982]) ).
thf(8245,plain,
! [SV1918: $i,SV1794: $i,SV1578: $i,SV1269: $i,SV12: $i] :
( ( ~ ( c_in @ SV12 @ ( c_Datatype__Universe_Ouprod @ SV1269 @ SV1578 @ SV1794 @ SV1918 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SV1918 ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ SV1269 @ SV1578 @ SV12 @ SV1794 @ SV1918 ) @ SV1578 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SV1918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7983]) ).
thf(8246,plain,
! [SV1919: $i,SV1795: $i,SV1579: $i,SV1270: $i,SV13: $i] :
( ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1270 @ SV1579 @ SV1795 @ SV1919 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SV1919 ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ SV1270 @ SV1579 @ SV13 @ SV1795 @ SV1919 ) @ SV1270 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SV1919 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7984]) ).
thf(8247,plain,
! [SV1920: $i,SV1796: $i,SV1580: $i,SV1271: $i,SV14: $i] :
( ( ! [SY3404: $i] :
( ~ ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ~ ( c_in @ SV1920 @ SY3404 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SV1920 @ SV14 @ SV1580 @ SV1796 ) @ ( c_Datatype__Universe_Ouprod @ SY3404 @ SV1271 @ SV1580 @ SV1796 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7985]) ).
thf(8248,plain,
! [SV1921: $i,SV1797: $i,SV1581: $i,SV1272: $i,SV15: $i] :
( ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SV1272 @ SV1581 @ SV1797 @ SV1921 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1797 @ SV1921 ) ) )
| ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1272 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) )
| ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1581 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7986]) ).
thf(8249,plain,
! [SV1922: $i,SV1798: $i,SV1582: $i,SV1273: $i,SV16: $i] :
( ( ~ ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SV1273 @ SV1582 @ SV1798 @ SV1922 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1582 @ SV16 @ SV1798 @ SV1922 ) @ SV1582 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) )
| ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1273 @ SV16 @ SV1798 @ SV1922 ) @ SV1798 @ SV1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7987]) ).
thf(8250,plain,
! [SV1923: $i,SV1799: $i,SV1583: $i,SV1274: $i,SV17: $i] :
( ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1274 @ SV1583 @ SV1799 @ SV1923 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1274 @ SV17 @ SV1799 @ SV1923 ) @ SV1274 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) )
| ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1583 @ SV17 @ SV1799 @ SV1923 ) @ SV1799 @ SV1923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7988]) ).
thf(8251,plain,
! [SV1924: $i,SV1800: $i,SV1584: $i,SV1275: $i,SV18: $i] :
( ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1275 @ SV1584 @ SV1800 @ SV1924 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
| ( c_in @ ( c_Main_OusumE__1 @ SV1275 @ SV18 @ SV1800 @ SV1924 ) @ SV1275 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1584 @ SV18 @ SV1800 @ SV1924 ) @ SV1584 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7989]) ).
thf(8252,plain,
! [SV1925: $i,SV1801: $i,SV1585: $i,SV1276: $i,SV19: $i] :
( ( ~ ( c_in @ SV19 @ SV1276 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn0 @ SV19 @ SV1585 @ SV1801 ) @ ( c_Datatype__Universe_Ousum @ SV1276 @ SV1925 @ SV1585 @ SV1801 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7990]) ).
thf(8253,plain,
! [SV1926: $i,SV1802: $i,SV1586: $i,SV1277: $i,SV20: $i] :
( ( ~ ( c_in @ SV20 @ SV1277 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) )
| ( c_in @ ( c_Datatype__Universe_OIn1 @ SV20 @ SV1586 @ SV1802 ) @ ( c_Datatype__Universe_Ousum @ SV1926 @ SV1277 @ SV1586 @ SV1802 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7991]) ).
thf(8254,plain,
! [SV1587: $i,SV1280: $i,SV26: $i] :
( ( ( c_in @ SV26 @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) )
= $false )
| ( ( c_in @ ( c_insert @ SV1587 @ SV26 @ SV1280 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7992]) ).
thf(8255,plain,
! [SV1588: $i,SV1281: $i,SV27: $i] :
( ( ( c_in @ SV27 @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) )
= $false )
| ( ( c_in @ ( c_inter @ SV27 @ SV1588 @ SV1281 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7993]) ).
thf(8256,plain,
! [SV1589: $i,SV1282: $i,SV28: $i] :
( ( ( c_in @ SV28 @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) )
= $false )
| ( ( c_in @ ( c_inter @ SV1589 @ SV28 @ SV1282 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7994]) ).
thf(8257,plain,
! [SV1283: $i,SV29: $i] :
( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV29 @ SV1283 ) @ SV29 @ ( tc_set @ SV1283 ) )
= $true )
| ( ( c_in @ ( c_Union @ SV29 @ SV1283 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1283 ) )
= $true )
| ( ( c_in @ SV29 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1283 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7995]) ).
thf(8258,plain,
! [SV1284: $i,SV30: $i] :
( ( ( ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) ) )
= $true )
| ( ( c_in @ ( c_Union @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) )
= $true )
| ( ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1284 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7996]) ).
thf(8259,plain,
! [SV1803: $i,SV1590: $i,SV1287: $i,SV33: $i] :
( ( ( ~ ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 ) )
= $true )
| ( ( ~ ( c_in @ SV1590 @ SV33 @ SV1287 )
| ~ ( c_in @ SV1803 @ SV33 @ SV1287 )
| ( SV1590 = SV1803 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7997]) ).
thf(8260,plain,
! [SV1804: $i,SV1591: $i,SV1294: $i,SV42: $i] :
( ( ( ~ ( c_in @ SV42 @ ( c_List_Olists @ SV1294 @ SV1591 ) @ ( tc_List_Olist @ SV1591 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1804 @ ( c_List_Oset @ SV42 @ SV1591 ) @ SV1591 )
| ( c_in @ SV1804 @ SV1294 @ SV1591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7998]) ).
thf(8261,plain,
! [SV1593: $i,SV1296: $i,SV44: $i] :
( ( ( c_in @ ( c_Main_Oin__listsI__1 @ SV44 @ SV1296 @ SV1593 ) @ SV44 @ SV1593 )
= $false )
| ( ( c_in @ SV1296 @ ( c_List_Olists @ SV44 @ SV1593 ) @ ( tc_List_Olist @ SV1593 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8000]) ).
thf(8262,plain,
! [SV1927: $i,SV1805: $i,SV1594: $i,SV1298: $i,SV46: $i] :
( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV46 @ SV1298 @ SV1594 ) @ SV1805 @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) @ ( c_List_Olistrel @ SV1927 @ SV1594 ) @ ( tc_prod @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) )
| ( SV1805
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SV1927 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ ( c_Main_Olistrel__Cons1__2 @ SV1927 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ SV1594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8001]) ).
thf(8263,plain,
! [SV1928: $i,SV1806: $i,SV1595: $i,SV1299: $i,SV47: $i] :
( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV47 @ SV1299 @ SV1595 ) @ SV1806 @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SV1928 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) )
| ( c_in @ ( c_Pair @ SV1299 @ ( c_Main_Olistrel__Cons1__2 @ SV1928 @ SV1806 @ SV47 @ SV1299 @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SV1928 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8002]) ).
thf(8264,plain,
! [SV1929: $i,SV1807: $i,SV1596: $i,SV1300: $i,SV48: $i] :
( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV48 @ SV1300 @ SV1596 ) @ SV1807 @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) @ ( c_List_Olistrel @ SV1929 @ SV1596 ) @ ( tc_prod @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) )
| ( c_in @ ( c_Pair @ SV48 @ ( c_Main_Olistrel__Cons1__1 @ SV1929 @ SV1807 @ SV48 @ SV1300 @ SV1596 ) @ SV1596 @ SV1596 ) @ SV1929 @ ( tc_prod @ SV1596 @ SV1596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8003]) ).
thf(8265,plain,
! [SV1930: $i,SV1808: $i,SV1597: $i,SV1301: $i,SV49: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV49 @ ( c_List_Olist_OCons @ SV1301 @ SV1597 @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) @ ( c_List_Olistrel @ SV1930 @ SV1808 ) @ ( tc_prod @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) )
| ( SV49
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SV1930 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ ( c_Main_Olistrel__Cons2__2 @ SV1930 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ SV1808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8004]) ).
thf(8266,plain,
! [SV1931: $i,SV1809: $i,SV1598: $i,SV1302: $i,SV50: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV50 @ ( c_List_Olist_OCons @ SV1302 @ SV1598 @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SV1931 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SV1931 @ SV50 @ SV1302 @ SV1598 @ SV1809 ) @ SV1598 @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SV1931 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8005]) ).
thf(8267,plain,
! [SV1932: $i,SV1810: $i,SV1599: $i,SV1303: $i,SV51: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV51 @ ( c_List_Olist_OCons @ SV1303 @ SV1599 @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) @ ( c_List_Olistrel @ SV1932 @ SV1810 ) @ ( tc_prod @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SV1932 @ SV51 @ SV1303 @ SV1599 @ SV1810 ) @ SV1303 @ SV1810 @ SV1810 ) @ SV1932 @ ( tc_prod @ SV1810 @ SV1810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8006]) ).
thf(8268,plain,
! [SV1600: $i,SV1304: $i,SV52: $i] :
( ( ( c_in @ ( c_Pair @ c_List_Olist_ONil @ SV52 @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) @ ( c_List_Olistrel @ SV1600 @ SV1304 ) @ ( tc_prod @ ( tc_List_Olist @ SV1304 ) @ ( tc_List_Olist @ SV1304 ) ) )
= $false )
| ( ( SV52 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8007]) ).
thf(8269,plain,
! [SV1601: $i,SV1305: $i,SV53: $i] :
( ( ( c_in @ ( c_Pair @ SV53 @ c_List_Olist_ONil @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) @ ( c_List_Olistrel @ SV1601 @ SV1305 ) @ ( tc_prod @ ( tc_List_Olist @ SV1305 ) @ ( tc_List_Olist @ SV1305 ) ) )
= $false )
| ( ( SV53 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8008]) ).
thf(8270,plain,
! [SV1811: $i,SV1602: $i,SV1306: $i,SV54: $i] :
( ( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV54 @ SV1306 @ SV1602 ) @ ( c_List_Olists @ SV1811 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) ) )
= $true )
| ( ( c_in @ SV1306 @ ( c_List_Olists @ SV1811 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8009]) ).
thf(8271,plain,
! [SV1812: $i,SV1603: $i,SV1307: $i,SV55: $i] :
( ( ( ~ ( c_in @ ( c_List_Olist_OCons @ SV55 @ SV1307 @ SV1603 ) @ ( c_List_Olists @ SV1812 @ SV1603 ) @ ( tc_List_Olist @ SV1603 ) ) )
= $true )
| ( ( c_in @ SV55 @ SV1812 @ SV1603 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8010]) ).
thf(8272,plain,
! [SV1813: $i,SV1604: $i,SV1308: $i,SV56: $i] :
( ( ( ~ ( c_in @ SV56 @ SV1308 @ SV1604 ) )
= $true )
| ( ( ~ ( c_in @ SV1813 @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) )
| ( c_in @ ( c_List_Olist_OCons @ SV56 @ SV1813 @ SV1604 ) @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8011]) ).
thf(8273,plain,
! [SV1814: $i,SV1605: $i,SV1313: $i,SV65: $i] :
( ( ( ~ ( c_in @ SV65 @ ( c_Relation_ODomain @ SV1313 @ SV1605 @ SV1814 ) @ SV1605 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV65 @ ( c_Main_ODomainE__1 @ SV65 @ SV1313 @ SV1605 @ SV1814 ) @ SV1605 @ SV1814 ) @ SV1313 @ ( tc_prod @ SV1605 @ SV1814 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8015]) ).
thf(8274,plain,
! [SV1933: $i,SV1815: $i,SV1606: $i,SV1314: $i,SV66: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV66 @ SV1314 @ SV1606 @ SV1815 ) @ SV1933 @ ( tc_prod @ SV1606 @ SV1815 ) )
| ( c_in @ SV66 @ ( c_Relation_ODomain @ SV1933 @ SV1606 @ SV1815 ) @ SV1606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8016]) ).
thf(8275,plain,
! [SV1934: $i,SV1816: $i,SV1607: $i,SV1316: $i,SV68: $i] :
( ( ~ ( c_in @ SV68 @ ( c_Relation_OImage @ SV1316 @ SV1607 @ SV1816 @ SV1934 ) @ SV1934 )
| ( c_in @ ( c_Main_OImageE__1 @ SV1607 @ SV68 @ SV1316 @ SV1816 @ SV1934 ) @ SV1607 @ SV1816 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8018]) ).
thf(8276,plain,
! [SV1935: $i,SV1817: $i,SV1608: $i,SV1317: $i,SV69: $i] :
( ( ~ ( c_in @ SV69 @ ( c_Relation_OImage @ SV1317 @ SV1608 @ SV1817 @ SV1935 ) @ SV1935 )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1608 @ SV69 @ SV1317 @ SV1817 @ SV1935 ) @ SV69 @ SV1817 @ SV1935 ) @ SV1317 @ ( tc_prod @ SV1817 @ SV1935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8019]) ).
thf(8277,plain,
! [SV1936: $i,SV1818: $i,SV1609: $i,SV1318: $i,SV70: $i] :
( ( ! [SY3405: $i] :
( ~ ( c_in @ SV70 @ SV1318 @ SV1609 )
| ~ ( c_in @ ( c_Pair @ SV70 @ SV1818 @ SV1609 @ SV1936 ) @ SY3405 @ ( tc_prod @ SV1609 @ SV1936 ) )
| ( c_in @ SV1818 @ ( c_Relation_OImage @ SY3405 @ SV1318 @ SV1609 @ SV1936 ) @ SV1936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8020]) ).
thf(8278,plain,
! [SV1819: $i,SV1610: $i,SV1319: $i,SV71: $i] :
( ( ( ~ ( c_in @ SV71 @ ( c_Relation_ORange @ SV1319 @ SV1610 @ SV1819 ) @ SV1819 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV71 @ SV1319 @ SV1819 @ SV1610 ) @ SV71 @ SV1610 @ SV1819 ) @ SV1319 @ ( tc_prod @ SV1610 @ SV1819 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8021]) ).
thf(8279,plain,
! [SV1937: $i,SV1820: $i,SV1611: $i,SV1320: $i,SV72: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV72 @ SV1320 @ SV1611 @ SV1820 ) @ SV1937 @ ( tc_prod @ SV1611 @ SV1820 ) )
| ( c_in @ SV1320 @ ( c_Relation_ORange @ SV1937 @ SV1611 @ SV1820 ) @ SV1820 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8022]) ).
thf(8280,plain,
! [SV1821: $i,SV1612: $i,SV1321: $i,SV73: $i] :
( ( ( ~ ( c_in @ SV73 @ ( c_Relation_Oconverse @ SV1321 @ SV1612 @ SV1821 ) @ ( tc_prod @ SV1821 @ SV1612 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1321 @ SV73 @ SV1612 @ SV1821 ) @ ( c_Main_OconverseE__2 @ SV1321 @ SV73 @ SV1612 @ SV1821 ) @ SV1612 @ SV1821 ) @ SV1321 @ ( tc_prod @ SV1612 @ SV1821 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8023]) ).
thf(8281,plain,
! [SV1822: $i,SV1613: $i,SV1322: $i,SV74: $i] :
( ( ( ~ ( c_in @ SV74 @ ( c_Relation_Oconverse @ SV1322 @ SV1613 @ SV1822 ) @ ( tc_prod @ SV1822 @ SV1613 ) ) )
= $true )
| ( ( SV74
= ( c_Pair @ ( c_Main_OconverseE__2 @ SV1322 @ SV74 @ SV1613 @ SV1822 ) @ ( c_Main_OconverseE__1 @ SV1322 @ SV74 @ SV1613 @ SV1822 ) @ SV1822 @ SV1613 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8024]) ).
thf(8282,plain,
! [SV1614: $i,SV1323: $i,SV75: $i] :
( ( ( c_in @ SV75 @ ( c_Relation_Odiag @ SV1323 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $false )
| ( ( SV75
= ( c_Pair @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SV1614 ) @ ( c_Main_OdiagE__1 @ SV1323 @ SV75 @ SV1614 ) @ SV1614 @ SV1614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8025]) ).
thf(8283,plain,
! [SV1615: $i,SV1324: $i,SV76: $i] :
( ( ( c_in @ SV76 @ ( c_Relation_Odiag @ SV1324 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $false )
| ( ( c_in @ ( c_Main_OdiagE__1 @ SV1324 @ SV76 @ SV1615 ) @ SV1324 @ SV1615 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8026]) ).
thf(8284,plain,
! [SV1616: $i,SV1325: $i,SV77: $i] :
( ( ( c_in @ SV77 @ SV1325 @ SV1616 )
= $false )
| ( ( c_in @ ( c_Pair @ SV77 @ SV77 @ SV1616 @ SV1616 ) @ ( c_Relation_Odiag @ SV1325 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8027]) ).
thf(8285,plain,
! [SV1938: $i,SV1823: $i,SV1617: $i,SV1326: $i,SV78: $i] :
( ( ! [SY3406: $i] :
( ~ ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SV1326 @ SV1617 @ SV1823 @ SV1938 @ SY3406 ) @ ( tc_prod @ SY3406 @ SV1938 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SY3406 ) @ ( c_Main_Orel__compE__3 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SY3406 ) @ SV1823 @ SV1938 ) @ SV1326 @ ( tc_prod @ SV1823 @ SV1938 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8028]) ).
thf(8286,plain,
! [SV1939: $i,SV1824: $i,SV1618: $i,SV1327: $i,SV79: $i] :
( ( ! [SY3407: $i] :
( ~ ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SV1327 @ SV1618 @ SV1824 @ SV1939 @ SY3407 ) @ ( tc_prod @ SY3407 @ SV1939 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SY3407 ) @ ( c_Main_Orel__compE__2 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SY3407 ) @ SY3407 @ SV1824 ) @ SV1618 @ ( tc_prod @ SY3407 @ SV1824 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8029]) ).
thf(8287,plain,
! [SV1940: $i,SV1825: $i,SV1619: $i,SV1328: $i,SV80: $i] :
( ( ! [SY3408: $i] :
( ~ ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SV1328 @ SV1619 @ SV1825 @ SV1940 @ SY3408 ) @ ( tc_prod @ SY3408 @ SV1940 ) )
| ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SY3408 ) @ ( c_Main_Orel__compE__3 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SY3408 ) @ SY3408 @ SV1940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8030]) ).
thf(8288,plain,
! [SV1941: $i,SV1826: $i,SV1620: $i,SV1329: $i,SV81: $i] :
( ( ! [SY3409: $i,SY3410: $i,SY3411: $i] :
( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) )
| ~ ( c_in @ ( c_Pair @ SY3409 @ SV81 @ SY3410 @ SV1620 ) @ SY3411 @ ( tc_prod @ SY3410 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SY3409 @ SV1329 @ SY3410 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SY3411 @ SV1620 @ SV1826 @ SY3410 ) @ ( tc_prod @ SY3410 @ SV1826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8031]) ).
thf(8289,plain,
! [SV1622: $i,SV1339: $i,SV93: $i] :
( ( ( c_in @ SV93 @ ( c_Main_OInterI__1 @ SV93 @ SV1339 @ SV1622 ) @ SV1622 )
= $false )
| ( ( c_in @ SV93 @ ( c_Inter @ SV1339 @ SV1622 ) @ SV1622 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8033]) ).
thf(8290,plain,
! [SV1623: $i,SV1341: $i,SV95: $i] :
( ( ( c_in @ SV95 @ ( c_Union @ SV1341 @ SV1623 ) @ SV1623 )
= $false )
| ( ( c_in @ ( c_Main_OUnionE__1 @ SV95 @ SV1341 @ SV1623 ) @ SV1341 @ ( tc_set @ SV1623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8034]) ).
thf(8291,plain,
! [SV1624: $i,SV1342: $i,SV96: $i] :
( ( ( c_in @ SV96 @ ( c_Union @ SV1342 @ SV1624 ) @ SV1624 )
= $false )
| ( ( c_in @ SV96 @ ( c_Main_OUnionE__1 @ SV96 @ SV1342 @ SV1624 ) @ SV1624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8035]) ).
thf(8292,plain,
! [SV1625: $i,SV1344: $i,SV98: $i] :
( ( ( c_less @ SV98 @ SV1344 @ ( tc_set @ SV1625 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1344 @ SV98 @ ( tc_set @ SV1625 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8036]) ).
thf(8293,plain,
! [SV1626: $i,SV1345: $i,SV99: $i] :
( ( ( c_less @ SV99 @ SV1345 @ ( tc_set @ SV1626 ) )
= $false )
| ( ( c_lessequals @ SV99 @ SV1345 @ ( tc_set @ SV1626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8037]) ).
thf(8294,plain,
! [SV1627: $i,SV1346: $i,SV100: $i] :
( ( ( c_lessequals @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) )
= $false )
| ( ( ( c_less @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) )
| ( SV100 = SV1346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8038]) ).
thf(8295,plain,
! [SV1628: $i,SV1347: $i,SV101: $i] :
( ( ( c_in @ SV101 @ ( c_insert @ SV1347 @ c_emptyset @ SV1628 ) @ SV1628 )
= $false )
| ( ( SV101 = SV1347 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8039]) ).
thf(8296,plain,
! [SV1827: $i,SV1629: $i,SV1349: $i,SV103: $i] :
( ( ( ~ ( c_in @ SV103 @ SV1349 @ SV1629 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1349 @ SV1827 @ ( tc_set @ SV1629 ) )
| ( c_in @ SV103 @ SV1827 @ SV1629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8040]) ).
thf(8297,plain,
! [SV1631: $i,SV1351: $i,SV105: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV105 @ SV1351 @ SV1631 ) @ SV1351 @ SV1631 )
= $false )
| ( ( c_lessequals @ SV105 @ SV1351 @ ( tc_set @ SV1631 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8042]) ).
thf(8298,plain,
! [SV1632: $i,SV1352: $i,SV106: $i] :
( ( ( c_lessequals @ SV106 @ SV1352 @ ( tc_set @ SV1632 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1352 @ SV106 @ ( tc_set @ SV1632 ) )
| ( SV1352 = SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8043]) ).
thf(8299,plain,
! [SV1942: $i,SV1828: $i,SV1633: $i,SV1354: $i,SV108: $i] :
( ( ~ ( c_in @ SV108 @ SV1354 @ SV1633 )
| ( c_in @ ( c_Sum__Type_OInl @ SV108 @ SV1633 @ SV1828 ) @ ( c_Sum__Type_OPlus @ SV1354 @ SV1942 @ SV1633 @ SV1828 ) @ ( tc_sum @ SV1633 @ SV1828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8044]) ).
thf(8300,plain,
! [SV1943: $i,SV1829: $i,SV1634: $i,SV1355: $i,SV109: $i] :
( ( ~ ( c_in @ SV109 @ SV1355 @ SV1634 )
| ( c_in @ ( c_Sum__Type_OInr @ SV109 @ SV1634 @ SV1829 ) @ ( c_Sum__Type_OPlus @ SV1943 @ SV1355 @ SV1829 @ SV1634 ) @ ( tc_sum @ SV1829 @ SV1634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8045]) ).
thf(8301,plain,
! [SV1944: $i,SV1830: $i,SV1635: $i,SV1356: $i,SV110: $i] :
( ( ~ ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SV1356 @ SV1635 @ SV1830 @ SV1944 ) @ ( tc_sum @ SV1830 @ SV1944 ) )
| ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1356 @ SV110 @ SV1830 @ SV1944 ) @ SV1830 @ SV1944 ) )
| ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1635 @ SV110 @ SV1944 @ SV1830 ) @ SV1944 @ SV1830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8046]) ).
thf(8302,plain,
! [SV1945: $i,SV1831: $i,SV1636: $i,SV1357: $i,SV111: $i] :
( ( ~ ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SV1357 @ SV1636 @ SV1831 @ SV1945 ) @ ( tc_sum @ SV1831 @ SV1945 ) )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1636 @ SV111 @ SV1945 @ SV1831 ) @ SV1636 @ SV1945 )
| ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1357 @ SV111 @ SV1831 @ SV1945 ) @ SV1831 @ SV1945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8047]) ).
thf(8303,plain,
! [SV1946: $i,SV1832: $i,SV1637: $i,SV1358: $i,SV112: $i] :
( ( ~ ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SV1358 @ SV1637 @ SV1832 @ SV1946 ) @ ( tc_sum @ SV1832 @ SV1946 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1358 @ SV112 @ SV1832 @ SV1946 ) @ SV1358 @ SV1832 )
| ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1637 @ SV112 @ SV1946 @ SV1832 ) @ SV1946 @ SV1832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8048]) ).
thf(8304,plain,
! [SV1947: $i,SV1833: $i,SV1638: $i,SV1359: $i,SV113: $i] :
( ( ~ ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SV1359 @ SV1638 @ SV1833 @ SV1947 ) @ ( tc_sum @ SV1833 @ SV1947 ) )
| ( c_in @ ( c_Main_OPlusE__1 @ SV1359 @ SV113 @ SV1833 @ SV1947 ) @ SV1359 @ SV1833 )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1638 @ SV113 @ SV1947 @ SV1833 ) @ SV1638 @ SV1947 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8049]) ).
thf(8305,plain,
! [SV1639: $i,SV1360: $i,SV114: $i] :
( ( ( c_in @ SV114 @ SV1360 @ ( tc_prod @ SV1639 @ SV1639 ) )
= $false )
| ( ( c_in @ SV114 @ ( c_Transitive__Closure_Ortrancl @ SV1360 @ SV1639 ) @ ( tc_prod @ SV1639 @ SV1639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8050]) ).
thf(8306,plain,
! [SV1834: $i,SV1641: $i,SV1362: $i,SV116: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ SV1834 @ ( tc_prod @ SV1641 @ SV1641 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ ( c_Transitive__Closure_Otrancl @ SV1834 @ SV1641 ) @ ( tc_prod @ SV1641 @ SV1641 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8051]) ).
thf(8307,plain,
! [SV1835: $i,SV1642: $i,SV1363: $i,SV117: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Otrancl @ SV1835 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Ortrancl @ SV1835 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8052]) ).
thf(8308,plain,
! [SV1836: $i,SV1643: $i,SV1364: $i,SV119: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV119 @ SV1364 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV1643 @ SV1836 )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1643 @ SV119 @ SV1836 @ SV1364 ) @ ( tc_prod @ SV1836 @ SV1364 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8053]) ).
thf(8309,plain,
! [SV1837: $i,SV1644: $i,SV1365: $i,SV120: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV120 @ SV1365 ) )
= $true )
| ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1644 @ SV1837 )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1644 @ SV120 @ SV1837 @ SV1365 ) @ ( tc_prod @ SV1837 @ SV1365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8054]) ).
thf(8310,plain,
! [SV122: $i,SV1366: $i] :
( ( ( class_Finite__Set_Ofinite @ SV1366 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV122 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV122 @ SV1366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8055]) ).
thf(8311,plain,
! [SV124: $i,SV1368: $i] :
( ( ( class_Finite__Set_Ofinite @ SV1368 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV124 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV124 @ SV1368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8056]) ).
thf(8312,plain,
! [SV130: $i,SV1369: $i] :
( ( ( class_Finite__Set_Ofinite @ SV1369 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite @ SV130 ) )
= $true )
| ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV130 @ SV1369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8057]) ).
thf(8313,plain,
! [SV1645: $i,SV1370: $i,SV1038: $i] :
( ( ( c_in @ SV1038 @ ( c_Datatype_Oo2s @ SV1370 @ SV1645 ) @ SV1645 )
= $false )
| ( ( SV1370
= ( c_Datatype_Ooption_OSome @ SV1038 @ SV1645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8058]) ).
thf(8314,plain,
! [SV1838: $i,SV1646: $i,SV1376: $i,SV1045: $i] :
( ( ( ~ ( c_in @ ( c_minus @ SV1045 @ ( c_insert @ SV1376 @ SV1646 @ SV1838 ) @ ( tc_set @ SV1838 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1838 ) ) )
= $true )
| ( ( c_in @ ( c_minus @ SV1045 @ SV1646 @ ( tc_set @ SV1838 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8059]) ).
thf(8315,plain,
! [SV1839: $i,SV1647: $i,SV1377: $i,SV1046: $i] :
( ( ( ~ ( c_in @ ( c_minus @ SV1046 @ SV1377 @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) ) )
= $true )
| ( ( c_in @ ( c_minus @ SV1046 @ ( c_insert @ SV1839 @ SV1377 @ SV1647 ) @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8060]) ).
thf(8316,plain,
! [SV1648: $i,SV1380: $i,SV1049: $i] :
( ( ( c_in @ ( c_union @ SV1049 @ SV1380 @ SV1648 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1648 ) )
= $false )
| ( ( c_in @ SV1049 @ c_Finite__Set_OFinites @ ( tc_set @ SV1648 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8063]) ).
thf(8317,plain,
! [SV1649: $i,SV1381: $i,SV1050: $i] :
( ( ( c_in @ ( c_union @ SV1050 @ SV1381 @ SV1649 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1649 ) )
= $false )
| ( ( c_in @ SV1381 @ c_Finite__Set_OFinites @ ( tc_set @ SV1649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8064]) ).
thf(8318,plain,
! [SV1650: $i,SV1382: $i,SV1051: $i] :
( ( ( c_in @ SV1051 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
= $false )
| ( ( ~ ( c_in @ SV1650 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
| ( c_in @ ( c_union @ SV1650 @ SV1051 @ SV1382 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8065]) ).
thf(8319,plain,
! [SV1651: $i,SV1383: $i,SV1052: $i] :
( ( ( c_in @ ( c_Relation_Oconverse @ SV1052 @ SV1383 @ SV1651 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1651 @ SV1383 ) ) )
= $false )
| ( ( c_in @ SV1052 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1383 @ SV1651 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8066]) ).
thf(8320,plain,
! [SV1652: $i,SV1384: $i,SV1053: $i] :
( ( ( c_in @ SV1053 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1384 @ SV1652 ) ) )
= $false )
| ( ( c_in @ ( c_Relation_Oconverse @ SV1053 @ SV1384 @ SV1652 ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ SV1652 @ SV1384 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8067]) ).
thf(8321,plain,
! [SV1653: $i,SV1385: $i,SV1054: $i] :
( ( ( c_Divides_Oop_Advd @ SV1054 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1385 @ SV1653 @ tc_nat @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( c_Divides_Oop_Advd @ SV1054 @ SV1385 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8068]) ).
thf(8322,plain,
! [SV1654: $i,SV1386: $i,SV1055: $i] :
( ( ( c_Divides_Oop_Advd @ SV1055 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1386 @ SV1654 @ tc_nat @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( c_Divides_Oop_Advd @ SV1055 @ SV1654 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8069]) ).
thf(8323,plain,
! [SV1655: $i,SV1387: $i,SV1056: $i] :
( ( ( c_Divides_Oop_Advd @ SV1056 @ SV1387 @ tc_nat )
= $false )
| ( ( ~ ( c_Divides_Oop_Advd @ SV1056 @ SV1655 @ tc_nat )
| ( c_Divides_Oop_Advd @ SV1056 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1655 @ SV1387 @ tc_nat @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8070]) ).
thf(8324,plain,
! [SV1840: $i,SV1658: $i,SV1394: $i,SV1066: $i] :
( ( ( ~ ( c_in @ ( c_append @ SV1066 @ SV1394 @ SV1658 ) @ ( c_List_Olists @ SV1840 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) ) )
= $true )
| ( ( c_in @ SV1066 @ ( c_List_Olists @ SV1840 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8077]) ).
thf(8325,plain,
! [SV1841: $i,SV1659: $i,SV1395: $i,SV1067: $i] :
( ( ( ~ ( c_in @ ( c_append @ SV1067 @ SV1395 @ SV1659 ) @ ( c_List_Olists @ SV1841 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) ) )
= $true )
| ( ( c_in @ SV1395 @ ( c_List_Olists @ SV1841 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8078]) ).
thf(8326,plain,
! [SV1842: $i,SV1660: $i,SV1396: $i,SV1068: $i] :
( ( ( ~ ( c_in @ SV1068 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1842 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
| ( c_in @ ( c_append @ SV1842 @ SV1068 @ SV1660 ) @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8079]) ).
thf(8327,plain,
! [SV1085: $i,SV1407: $i] :
( ( ( c_less @ c_0 @ SV1407 @ tc_nat )
= $true )
| ( ( c_less @ c_0 @ SV1085 @ tc_nat )
= $true )
| ( ( c_less @ c_0 @ ( c_plus @ SV1085 @ SV1407 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8084]) ).
thf(8328,plain,
! [SV1095: $i,SV1412: $i] :
( ( ( c_less @ SV1412 @ SV1412 @ SV1095 )
= $false )
| ( ( class_Orderings_Oorder @ SV1095 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8087]) ).
thf(8329,plain,
! [SV1948: $i,SV1843: $i,SV1662: $i,SV1414: $i,SV1097: $i] :
( ( ~ ( c_in @ SV1097 @ ( c_Relation_OImage @ SV1414 @ ( c_insert @ SV1662 @ c_emptyset @ SV1843 ) @ SV1843 @ SV1948 ) @ SV1948 )
| ( c_in @ ( c_Pair @ SV1662 @ SV1097 @ SV1843 @ SV1948 ) @ SV1414 @ ( tc_prod @ SV1843 @ SV1948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8088]) ).
thf(8330,plain,
! [SV1949: $i,SV1844: $i,SV1663: $i,SV1415: $i,SV1098: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV1098 @ SV1415 @ SV1663 @ SV1844 ) @ SV1949 @ ( tc_prod @ SV1663 @ SV1844 ) )
| ( c_in @ SV1415 @ ( c_Relation_OImage @ SV1949 @ ( c_insert @ SV1098 @ c_emptyset @ SV1663 ) @ SV1663 @ SV1844 ) @ SV1844 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8089]) ).
thf(8331,plain,
! [SV1950: $i,SV1845: $i,SV1664: $i,SV1416: $i,SV1099: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV1099 @ SV1416 @ SV1664 @ SV1845 ) @ ( c_Relation_Oconverse @ SV1950 @ SV1845 @ SV1664 ) @ ( tc_prod @ SV1664 @ SV1845 ) )
| ( c_in @ ( c_Pair @ SV1416 @ SV1099 @ SV1845 @ SV1664 ) @ SV1950 @ ( tc_prod @ SV1845 @ SV1664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8090]) ).
thf(8332,plain,
! [SV1951: $i,SV1846: $i,SV1665: $i,SV1417: $i,SV1100: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV1100 @ SV1417 @ SV1665 @ SV1846 ) @ SV1951 @ ( tc_prod @ SV1665 @ SV1846 ) )
| ( c_in @ ( c_Pair @ SV1417 @ SV1100 @ SV1846 @ SV1665 ) @ ( c_Relation_Oconverse @ SV1951 @ SV1665 @ SV1846 ) @ ( tc_prod @ SV1846 @ SV1665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8091]) ).
thf(8333,plain,
! [SV1666: $i,SV1418: $i,SV1101: $i] :
( ( ( c_in @ ( c_Pair @ SV1101 @ SV1418 @ SV1666 @ SV1666 ) @ c_Relation_OId @ ( tc_prod @ SV1666 @ SV1666 ) )
= $false )
| ( ( SV1101 = SV1418 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8092]) ).
thf(8334,plain,
! [SV1667: $i,SV1419: $i,SV1102: $i] :
( ( ( class_Orderings_Oord @ SV1102 )
= $false )
| ( ( ~ ( c_in @ SV1419 @ ( c_SetInterval_OatLeast @ SV1667 @ SV1102 ) @ SV1102 )
| ( c_lessequals @ SV1667 @ SV1419 @ SV1102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8093]) ).
thf(8335,plain,
! [SV1668: $i,SV1420: $i,SV1103: $i] :
( ( ( class_Orderings_Oord @ SV1103 )
= $false )
| ( ( ~ ( c_lessequals @ SV1420 @ SV1668 @ SV1103 )
| ( c_in @ SV1668 @ ( c_SetInterval_OatLeast @ SV1420 @ SV1103 ) @ SV1103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8094]) ).
thf(8336,plain,
! [SV1669: $i,SV1421: $i,SV1104: $i] :
( ( ( class_Orderings_Oorder @ SV1104 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1421 @ SV1104 ) @ ( c_SetInterval_OatLeast @ SV1669 @ SV1104 ) @ ( tc_set @ SV1104 ) )
| ( c_lessequals @ SV1669 @ SV1421 @ SV1104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8095]) ).
thf(8337,plain,
! [SV1670: $i,SV1422: $i,SV1105: $i] :
( ( ( class_Orderings_Oorder @ SV1105 )
= $false )
| ( ( ~ ( c_lessequals @ SV1422 @ SV1670 @ SV1105 )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1670 @ SV1105 ) @ ( c_SetInterval_OatLeast @ SV1422 @ SV1105 ) @ ( tc_set @ SV1105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8096]) ).
thf(8338,plain,
! [SV1671: $i,SV1423: $i,SV1106: $i] :
( ( ( class_Orderings_Oord @ SV1106 )
= $false )
| ( ( ~ ( c_in @ SV1423 @ ( c_SetInterval_OatMost @ SV1671 @ SV1106 ) @ SV1106 )
| ( c_lessequals @ SV1423 @ SV1671 @ SV1106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8097]) ).
thf(8339,plain,
! [SV1672: $i,SV1424: $i,SV1107: $i] :
( ( ( class_Orderings_Oord @ SV1107 )
= $false )
| ( ( ~ ( c_lessequals @ SV1424 @ SV1672 @ SV1107 )
| ( c_in @ SV1424 @ ( c_SetInterval_OatMost @ SV1672 @ SV1107 ) @ SV1107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8098]) ).
thf(8340,plain,
! [SV1673: $i,SV1425: $i,SV1108: $i] :
( ( ( class_Orderings_Oorder @ SV1108 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1425 @ SV1108 ) @ ( c_SetInterval_OatMost @ SV1673 @ SV1108 ) @ ( tc_set @ SV1108 ) )
| ( c_lessequals @ SV1425 @ SV1673 @ SV1108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8099]) ).
thf(8341,plain,
! [SV1674: $i,SV1426: $i,SV1109: $i] :
( ( ( class_Orderings_Oorder @ SV1109 )
= $false )
| ( ( ~ ( c_lessequals @ SV1426 @ SV1674 @ SV1109 )
| ( c_lessequals @ ( c_SetInterval_OatMost @ SV1426 @ SV1109 ) @ ( c_SetInterval_OatMost @ SV1674 @ SV1109 ) @ ( tc_set @ SV1109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8100]) ).
thf(8342,plain,
! [SV1675: $i,SV1427: $i,SV1110: $i] :
( ( ( class_Orderings_Oord @ SV1110 )
= $false )
| ( ( ~ ( c_in @ SV1427 @ ( c_SetInterval_OgreaterThan @ SV1675 @ SV1110 ) @ SV1110 )
| ( c_less @ SV1675 @ SV1427 @ SV1110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8101]) ).
thf(8343,plain,
! [SV1676: $i,SV1428: $i,SV1111: $i] :
( ( ( class_Orderings_Oord @ SV1111 )
= $false )
| ( ( ~ ( c_less @ SV1428 @ SV1676 @ SV1111 )
| ( c_in @ SV1676 @ ( c_SetInterval_OgreaterThan @ SV1428 @ SV1111 ) @ SV1111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8102]) ).
thf(8344,plain,
! [SV1677: $i,SV1429: $i,SV1112: $i] :
( ( ( class_Orderings_Olinorder @ SV1112 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1429 @ SV1112 ) @ ( c_SetInterval_OgreaterThan @ SV1677 @ SV1112 ) @ ( tc_set @ SV1112 ) )
| ( c_lessequals @ SV1677 @ SV1429 @ SV1112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8103]) ).
thf(8345,plain,
! [SV1678: $i,SV1430: $i,SV1113: $i] :
( ( ( class_Orderings_Olinorder @ SV1113 )
= $false )
| ( ( ~ ( c_lessequals @ SV1430 @ SV1678 @ SV1113 )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1678 @ SV1113 ) @ ( c_SetInterval_OgreaterThan @ SV1430 @ SV1113 ) @ ( tc_set @ SV1113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8104]) ).
thf(8346,plain,
! [SV1679: $i,SV1431: $i,SV1114: $i] :
( ( ( class_Orderings_Oord @ SV1114 )
= $false )
| ( ( ~ ( c_in @ SV1431 @ ( c_SetInterval_OlessThan @ SV1679 @ SV1114 ) @ SV1114 )
| ( c_less @ SV1431 @ SV1679 @ SV1114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8105]) ).
thf(8347,plain,
! [SV1680: $i,SV1432: $i,SV1115: $i] :
( ( ( class_Orderings_Oord @ SV1115 )
= $false )
| ( ( ~ ( c_less @ SV1432 @ SV1680 @ SV1115 )
| ( c_in @ SV1432 @ ( c_SetInterval_OlessThan @ SV1680 @ SV1115 ) @ SV1115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8106]) ).
thf(8348,plain,
! [SV1681: $i,SV1433: $i,SV1116: $i] :
( ( ( class_Orderings_Olinorder @ SV1116 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1433 @ SV1116 ) @ ( c_SetInterval_OlessThan @ SV1681 @ SV1116 ) @ ( tc_set @ SV1116 ) )
| ( c_lessequals @ SV1433 @ SV1681 @ SV1116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8107]) ).
thf(8349,plain,
! [SV1682: $i,SV1434: $i,SV1117: $i] :
( ( ( class_Orderings_Olinorder @ SV1117 )
= $false )
| ( ( ~ ( c_lessequals @ SV1434 @ SV1682 @ SV1117 )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1434 @ SV1117 ) @ ( c_SetInterval_OlessThan @ SV1682 @ SV1117 ) @ ( tc_set @ SV1117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8108]) ).
thf(8350,plain,
! [SV1683: $i,SV1435: $i,SV1118: $i] :
( ( ( c_in @ SV1118 @ SV1435 @ SV1683 )
= $false )
| ( ( ~ ( c_in @ SV1118 @ ( c_uminus @ SV1435 @ ( tc_set @ SV1683 ) ) @ SV1683 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8109]) ).
thf(8351,plain,
! [SV1685: $i,SV1437: $i,SV1120: $i] :
( ( ( c_lessequals @ ( c_uminus @ SV1120 @ ( tc_set @ SV1437 ) ) @ ( c_uminus @ SV1685 @ ( tc_set @ SV1437 ) ) @ ( tc_set @ SV1437 ) )
= $false )
| ( ( c_lessequals @ SV1685 @ SV1120 @ ( tc_set @ SV1437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8111]) ).
thf(8352,plain,
! [SV1686: $i,SV1438: $i,SV1121: $i] :
( ( ( c_lessequals @ SV1121 @ SV1438 @ ( tc_set @ SV1686 ) )
= $false )
| ( ( c_lessequals @ ( c_uminus @ SV1438 @ ( tc_set @ SV1686 ) ) @ ( c_uminus @ SV1121 @ ( tc_set @ SV1686 ) ) @ ( tc_set @ SV1686 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8112]) ).
thf(8353,plain,
! [SV1847: $i,SV1687: $i,SV1439: $i,SV1122: $i] :
( ( ( ~ ( c_in @ SV1122 @ SV1439 @ SV1687 ) )
= $true )
| ( ( ~ ( c_in @ SV1122 @ ( c_minus @ SV1847 @ SV1439 @ ( tc_set @ SV1687 ) ) @ SV1687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8113]) ).
thf(8354,plain,
! [SV1848: $i,SV1688: $i,SV1440: $i,SV1123: $i] :
( ( ( ~ ( c_in @ SV1123 @ ( c_minus @ SV1440 @ SV1688 @ ( tc_set @ SV1848 ) ) @ SV1848 ) )
= $true )
| ( ( c_in @ SV1123 @ SV1440 @ SV1848 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8114]) ).
thf(8355,plain,
! [SV1849: $i,SV1689: $i,SV1441: $i,SV1124: $i] :
( ( ( ~ ( c_in @ SV1124 @ SV1441 @ SV1689 ) )
= $true )
| ( ( ( c_in @ SV1124 @ SV1849 @ SV1689 )
| ( c_in @ SV1124 @ ( c_minus @ SV1441 @ SV1849 @ ( tc_set @ SV1689 ) ) @ SV1689 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8115]) ).
thf(8356,plain,
! [SV1850: $i,SV1690: $i,SV1442: $i,SV1125: $i] :
( ( ( ~ ( c_in @ SV1125 @ ( c_inter @ SV1442 @ SV1690 @ SV1850 ) @ SV1850 ) )
= $true )
| ( ( c_in @ SV1125 @ SV1690 @ SV1850 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8116]) ).
thf(8357,plain,
! [SV1851: $i,SV1691: $i,SV1443: $i,SV1126: $i] :
( ( ( ~ ( c_in @ SV1126 @ ( c_inter @ SV1443 @ SV1691 @ SV1851 ) @ SV1851 ) )
= $true )
| ( ( c_in @ SV1126 @ SV1443 @ SV1851 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8117]) ).
thf(8358,plain,
! [SV1852: $i,SV1692: $i,SV1444: $i,SV1127: $i] :
( ( ( ~ ( c_in @ SV1127 @ SV1444 @ SV1692 ) )
= $true )
| ( ( ~ ( c_in @ SV1127 @ SV1852 @ SV1692 )
| ( c_in @ SV1127 @ ( c_inter @ SV1852 @ SV1444 @ SV1692 ) @ SV1692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8118]) ).
thf(8359,plain,
! [SV1853: $i,SV1693: $i,SV1445: $i,SV1128: $i] :
( ( ( ~ ( c_in @ SV1128 @ SV1445 @ ( tc_set @ SV1693 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1853 @ ( c_Inter @ SV1445 @ SV1693 ) @ SV1693 )
| ( c_in @ SV1853 @ SV1128 @ SV1693 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8119]) ).
thf(8360,plain,
! [SV1694: $i,SV1446: $i,SV1129: $i] :
( ( ( c_in @ SV1129 @ ( c_Pow @ SV1446 @ SV1694 ) @ ( tc_set @ SV1694 ) )
= $false )
| ( ( c_lessequals @ SV1129 @ SV1446 @ ( tc_set @ SV1694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8120]) ).
thf(8361,plain,
! [SV1695: $i,SV1447: $i,SV1130: $i] :
( ( ( c_lessequals @ SV1130 @ SV1447 @ ( tc_set @ SV1695 ) )
= $false )
| ( ( c_in @ SV1130 @ ( c_Pow @ SV1447 @ SV1695 ) @ ( tc_set @ SV1695 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8121]) ).
thf(8362,plain,
! [SV1854: $i,SV1696: $i,SV1448: $i,SV1131: $i] :
( ( ( ~ ( c_in @ SV1131 @ SV1448 @ SV1696 ) )
= $true )
| ( ( c_in @ SV1131 @ ( c_union @ SV1854 @ SV1448 @ SV1696 ) @ SV1696 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8122]) ).
thf(8363,plain,
! [SV1855: $i,SV1697: $i,SV1449: $i,SV1132: $i] :
( ( ( ~ ( c_in @ SV1132 @ SV1449 @ SV1697 ) )
= $true )
| ( ( c_in @ SV1132 @ ( c_union @ SV1449 @ SV1855 @ SV1697 ) @ SV1697 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8123]) ).
thf(8364,plain,
! [SV1856: $i,SV1698: $i,SV1450: $i,SV1133: $i] :
( ( ( ~ ( c_in @ SV1133 @ ( c_union @ SV1450 @ SV1698 @ SV1856 ) @ SV1856 ) )
= $true )
| ( ( ( c_in @ SV1133 @ SV1698 @ SV1856 )
| ( c_in @ SV1133 @ SV1450 @ SV1856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8124]) ).
thf(8365,plain,
! [SV1857: $i,SV1699: $i,SV1451: $i,SV1135: $i] :
( ( ( ~ ( c_in @ SV1135 @ SV1451 @ SV1699 ) )
= $true )
| ( ( ~ ( c_in @ SV1451 @ SV1857 @ ( tc_set @ SV1699 ) )
| ( c_in @ SV1135 @ ( c_Union @ SV1857 @ SV1699 ) @ SV1699 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8125]) ).
thf(8366,plain,
! [SV1858: $i,SV1700: $i,SV1453: $i,SV1137: $i] :
( ( ( ~ ( c_in @ SV1137 @ SV1453 @ SV1700 ) )
= $true )
| ( ( c_in @ SV1137 @ ( c_insert @ SV1858 @ SV1453 @ SV1700 ) @ SV1700 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8126]) ).
thf(8367,plain,
! [SV1859: $i,SV1702: $i,SV1455: $i,SV1139: $i] :
( ( ( ~ ( c_in @ SV1139 @ ( c_insert @ SV1455 @ SV1702 @ SV1859 ) @ SV1859 ) )
= $true )
| ( ( ( c_in @ SV1139 @ SV1702 @ SV1859 )
| ( SV1139 = SV1455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8127]) ).
thf(8368,plain,
! [SV1703: $i,SV1457: $i,SV1141: $i] :
( ( ( c_lessequals @ SV1141 @ ( c_insert @ SV1457 @ c_emptyset @ SV1703 ) @ ( tc_set @ SV1703 ) )
= $false )
| ( ( ( c_insert @ SV1457 @ SV1141 @ SV1703 )
= ( c_insert @ SV1457 @ c_emptyset @ SV1703 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8128]) ).
thf(8369,plain,
! [SV1704: $i,SV1458: $i,SV1142: $i] :
( ( ( c_lessequals @ SV1142 @ ( c_insert @ SV1458 @ c_emptyset @ SV1704 ) @ ( tc_set @ SV1704 ) )
= $false )
| ( ( ( c_insert @ SV1458 @ c_emptyset @ SV1704 )
= ( c_insert @ SV1458 @ SV1142 @ SV1704 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8129]) ).
thf(8370,plain,
! [SV1860: $i,SV1705: $i,SV1461: $i,SV1145: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1145 @ SV1461 @ SV1705 @ SV1705 ) @ SV1860 @ ( tc_prod @ SV1705 @ SV1705 ) ) @ SV1705 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Oacyclic @ SV1860 @ SV1705 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8132]) ).
thf(8371,plain,
! [SV1861: $i,SV1706: $i,SV1462: $i,SV1146: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1146 @ SV1462 @ SV1706 @ SV1706 ) @ SV1861 @ ( tc_prod @ SV1706 @ SV1706 ) ) @ SV1706 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1462 @ SV1146 @ SV1706 @ SV1706 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1706 ) @ ( tc_prod @ SV1706 @ SV1706 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8133]) ).
thf(8372,plain,
! [SV1862: $i,SV1707: $i,SV1463: $i,SV1147: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Oacyclic @ SV1147 @ SV1463 ) )
= $true )
| ( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1707 @ SV1862 @ SV1463 @ SV1463 ) @ SV1147 @ ( tc_prod @ SV1463 @ SV1463 ) ) @ SV1463 )
| ( c_in @ ( c_Pair @ SV1862 @ SV1707 @ SV1463 @ SV1463 ) @ ( c_Transitive__Closure_Ortrancl @ SV1147 @ SV1463 ) @ ( tc_prod @ SV1463 @ SV1463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8134]) ).
thf(8373,plain,
! [SV1863: $i,SV1708: $i,SV1464: $i,SV1148: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1148 @ SV1464 @ SV1708 @ SV1708 ) @ SV1863 @ ( tc_prod @ SV1708 @ SV1708 ) ) @ SV1708 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Owf @ SV1863 @ SV1708 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8135]) ).
thf(8374,plain,
! [SV1864: $i,SV1709: $i,SV1465: $i,SV1149: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1149 @ SV1465 @ SV1709 @ SV1709 ) @ SV1864 @ ( tc_prod @ SV1709 @ SV1709 ) ) @ SV1709 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1465 @ SV1149 @ SV1709 @ SV1709 ) @ ( c_Transitive__Closure_Ortrancl @ SV1864 @ SV1709 ) @ ( tc_prod @ SV1709 @ SV1709 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8136]) ).
thf(8375,plain,
! [SV1865: $i,SV1710: $i,SV1466: $i,SV1150: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1150 @ SV1466 ) )
= $true )
| ( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1710 @ SV1865 @ SV1466 @ SV1466 ) @ SV1150 @ ( tc_prod @ SV1466 @ SV1466 ) ) @ SV1466 )
| ( c_in @ ( c_Pair @ SV1865 @ SV1710 @ SV1466 @ SV1466 ) @ ( c_Transitive__Closure_Ortrancl @ SV1150 @ SV1466 ) @ ( tc_prod @ SV1466 @ SV1466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8137]) ).
thf(8376,plain,
! [SV1711: $i,SV1469: $i,SV1153: $i] :
( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1153 @ SV1469 ) @ ( c_Message_Oanalz @ SV1711 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1469 @ ( c_Message_Oanalz @ SV1711 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8140]) ).
thf(8377,plain,
! [SV1712: $i,SV1470: $i,SV1154: $i] :
( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1154 @ SV1470 ) @ ( c_Message_Oanalz @ SV1712 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1154 @ ( c_Message_Oanalz @ SV1712 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8141]) ).
thf(8378,plain,
! [SV1713: $i,SV1471: $i,SV1155: $i] :
( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1155 @ SV1471 ) @ ( c_Message_Oparts @ SV1713 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1471 @ ( c_Message_Oparts @ SV1713 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8142]) ).
thf(8379,plain,
! [SV1714: $i,SV1472: $i,SV1156: $i] :
( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1156 @ SV1472 ) @ ( c_Message_Oparts @ SV1714 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1156 @ ( c_Message_Oparts @ SV1714 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8143]) ).
thf(8380,plain,
! [SV1715: $i,SV1473: $i,SV1157: $i] :
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1157 @ SV1473 ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1157 ) ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
| ( c_in @ SV1473 @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8144]) ).
thf(8381,plain,
! [SV1716: $i,SV1477: $i,SV1161: $i] :
( ( ( c_in @ SV1161 @ ( c_Message_Oparts @ ( c_union @ SV1477 @ SV1716 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1716 ) @ tc_Message_Omsg )
| ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1477 ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8148]) ).
thf(8382,plain,
! [SV1717: $i,SV1478: $i,SV1162: $i] :
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1162 @ SV1478 ) @ ( c_Message_Oparts @ SV1717 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1478 @ ( c_Message_Oparts @ SV1717 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8149]) ).
thf(8383,plain,
! [SV1866: $i,SV1720: $i,SV1483: $i,SV1168: $i] :
( ( ( ~ ( c_lessequals @ SV1168 @ SV1483 @ ( tc_set @ SV1720 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1866 @ SV1168 @ ( tc_set @ SV1720 ) )
| ( c_lessequals @ SV1866 @ SV1483 @ ( tc_set @ SV1720 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8152]) ).
thf(8384,plain,
! [SV1867: $i,SV1721: $i,SV1484: $i,SV1169: $i] :
( ( ( c_Datatype__Universe_OIn0 @ SV1169 @ SV1484 @ SV1721 )
= ( c_Datatype__Universe_OIn1 @ SV1867 @ SV1484 @ SV1721 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8153]) ).
thf(8385,plain,
! [SV1868: $i,SV1722: $i,SV1485: $i,SV1170: $i] :
( ( ( ( c_Message_Omsg_OCrypt @ SV1170 @ SV1485 )
!= ( c_Message_Omsg_OCrypt @ SV1722 @ SV1868 ) )
= $true )
| ( ( SV1170 = SV1722 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8154]) ).
thf(8386,plain,
! [SV1952: $i,SV1869: $i,SV1723: $i,SV1487: $i,SV1172: $i] :
( ( ( ( c_append @ SV1172 @ ( c_List_Olist_OCons @ SV1487 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 )
!= ( c_append @ SV1869 @ ( c_List_Olist_OCons @ SV1952 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 ) )
| ( SV1487 = SV1952 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8156]) ).
thf(8387,plain,
! [SV1953: $i,SV1870: $i,SV1724: $i,SV1488: $i,SV1173: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1173 @ SV1488 @ SV1724 @ SV1870 )
!= ( c_Datatype__Universe_ONumb @ SV1953 @ SV1724 @ SV1870 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8157]) ).
thf(8388,plain,
! [SV1871: $i,SV1725: $i,SV1491: $i,SV1176: $i] :
( ( ( ( c_Datatype__Universe_OLeaf @ SV1176 @ SV1491 @ SV1725 )
!= ( c_Datatype__Universe_OLeaf @ SV1871 @ SV1491 @ SV1725 ) )
= $true )
| ( ( SV1176 = SV1871 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8159]) ).
thf(8389,plain,
! [SV1872: $i,SV1726: $i,SV1492: $i,SV1177: $i] :
( ( ( c_Datatype__Universe_OIn1 @ SV1177 @ SV1492 @ SV1726 )
= ( c_Datatype__Universe_OIn0 @ SV1872 @ SV1492 @ SV1726 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8160]) ).
thf(8390,plain,
! [SV1873: $i,SV1727: $i,SV1494: $i,SV1180: $i] :
( ( ( ( c_Datatype__Universe_ONumb @ SV1180 @ SV1494 @ SV1727 )
!= ( c_Datatype__Universe_ONumb @ SV1873 @ SV1494 @ SV1727 ) )
= $true )
| ( ( SV1180 = SV1873 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8162]) ).
thf(8391,plain,
! [SV1728: $i,SV1495: $i,SV1182: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ SV1182 @ SV1495 @ SV1728 )
= c_emptyset )
= $false )
| ( ( SV1182 = c_emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8163]) ).
thf(8392,plain,
! [SV1874: $i,SV1729: $i,SV1497: $i,SV1184: $i] :
( ( ( ( c_Message_Omsg_OMPair @ SV1184 @ SV1497 )
!= ( c_Message_Omsg_OMPair @ SV1729 @ SV1874 ) )
= $true )
| ( ( SV1184 = SV1729 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8165]) ).
thf(8393,plain,
! [SV1954: $i,SV1875: $i,SV1730: $i,SV1498: $i,SV1185: $i] :
( ( ( ( c_List_Olist_OCons @ SV1185 @ SV1498 @ SV1730 )
!= ( c_List_Olist_OCons @ SV1875 @ SV1954 @ SV1730 ) )
| ( SV1498 = SV1954 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8166]) ).
thf(8394,plain,
! [SV1876: $i,SV1731: $i,SV1499: $i,SV1186: $i] :
( ( ( c_Sum__Type_OInr @ SV1186 @ SV1499 @ SV1731 )
= ( c_Sum__Type_OInl @ SV1876 @ SV1731 @ SV1499 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8167]) ).
thf(8395,plain,
! [SV1955: $i,SV1877: $i,SV1732: $i,SV1501: $i,SV1188: $i] :
( ( ( ( c_append @ SV1188 @ ( c_List_Olist_OCons @ SV1501 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 )
!= ( c_append @ SV1877 @ ( c_List_Olist_OCons @ SV1955 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 ) )
| ( SV1188 = SV1877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8169]) ).
thf(8396,plain,
! [SV1878: $i,SV1733: $i,SV1502: $i,SV1189: $i] :
( ( ( ( c_Datatype__Universe_OAtom @ SV1189 @ SV1502 @ SV1733 )
!= ( c_Datatype__Universe_OAtom @ SV1878 @ SV1502 @ SV1733 ) )
= $true )
| ( ( SV1189 = SV1878 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8170]) ).
thf(8397,plain,
! [SV1734: $i,SV1503: $i,SV1191: $i] :
( ( ( ( c_append @ SV1191 @ SV1503 @ SV1734 )
= c_List_Olist_ONil )
= $false )
| ( ( SV1503 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8171]) ).
thf(8398,plain,
! [SV1879: $i,SV1735: $i,SV1504: $i,SV1192: $i] :
( ( ( ( c_Datatype__Universe_OIn1 @ SV1192 @ SV1504 @ SV1735 )
!= ( c_Datatype__Universe_OIn1 @ SV1879 @ SV1504 @ SV1735 ) )
= $true )
| ( ( SV1192 = SV1879 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8172]) ).
thf(8399,plain,
! [SV1736: $i,SV1505: $i,SV1193: $i] :
( ( ( ( c_union @ SV1193 @ SV1505 @ SV1736 )
= c_emptyset )
= $false )
| ( ( SV1505 = c_emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8173]) ).
thf(8400,plain,
! [SV1737: $i,SV1506: $i,SV1194: $i] :
( ( ( class_Orderings_Olinorder @ SV1194 )
= $false )
| ( ( ( ( c_SetInterval_OlessThan @ SV1506 @ SV1194 )
!= ( c_SetInterval_OlessThan @ SV1737 @ SV1194 ) )
| ( SV1506 = SV1737 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8174]) ).
thf(8401,plain,
! [SV1956: $i,SV1880: $i,SV1738: $i,SV1507: $i,SV1195: $i] :
( ( ! [SY3412: $i] :
( ( ( c_Pair @ SV1195 @ SV1507 @ SV1738 @ SV1880 )
!= ( c_Pair @ SV1956 @ SY3412 @ SV1738 @ SV1880 ) )
| ( SV1195 = SV1956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8175]) ).
thf(8402,plain,
! [SV1881: $i,SV1740: $i,SV1510: $i,SV1198: $i] :
( ( ( ( c_List_Ochar_OChar @ SV1198 @ SV1510 )
!= ( c_List_Ochar_OChar @ SV1740 @ SV1881 ) )
= $true )
| ( ( SV1510 = SV1881 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8178]) ).
thf(8403,plain,
! [SV1957: $i,SV1882: $i,SV1741: $i,SV1512: $i,SV1200: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SV1200 @ SV1512 @ SV1741 )
!= ( c_Datatype__Universe_OScons @ SV1882 @ SV1957 @ SV1512 @ SV1741 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8180]) ).
thf(8404,plain,
! [SV1742: $i,SV1513: $i,SV1201: $i] :
( ( ( c_List_Olist_ONil
= ( c_append @ SV1201 @ SV1513 @ SV1742 ) )
= $false )
| ( ( SV1513 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8181]) ).
thf(8405,plain,
! [SV1883: $i,SV1743: $i,SV1514: $i,SV1202: $i] :
( ( ( ( c_append @ SV1202 @ SV1514 @ SV1743 )
!= ( c_append @ SV1202 @ SV1883 @ SV1743 ) )
= $true )
| ( ( SV1514 = SV1883 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8182]) ).
thf(8406,plain,
! [SV1744: $i,SV1515: $i,SV1203: $i] :
( ( ( ( c_union @ SV1203 @ SV1515 @ SV1744 )
= c_emptyset )
= $false )
| ( ( SV1203 = c_emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8183]) ).
thf(8407,plain,
! [SV1884: $i,SV1745: $i,SV1516: $i,SV1205: $i] :
( ( ( ( c_Datatype__Universe_OIn0 @ SV1205 @ SV1516 @ SV1745 )
!= ( c_Datatype__Universe_OIn0 @ SV1884 @ SV1516 @ SV1745 ) )
= $true )
| ( ( SV1205 = SV1884 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8184]) ).
thf(8408,plain,
! [SV1958: $i,SV1885: $i,SV1746: $i,SV1517: $i,SV1206: $i] :
( ( ! [SY3413: $i] :
( ( ( c_Pair @ SV1206 @ SV1517 @ SV1746 @ SV1885 )
!= ( c_Pair @ SV1958 @ SY3413 @ SV1746 @ SV1885 ) )
| ( SV1517 = SY3413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8185]) ).
thf(8409,plain,
! [SV1959: $i,SV1886: $i,SV1747: $i,SV1518: $i,SV1207: $i] :
( ( ( c_Datatype__Universe_OAtom @ SV1207 @ SV1518 @ SV1747 )
!= ( c_Datatype__Universe_OScons @ SV1886 @ SV1959 @ SV1518 @ SV1747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8186]) ).
thf(8410,plain,
! [SV1887: $i,SV1748: $i,SV1519: $i,SV1209: $i] :
( ( ( ( c_List_Orev @ SV1209 @ SV1519 )
!= ( c_List_Olist_OCons @ SV1748 @ SV1887 @ SV1519 ) )
= $true )
| ( ( SV1209
= ( c_append @ ( c_List_Orev @ SV1887 @ SV1519 ) @ ( c_List_Olist_OCons @ SV1748 @ c_List_Olist_ONil @ SV1519 ) @ SV1519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8187]) ).
thf(8411,plain,
! [SV1749: $i,SV1520: $i,SV1210: $i] :
( ( ( class_Orderings_Olinorder @ SV1210 )
= $false )
| ( ( ( ( c_SetInterval_OatLeast @ SV1520 @ SV1210 )
!= ( c_SetInterval_OatLeast @ SV1749 @ SV1210 ) )
| ( SV1520 = SV1749 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8188]) ).
thf(8412,plain,
! [SV1750: $i,SV1521: $i,SV1211: $i] :
( ( ( ( c_uminus @ SV1211 @ ( tc_set @ SV1521 ) )
= ( c_uminus @ SV1750 @ ( tc_set @ SV1521 ) ) )
= $false )
| ( ( SV1211 = SV1750 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8189]) ).
thf(8413,plain,
! [SV1960: $i,SV1888: $i,SV1751: $i,SV1522: $i,SV1212: $i] :
( ( ( c_Datatype__Universe_ONumb @ SV1212 @ SV1522 @ SV1751 )
!= ( c_Datatype__Universe_OScons @ SV1888 @ SV1960 @ SV1522 @ SV1751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8190]) ).
thf(8414,plain,
! [SV1889: $i,SV1752: $i,SV1523: $i,SV1213: $i] :
( ( ( ( c_insert @ SV1213 @ c_emptyset @ SV1523 )
!= ( c_insert @ SV1752 @ SV1889 @ SV1523 ) )
= $true )
| ( ( SV1752 = SV1213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8191]) ).
thf(8415,plain,
! [SV1753: $i,SV1524: $i,SV1214: $i] :
( ( ( SV1214
= ( c_append @ SV1524 @ SV1214 @ SV1753 ) )
= $false )
| ( ( SV1524 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8192]) ).
thf(8416,plain,
! [SV1754: $i,SV1526: $i,SV1217: $i] :
( ( ( c_emptyset
= ( c_Equiv__Relations_Oquotient @ SV1217 @ SV1526 @ SV1754 ) )
= $false )
| ( ( SV1217 = c_emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8194]) ).
thf(8417,plain,
! [SV1755: $i,SV1527: $i,SV1218: $i] :
( ( ( c_List_Olist_ONil
= ( c_append @ SV1218 @ SV1527 @ SV1755 ) )
= $false )
| ( ( SV1218 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8195]) ).
thf(8418,plain,
! [SV1756: $i,SV1529: $i,SV1220: $i] :
( ( ( ( c_append @ SV1220 @ SV1529 @ SV1756 )
= SV1220 )
= $false )
| ( ( SV1529 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8196]) ).
thf(8419,plain,
! [SV1757: $i,SV1530: $i,SV1221: $i] :
( ( ( class_Orderings_Olinorder @ SV1221 )
= $false )
| ( ( ( ( c_SetInterval_OgreaterThan @ SV1530 @ SV1221 )
!= ( c_SetInterval_OgreaterThan @ SV1757 @ SV1221 ) )
| ( SV1530 = SV1757 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8197]) ).
thf(8420,plain,
! [SV1890: $i,SV1758: $i,SV1531: $i,SV1222: $i] :
( ( ( ( c_Message_Omsg_OCrypt @ SV1222 @ SV1531 )
!= ( c_Message_Omsg_OCrypt @ SV1758 @ SV1890 ) )
= $true )
| ( ( SV1531 = SV1890 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8198]) ).
thf(8421,plain,
! [SV1759: $i,SV1533: $i,SV1224: $i] :
( ( ( ( c_Datatype_Ooption_OSome @ SV1224 @ SV1533 )
= ( c_Datatype_Ooption_OSome @ SV1759 @ SV1533 ) )
= $false )
| ( ( SV1224 = SV1759 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8200]) ).
thf(8422,plain,
! [SV1760: $i,SV1535: $i,SV1226: $i] :
( ( ( ( c_append @ SV1226 @ SV1535 @ SV1760 )
= SV1535 )
= $false )
| ( ( SV1226 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8202]) ).
thf(8423,plain,
! [SV1761: $i,SV1536: $i,SV1227: $i] :
( ( ( SV1227
= ( c_append @ SV1227 @ SV1536 @ SV1761 ) )
= $false )
| ( ( SV1536 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8203]) ).
thf(8424,plain,
! [SV1762: $i,SV1539: $i,SV1230: $i] :
( ( ( ( c_insert @ SV1230 @ c_emptyset @ SV1539 )
= ( c_insert @ SV1762 @ c_emptyset @ SV1539 ) )
= $false )
| ( ( SV1230 = SV1762 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8206]) ).
thf(8425,plain,
! [SV1891: $i,SV1763: $i,SV1541: $i,SV1232: $i] :
( ( ( c_Sum__Type_OInl @ SV1232 @ SV1541 @ SV1763 )
= ( c_Sum__Type_OInr @ SV1891 @ SV1763 @ SV1541 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8208]) ).
thf(8426,plain,
! [SV1961: $i,SV1892: $i,SV1764: $i,SV1543: $i,SV1234: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1234 @ SV1543 @ SV1764 @ SV1892 )
!= ( c_Datatype__Universe_OLeaf @ SV1961 @ SV1764 @ SV1892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8210]) ).
thf(8427,plain,
! [SV1962: $i,SV1893: $i,SV1765: $i,SV1544: $i,SV1235: $i] :
( ( ( ( c_List_Olist_OCons @ SV1235 @ SV1544 @ SV1765 )
!= ( c_List_Olist_OCons @ SV1893 @ SV1962 @ SV1765 ) )
| ( SV1235 = SV1893 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8211]) ).
thf(8428,plain,
! [SV1894: $i,SV1766: $i,SV1546: $i,SV1237: $i] :
( ( ( c_Datatype__Universe_ONumb @ SV1237 @ SV1546 @ SV1766 )
= ( c_Datatype__Universe_OLeaf @ SV1894 @ SV1546 @ SV1766 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8213]) ).
thf(8429,plain,
! [SV1895: $i,SV1768: $i,SV1549: $i,SV1240: $i] :
( ( ( ( c_Sum__Type_OInl @ SV1240 @ SV1549 @ SV1768 )
!= ( c_Sum__Type_OInl @ SV1895 @ SV1549 @ SV1768 ) )
= $true )
| ( ( SV1240 = SV1895 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8216]) ).
thf(8430,plain,
! [SV1963: $i,SV1896: $i,SV1769: $i,SV1550: $i,SV1241: $i] :
( ( ! [SY3414: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1241 @ SV1550 @ SV1769 @ SV1896 )
!= ( c_Datatype__Universe_OScons @ SV1963 @ SY3414 @ SV1769 @ SV1896 ) )
| ( SV1241 = SV1963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8217]) ).
thf(8431,plain,
! [SV1897: $i,SV1770: $i,SV1551: $i,SV1242: $i] :
( ( ( ( c_append @ SV1242 @ SV1551 @ SV1770 )
!= ( c_append @ SV1897 @ SV1551 @ SV1770 ) )
= $true )
| ( ( SV1242 = SV1897 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8218]) ).
thf(8432,plain,
! [SV1964: $i,SV1898: $i,SV1771: $i,SV1553: $i,SV1244: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1244 @ SV1553 @ SV1771 @ SV1898 )
!= ( c_Datatype__Universe_OAtom @ SV1964 @ SV1771 @ SV1898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8220]) ).
thf(8433,plain,
! [SV1899: $i,SV1772: $i,SV1554: $i,SV1245: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SV1245 @ SV1554 @ SV1772 )
= ( c_Datatype__Universe_ONumb @ SV1899 @ SV1554 @ SV1772 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8221]) ).
thf(8434,plain,
! [SV1900: $i,SV1773: $i,SV1555: $i,SV1246: $i] :
( ( ( ( c_List_Ochar_OChar @ SV1246 @ SV1555 )
!= ( c_List_Ochar_OChar @ SV1773 @ SV1900 ) )
= $true )
| ( ( SV1246 = SV1773 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8222]) ).
thf(8435,plain,
! [SV1774: $i,SV1556: $i,SV1247: $i] :
( ( ( ( c_append @ SV1247 @ SV1556 @ SV1774 )
= c_List_Olist_ONil )
= $false )
| ( ( SV1247 = c_List_Olist_ONil )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8223]) ).
thf(8436,plain,
! [SV1965: $i,SV1901: $i,SV1775: $i,SV1557: $i,SV1248: $i] :
( ( ! [SY3415: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1248 @ SV1557 @ SV1775 @ SV1901 )
!= ( c_Datatype__Universe_OScons @ SV1965 @ SY3415 @ SV1775 @ SV1901 ) )
| ( SV1557 = SY3415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8224]) ).
thf(8437,plain,
! [SV1776: $i,SV1558: $i,SV1249: $i] :
( ( ( class_Orderings_Olinorder @ SV1249 )
= $false )
| ( ( ( ( c_SetInterval_OatMost @ SV1558 @ SV1249 )
!= ( c_SetInterval_OatMost @ SV1776 @ SV1249 ) )
| ( SV1558 = SV1776 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8225]) ).
thf(8438,plain,
! [SV1777: $i,SV1560: $i,SV1251: $i] :
( ( ( ( c_List_Orev @ SV1251 @ SV1560 )
= ( c_List_Orev @ SV1777 @ SV1560 ) )
= $false )
| ( ( SV1251 = SV1777 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8227]) ).
thf(8439,plain,
! [SV1902: $i,SV1778: $i,SV1561: $i,SV1252: $i] :
( ( ( ( c_Message_Omsg_OMPair @ SV1252 @ SV1561 )
!= ( c_Message_Omsg_OMPair @ SV1778 @ SV1902 ) )
= $true )
| ( ( SV1561 = SV1902 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8228]) ).
thf(8440,plain,
! [SV1903: $i,SV1779: $i,SV1562: $i,SV1253: $i] :
( ( ( ( c_insert @ SV1253 @ c_emptyset @ SV1562 )
!= ( c_insert @ SV1779 @ SV1903 @ SV1562 ) )
= $true )
| ( ( c_lessequals @ SV1903 @ ( c_insert @ SV1253 @ c_emptyset @ SV1562 ) @ ( tc_set @ SV1562 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8229]) ).
thf(8441,plain,
! [SV1904: $i,SV1780: $i,SV1564: $i,SV1255: $i] :
( ( ( ( c_Sum__Type_OInr @ SV1255 @ SV1564 @ SV1780 )
!= ( c_Sum__Type_OInr @ SV1904 @ SV1564 @ SV1780 ) )
= $true )
| ( ( SV1255 = SV1904 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8231]) ).
thf(8442,plain,
! [SV1905: $i,SV1781: $i,SV1565: $i,SV1256: $i] :
( ( ( ( c_insert @ SV1256 @ SV1565 @ SV1781 )
!= ( c_insert @ SV1905 @ c_emptyset @ SV1781 ) )
= $true )
| ( ( c_lessequals @ SV1565 @ ( c_insert @ SV1905 @ c_emptyset @ SV1781 ) @ ( tc_set @ SV1781 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8232]) ).
thf(8443,plain,
! [SV1906: $i,SV1782: $i,SV1566: $i,SV1257: $i] :
( ( ( ( c_insert @ SV1257 @ SV1566 @ SV1782 )
!= ( c_insert @ SV1906 @ c_emptyset @ SV1782 ) )
= $true )
| ( ( SV1257 = SV1906 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8233]) ).
thf(8444,plain,
! [SV1907: $i,SV1783: $i,SV1567: $i,SV1258: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ ( c_Datatype__Universe_Odprod @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) ) ) )
= $true )
| ( ( SV1
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( c_Main_OdprodE__2 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ SV1783 @ SV1907 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( c_Main_OdprodE__4 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ SV1783 @ SV1907 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8234]) ).
thf(8445,plain,
! [SV1908: $i,SV1784: $i,SV1568: $i,SV1259: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ ( c_Datatype__Universe_Odprod @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( c_Main_OdprodE__4 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) @ SV1568 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8235]) ).
thf(8446,plain,
! [SV1909: $i,SV1785: $i,SV1569: $i,SV1260: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( c_Main_OdprodE__3 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) @ SV1260 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8236]) ).
thf(8447,plain,
! [SV1966: $i,SV1910: $i,SV1786: $i,SV1570: $i,SV1261: $i,SV4: $i] :
( ( ! [SY3416: $i,SY3417: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SV1966 @ SY3416 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SY3417 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1966 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SY3416 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3417 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8237]) ).
thf(8448,plain,
! [SV1911: $i,SV1787: $i,SV1571: $i,SV1262: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SV1262 @ SV1571 @ SV1787 @ SV1911 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) ) )
= $true )
| ( ( ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8238]) ).
thf(8449,plain,
! [SV1912: $i,SV1788: $i,SV1572: $i,SV1263: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SV1263 @ SV1572 @ SV1788 @ SV1912 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( c_Main_OdsumE__4 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) @ SV1572 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
| ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8239]) ).
thf(8450,plain,
! [SV1913: $i,SV1789: $i,SV1573: $i,SV1264: $i,SV7: $i] :
( ( ( ~ ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1264 @ SV1573 @ SV1789 @ SV1913 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( c_Main_OdsumE__2 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) @ SV1264 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
| ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8240]) ).
thf(8451,plain,
! [SV1914: $i,SV1790: $i,SV1574: $i,SV1265: $i,SV8: $i] :
( ( ( ~ ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1265 @ SV1574 @ SV1790 @ SV1914 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__2 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1265 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__4 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1574 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8241]) ).
thf(8452,plain,
! [SV1967: $i,SV1915: $i,SV1791: $i,SV1575: $i,SV1266: $i,SV9: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV9 @ SV1266 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ SV1915 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SV1575 @ SV1791 ) @ ( c_Datatype__Universe_OIn0 @ SV1266 @ SV1575 @ SV1791 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1915 @ SV1967 @ SV1575 @ SV1791 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8242]) ).
thf(8453,plain,
! [SV1968: $i,SV1916: $i,SV1792: $i,SV1576: $i,SV1267: $i,SV10: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV10 @ SV1267 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ SV1916 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SV1576 @ SV1792 ) @ ( c_Datatype__Universe_OIn1 @ SV1267 @ SV1576 @ SV1792 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1968 @ SV1916 @ SV1576 @ SV1792 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8243]) ).
thf(8454,plain,
! [SV1917: $i,SV1793: $i,SV1577: $i,SV1268: $i,SV11: $i] :
( ( ( ~ ( c_in @ SV11 @ ( c_Datatype__Universe_Ouprod @ SV1268 @ SV1577 @ SV1793 @ SV1917 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1793 @ SV1917 ) ) ) )
= $true )
| ( ( SV11
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SV1917 ) @ ( c_Main_OuprodE__2 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SV1917 ) @ SV1793 @ SV1917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8244]) ).
thf(8455,plain,
! [SV1918: $i,SV1794: $i,SV1578: $i,SV1269: $i,SV12: $i] :
( ( ( ~ ( c_in @ SV12 @ ( c_Datatype__Universe_Ouprod @ SV1269 @ SV1578 @ SV1794 @ SV1918 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SV1918 ) ) ) )
= $true )
| ( ( c_in @ ( c_Main_OuprodE__2 @ SV1269 @ SV1578 @ SV12 @ SV1794 @ SV1918 ) @ SV1578 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SV1918 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8245]) ).
thf(8456,plain,
! [SV1919: $i,SV1795: $i,SV1579: $i,SV1270: $i,SV13: $i] :
( ( ( ~ ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1270 @ SV1579 @ SV1795 @ SV1919 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SV1919 ) ) ) )
= $true )
| ( ( c_in @ ( c_Main_OuprodE__1 @ SV1270 @ SV1579 @ SV13 @ SV1795 @ SV1919 ) @ SV1270 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SV1919 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8246]) ).
thf(8457,plain,
! [SV1969: $i,SV1920: $i,SV1796: $i,SV1580: $i,SV1271: $i,SV14: $i] :
( ( ~ ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ~ ( c_in @ SV1920 @ SV1969 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SV1920 @ SV14 @ SV1580 @ SV1796 ) @ ( c_Datatype__Universe_Ouprod @ SV1969 @ SV1271 @ SV1580 @ SV1796 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8247]) ).
thf(8458,plain,
! [SV1921: $i,SV1797: $i,SV1581: $i,SV1272: $i,SV15: $i] :
( ( ( ~ ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SV1272 @ SV1581 @ SV1797 @ SV1921 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1797 @ SV1921 ) ) ) )
= $true )
| ( ( ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1272 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) )
| ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1581 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8248]) ).
thf(8459,plain,
! [SV1922: $i,SV1798: $i,SV1582: $i,SV1273: $i,SV16: $i] :
( ( ( ~ ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SV1273 @ SV1582 @ SV1798 @ SV1922 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Main_OusumE__2 @ SV1582 @ SV16 @ SV1798 @ SV1922 ) @ SV1582 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) )
| ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1273 @ SV16 @ SV1798 @ SV1922 ) @ SV1798 @ SV1922 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8249]) ).
thf(8460,plain,
! [SV1923: $i,SV1799: $i,SV1583: $i,SV1274: $i,SV17: $i] :
( ( ( ~ ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1274 @ SV1583 @ SV1799 @ SV1923 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Main_OusumE__1 @ SV1274 @ SV17 @ SV1799 @ SV1923 ) @ SV1274 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) )
| ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1583 @ SV17 @ SV1799 @ SV1923 ) @ SV1799 @ SV1923 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8250]) ).
thf(8461,plain,
! [SV1924: $i,SV1800: $i,SV1584: $i,SV1275: $i,SV18: $i] :
( ( ( ~ ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1275 @ SV1584 @ SV1800 @ SV1924 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Main_OusumE__1 @ SV1275 @ SV18 @ SV1800 @ SV1924 ) @ SV1275 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1584 @ SV18 @ SV1800 @ SV1924 ) @ SV1584 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8251]) ).
thf(8462,plain,
! [SV1925: $i,SV1801: $i,SV1585: $i,SV1276: $i,SV19: $i] :
( ( ( ~ ( c_in @ SV19 @ SV1276 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) ) )
= $true )
| ( ( c_in @ ( c_Datatype__Universe_OIn0 @ SV19 @ SV1585 @ SV1801 ) @ ( c_Datatype__Universe_Ousum @ SV1276 @ SV1925 @ SV1585 @ SV1801 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8252]) ).
thf(8463,plain,
! [SV1926: $i,SV1802: $i,SV1586: $i,SV1277: $i,SV20: $i] :
( ( ( ~ ( c_in @ SV20 @ SV1277 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) ) )
= $true )
| ( ( c_in @ ( c_Datatype__Universe_OIn1 @ SV20 @ SV1586 @ SV1802 ) @ ( c_Datatype__Universe_Ousum @ SV1926 @ SV1277 @ SV1586 @ SV1802 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8253]) ).
thf(8464,plain,
! [SV1284: $i,SV30: $i] :
( ( ( c_in @ ( c_Main_Ofinite__Union__1 @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) )
= $false )
| ( ( c_in @ ( c_Union @ SV30 @ SV1284 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1284 ) )
= $true )
| ( ( c_in @ SV30 @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ SV1284 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8258]) ).
thf(8465,plain,
! [SV1803: $i,SV1590: $i,SV1287: $i,SV33: $i] :
( ( ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
= $false )
| ( ( ~ ( c_in @ SV1590 @ SV33 @ SV1287 )
| ~ ( c_in @ SV1803 @ SV33 @ SV1287 )
| ( SV1590 = SV1803 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8259]) ).
thf(8466,plain,
! [SV1804: $i,SV1591: $i,SV1294: $i,SV42: $i] :
( ( ( c_in @ SV42 @ ( c_List_Olists @ SV1294 @ SV1591 ) @ ( tc_List_Olist @ SV1591 ) )
= $false )
| ( ( ~ ( c_in @ SV1804 @ ( c_List_Oset @ SV42 @ SV1591 ) @ SV1591 )
| ( c_in @ SV1804 @ SV1294 @ SV1591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8260]) ).
thf(8467,plain,
! [SV1927: $i,SV1805: $i,SV1594: $i,SV1298: $i,SV46: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV46 @ SV1298 @ SV1594 ) @ SV1805 @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) @ ( c_List_Olistrel @ SV1927 @ SV1594 ) @ ( tc_prod @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) ) )
= $true )
| ( ( SV1805
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SV1927 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ ( c_Main_Olistrel__Cons1__2 @ SV1927 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ SV1594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8262]) ).
thf(8468,plain,
! [SV1928: $i,SV1806: $i,SV1595: $i,SV1299: $i,SV47: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV47 @ SV1299 @ SV1595 ) @ SV1806 @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SV1928 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1299 @ ( c_Main_Olistrel__Cons1__2 @ SV1928 @ SV1806 @ SV47 @ SV1299 @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SV1928 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8263]) ).
thf(8469,plain,
! [SV1929: $i,SV1807: $i,SV1596: $i,SV1300: $i,SV48: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV48 @ SV1300 @ SV1596 ) @ SV1807 @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) @ ( c_List_Olistrel @ SV1929 @ SV1596 ) @ ( tc_prod @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV48 @ ( c_Main_Olistrel__Cons1__1 @ SV1929 @ SV1807 @ SV48 @ SV1300 @ SV1596 ) @ SV1596 @ SV1596 ) @ SV1929 @ ( tc_prod @ SV1596 @ SV1596 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8264]) ).
thf(8470,plain,
! [SV1930: $i,SV1808: $i,SV1597: $i,SV1301: $i,SV49: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV49 @ ( c_List_Olist_OCons @ SV1301 @ SV1597 @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) @ ( c_List_Olistrel @ SV1930 @ SV1808 ) @ ( tc_prod @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) ) )
= $true )
| ( ( SV49
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SV1930 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ ( c_Main_Olistrel__Cons2__2 @ SV1930 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ SV1808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8265]) ).
thf(8471,plain,
! [SV1931: $i,SV1809: $i,SV1598: $i,SV1302: $i,SV50: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV50 @ ( c_List_Olist_OCons @ SV1302 @ SV1598 @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SV1931 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SV1931 @ SV50 @ SV1302 @ SV1598 @ SV1809 ) @ SV1598 @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SV1931 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8266]) ).
thf(8472,plain,
! [SV1932: $i,SV1810: $i,SV1599: $i,SV1303: $i,SV51: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV51 @ ( c_List_Olist_OCons @ SV1303 @ SV1599 @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) @ ( c_List_Olistrel @ SV1932 @ SV1810 ) @ ( tc_prod @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SV1932 @ SV51 @ SV1303 @ SV1599 @ SV1810 ) @ SV1303 @ SV1810 @ SV1810 ) @ SV1932 @ ( tc_prod @ SV1810 @ SV1810 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8267]) ).
thf(8473,plain,
! [SV1811: $i,SV1602: $i,SV1306: $i,SV54: $i] :
( ( ( c_in @ ( c_List_Olist_OCons @ SV54 @ SV1306 @ SV1602 ) @ ( c_List_Olists @ SV1811 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) )
= $false )
| ( ( c_in @ SV1306 @ ( c_List_Olists @ SV1811 @ SV1602 ) @ ( tc_List_Olist @ SV1602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8270]) ).
thf(8474,plain,
! [SV1812: $i,SV1603: $i,SV1307: $i,SV55: $i] :
( ( ( c_in @ ( c_List_Olist_OCons @ SV55 @ SV1307 @ SV1603 ) @ ( c_List_Olists @ SV1812 @ SV1603 ) @ ( tc_List_Olist @ SV1603 ) )
= $false )
| ( ( c_in @ SV55 @ SV1812 @ SV1603 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8271]) ).
thf(8475,plain,
! [SV1813: $i,SV1604: $i,SV1308: $i,SV56: $i] :
( ( ( c_in @ SV56 @ SV1308 @ SV1604 )
= $false )
| ( ( ~ ( c_in @ SV1813 @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) )
| ( c_in @ ( c_List_Olist_OCons @ SV56 @ SV1813 @ SV1604 ) @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8272]) ).
thf(8476,plain,
! [SV1814: $i,SV1605: $i,SV1313: $i,SV65: $i] :
( ( ( c_in @ SV65 @ ( c_Relation_ODomain @ SV1313 @ SV1605 @ SV1814 ) @ SV1605 )
= $false )
| ( ( c_in @ ( c_Pair @ SV65 @ ( c_Main_ODomainE__1 @ SV65 @ SV1313 @ SV1605 @ SV1814 ) @ SV1605 @ SV1814 ) @ SV1313 @ ( tc_prod @ SV1605 @ SV1814 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8273]) ).
thf(8477,plain,
! [SV1933: $i,SV1815: $i,SV1606: $i,SV1314: $i,SV66: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV66 @ SV1314 @ SV1606 @ SV1815 ) @ SV1933 @ ( tc_prod @ SV1606 @ SV1815 ) ) )
= $true )
| ( ( c_in @ SV66 @ ( c_Relation_ODomain @ SV1933 @ SV1606 @ SV1815 ) @ SV1606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8274]) ).
thf(8478,plain,
! [SV1934: $i,SV1816: $i,SV1607: $i,SV1316: $i,SV68: $i] :
( ( ( ~ ( c_in @ SV68 @ ( c_Relation_OImage @ SV1316 @ SV1607 @ SV1816 @ SV1934 ) @ SV1934 ) )
= $true )
| ( ( c_in @ ( c_Main_OImageE__1 @ SV1607 @ SV68 @ SV1316 @ SV1816 @ SV1934 ) @ SV1607 @ SV1816 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8275]) ).
thf(8479,plain,
! [SV1935: $i,SV1817: $i,SV1608: $i,SV1317: $i,SV69: $i] :
( ( ( ~ ( c_in @ SV69 @ ( c_Relation_OImage @ SV1317 @ SV1608 @ SV1817 @ SV1935 ) @ SV1935 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1608 @ SV69 @ SV1317 @ SV1817 @ SV1935 ) @ SV69 @ SV1817 @ SV1935 ) @ SV1317 @ ( tc_prod @ SV1817 @ SV1935 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8276]) ).
thf(8480,plain,
! [SV1970: $i,SV1936: $i,SV1818: $i,SV1609: $i,SV1318: $i,SV70: $i] :
( ( ~ ( c_in @ SV70 @ SV1318 @ SV1609 )
| ~ ( c_in @ ( c_Pair @ SV70 @ SV1818 @ SV1609 @ SV1936 ) @ SV1970 @ ( tc_prod @ SV1609 @ SV1936 ) )
| ( c_in @ SV1818 @ ( c_Relation_OImage @ SV1970 @ SV1318 @ SV1609 @ SV1936 ) @ SV1936 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8277]) ).
thf(8481,plain,
! [SV1819: $i,SV1610: $i,SV1319: $i,SV71: $i] :
( ( ( c_in @ SV71 @ ( c_Relation_ORange @ SV1319 @ SV1610 @ SV1819 ) @ SV1819 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ SV71 @ SV1319 @ SV1819 @ SV1610 ) @ SV71 @ SV1610 @ SV1819 ) @ SV1319 @ ( tc_prod @ SV1610 @ SV1819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8278]) ).
thf(8482,plain,
! [SV1937: $i,SV1820: $i,SV1611: $i,SV1320: $i,SV72: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV72 @ SV1320 @ SV1611 @ SV1820 ) @ SV1937 @ ( tc_prod @ SV1611 @ SV1820 ) ) )
= $true )
| ( ( c_in @ SV1320 @ ( c_Relation_ORange @ SV1937 @ SV1611 @ SV1820 ) @ SV1820 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8279]) ).
thf(8483,plain,
! [SV1821: $i,SV1612: $i,SV1321: $i,SV73: $i] :
( ( ( c_in @ SV73 @ ( c_Relation_Oconverse @ SV1321 @ SV1612 @ SV1821 ) @ ( tc_prod @ SV1821 @ SV1612 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ SV1321 @ SV73 @ SV1612 @ SV1821 ) @ ( c_Main_OconverseE__2 @ SV1321 @ SV73 @ SV1612 @ SV1821 ) @ SV1612 @ SV1821 ) @ SV1321 @ ( tc_prod @ SV1612 @ SV1821 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8280]) ).
thf(8484,plain,
! [SV1822: $i,SV1613: $i,SV1322: $i,SV74: $i] :
( ( ( c_in @ SV74 @ ( c_Relation_Oconverse @ SV1322 @ SV1613 @ SV1822 ) @ ( tc_prod @ SV1822 @ SV1613 ) )
= $false )
| ( ( SV74
= ( c_Pair @ ( c_Main_OconverseE__2 @ SV1322 @ SV74 @ SV1613 @ SV1822 ) @ ( c_Main_OconverseE__1 @ SV1322 @ SV74 @ SV1613 @ SV1822 ) @ SV1822 @ SV1613 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8281]) ).
thf(8485,plain,
! [SV1971: $i,SV1938: $i,SV1823: $i,SV1617: $i,SV1326: $i,SV78: $i] :
( ( ~ ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SV1326 @ SV1617 @ SV1823 @ SV1938 @ SV1971 ) @ ( tc_prod @ SV1971 @ SV1938 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SV1971 ) @ ( c_Main_Orel__compE__3 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SV1971 ) @ SV1823 @ SV1938 ) @ SV1326 @ ( tc_prod @ SV1823 @ SV1938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8285]) ).
thf(8486,plain,
! [SV1972: $i,SV1939: $i,SV1824: $i,SV1618: $i,SV1327: $i,SV79: $i] :
( ( ~ ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SV1327 @ SV1618 @ SV1824 @ SV1939 @ SV1972 ) @ ( tc_prod @ SV1972 @ SV1939 ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SV1972 ) @ ( c_Main_Orel__compE__2 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SV1972 ) @ SV1972 @ SV1824 ) @ SV1618 @ ( tc_prod @ SV1972 @ SV1824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8286]) ).
thf(8487,plain,
! [SV1973: $i,SV1940: $i,SV1825: $i,SV1619: $i,SV1328: $i,SV80: $i] :
( ( ~ ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SV1328 @ SV1619 @ SV1825 @ SV1940 @ SV1973 ) @ ( tc_prod @ SV1973 @ SV1940 ) )
| ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SV1973 ) @ ( c_Main_Orel__compE__3 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SV1973 ) @ SV1973 @ SV1940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8287]) ).
thf(8488,plain,
! [SV1974: $i,SV1941: $i,SV1826: $i,SV1620: $i,SV1329: $i,SV81: $i] :
( ( ! [SY3418: $i,SY3419: $i] :
( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) )
| ~ ( c_in @ ( c_Pair @ SV1974 @ SV81 @ SY3418 @ SV1620 ) @ SY3419 @ ( tc_prod @ SY3418 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SV1974 @ SV1329 @ SY3418 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SY3419 @ SV1620 @ SV1826 @ SY3418 ) @ ( tc_prod @ SY3418 @ SV1826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8288]) ).
thf(8489,plain,
! [SV1625: $i,SV98: $i,SV1344: $i] :
( ( ( c_lessequals @ SV1344 @ SV98 @ ( tc_set @ SV1625 ) )
= $false )
| ( ( c_less @ SV98 @ SV1344 @ ( tc_set @ SV1625 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8292]) ).
thf(8490,plain,
! [SV1627: $i,SV1346: $i,SV100: $i] :
( ( ( c_less @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) )
= $true )
| ( ( SV100 = SV1346 )
= $true )
| ( ( c_lessequals @ SV100 @ SV1346 @ ( tc_set @ SV1627 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8294]) ).
thf(8491,plain,
! [SV1827: $i,SV1629: $i,SV1349: $i,SV103: $i] :
( ( ( c_in @ SV103 @ SV1349 @ SV1629 )
= $false )
| ( ( ~ ( c_lessequals @ SV1349 @ SV1827 @ ( tc_set @ SV1629 ) )
| ( c_in @ SV103 @ SV1827 @ SV1629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8296]) ).
thf(8492,plain,
! [SV1632: $i,SV106: $i,SV1352: $i] :
( ( ( ~ ( c_lessequals @ SV1352 @ SV106 @ ( tc_set @ SV1632 ) ) )
= $true )
| ( ( SV1352 = SV106 )
= $true )
| ( ( c_lessequals @ SV106 @ SV1352 @ ( tc_set @ SV1632 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8298]) ).
thf(8493,plain,
! [SV1942: $i,SV1828: $i,SV1633: $i,SV1354: $i,SV108: $i] :
( ( ( ~ ( c_in @ SV108 @ SV1354 @ SV1633 ) )
= $true )
| ( ( c_in @ ( c_Sum__Type_OInl @ SV108 @ SV1633 @ SV1828 ) @ ( c_Sum__Type_OPlus @ SV1354 @ SV1942 @ SV1633 @ SV1828 ) @ ( tc_sum @ SV1633 @ SV1828 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8299]) ).
thf(8494,plain,
! [SV1943: $i,SV1829: $i,SV1634: $i,SV1355: $i,SV109: $i] :
( ( ( ~ ( c_in @ SV109 @ SV1355 @ SV1634 ) )
= $true )
| ( ( c_in @ ( c_Sum__Type_OInr @ SV109 @ SV1634 @ SV1829 ) @ ( c_Sum__Type_OPlus @ SV1943 @ SV1355 @ SV1829 @ SV1634 ) @ ( tc_sum @ SV1829 @ SV1634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8300]) ).
thf(8495,plain,
! [SV1944: $i,SV1830: $i,SV1635: $i,SV1356: $i,SV110: $i] :
( ( ( ~ ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SV1356 @ SV1635 @ SV1830 @ SV1944 ) @ ( tc_sum @ SV1830 @ SV1944 ) ) )
= $true )
| ( ( ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1356 @ SV110 @ SV1830 @ SV1944 ) @ SV1830 @ SV1944 ) )
| ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1635 @ SV110 @ SV1944 @ SV1830 ) @ SV1944 @ SV1830 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8301]) ).
thf(8496,plain,
! [SV1945: $i,SV1831: $i,SV1636: $i,SV1357: $i,SV111: $i] :
( ( ( ~ ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SV1357 @ SV1636 @ SV1831 @ SV1945 ) @ ( tc_sum @ SV1831 @ SV1945 ) ) )
= $true )
| ( ( ( c_in @ ( c_Main_OPlusE__2 @ SV1636 @ SV111 @ SV1945 @ SV1831 ) @ SV1636 @ SV1945 )
| ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1357 @ SV111 @ SV1831 @ SV1945 ) @ SV1831 @ SV1945 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8302]) ).
thf(8497,plain,
! [SV1946: $i,SV1832: $i,SV1637: $i,SV1358: $i,SV112: $i] :
( ( ( ~ ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SV1358 @ SV1637 @ SV1832 @ SV1946 ) @ ( tc_sum @ SV1832 @ SV1946 ) ) )
= $true )
| ( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1358 @ SV112 @ SV1832 @ SV1946 ) @ SV1358 @ SV1832 )
| ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1637 @ SV112 @ SV1946 @ SV1832 ) @ SV1946 @ SV1832 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8303]) ).
thf(8498,plain,
! [SV1947: $i,SV1833: $i,SV1638: $i,SV1359: $i,SV113: $i] :
( ( ( ~ ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SV1359 @ SV1638 @ SV1833 @ SV1947 ) @ ( tc_sum @ SV1833 @ SV1947 ) ) )
= $true )
| ( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1359 @ SV113 @ SV1833 @ SV1947 ) @ SV1359 @ SV1833 )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1638 @ SV113 @ SV1947 @ SV1833 ) @ SV1638 @ SV1947 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8304]) ).
thf(8499,plain,
! [SV1834: $i,SV1641: $i,SV1362: $i,SV116: $i] :
( ( ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ SV1834 @ ( tc_prod @ SV1641 @ SV1641 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV116 @ SV1362 @ SV1641 @ SV1641 ) @ ( c_Transitive__Closure_Otrancl @ SV1834 @ SV1641 ) @ ( tc_prod @ SV1641 @ SV1641 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8306]) ).
thf(8500,plain,
! [SV1835: $i,SV1642: $i,SV1363: $i,SV117: $i] :
( ( ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Otrancl @ SV1835 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV117 @ SV1363 @ SV1642 @ SV1642 ) @ ( c_Transitive__Closure_Ortrancl @ SV1835 @ SV1642 ) @ ( tc_prod @ SV1642 @ SV1642 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8307]) ).
thf(8501,plain,
! [SV1836: $i,SV1643: $i,SV1364: $i,SV119: $i] :
( ( ( c_Relation_Otrans @ SV119 @ SV1364 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV1643 @ SV1836 )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1643 @ SV119 @ SV1836 @ SV1364 ) @ ( tc_prod @ SV1836 @ SV1364 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8308]) ).
thf(8502,plain,
! [SV1837: $i,SV1644: $i,SV1365: $i,SV120: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ SV120 @ SV1365 )
= $false )
| ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1644 @ SV1837 )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1644 @ SV120 @ SV1837 @ SV1365 ) @ ( tc_prod @ SV1837 @ SV1365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8309]) ).
thf(8503,plain,
! [SV1366: $i,SV122: $i] :
( ( ( class_Finite__Set_Ofinite @ SV122 )
= $false )
| ( ( class_Finite__Set_Ofinite @ SV1366 )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_fun @ SV122 @ SV1366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8310]) ).
thf(8504,plain,
! [SV1368: $i,SV124: $i] :
( ( ( class_Finite__Set_Ofinite @ SV124 )
= $false )
| ( ( class_Finite__Set_Ofinite @ SV1368 )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_prod @ SV124 @ SV1368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8311]) ).
thf(8505,plain,
! [SV1369: $i,SV130: $i] :
( ( ( class_Finite__Set_Ofinite @ SV130 )
= $false )
| ( ( class_Finite__Set_Ofinite @ SV1369 )
= $false )
| ( ( class_Finite__Set_Ofinite @ ( tc_sum @ SV130 @ SV1369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8312]) ).
thf(8506,plain,
! [SV1838: $i,SV1646: $i,SV1376: $i,SV1045: $i] :
( ( ( c_in @ ( c_minus @ SV1045 @ ( c_insert @ SV1376 @ SV1646 @ SV1838 ) @ ( tc_set @ SV1838 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1838 ) )
= $false )
| ( ( c_in @ ( c_minus @ SV1045 @ SV1646 @ ( tc_set @ SV1838 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8314]) ).
thf(8507,plain,
! [SV1839: $i,SV1647: $i,SV1377: $i,SV1046: $i] :
( ( ( c_in @ ( c_minus @ SV1046 @ SV1377 @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) )
= $false )
| ( ( c_in @ ( c_minus @ SV1046 @ ( c_insert @ SV1839 @ SV1377 @ SV1647 ) @ ( tc_set @ SV1647 ) ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1647 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8315]) ).
thf(8508,plain,
! [SV1051: $i,SV1382: $i,SV1650: $i] :
( ( ( ~ ( c_in @ SV1650 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) ) )
= $true )
| ( ( c_in @ ( c_union @ SV1650 @ SV1051 @ SV1382 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
= $true )
| ( ( c_in @ SV1051 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8318]) ).
thf(8509,plain,
! [SV1387: $i,SV1655: $i,SV1056: $i] :
( ( ( ~ ( c_Divides_Oop_Advd @ SV1056 @ SV1655 @ tc_nat ) )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1056 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1655 @ SV1387 @ tc_nat @ tc_nat ) ) @ tc_nat )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1056 @ SV1387 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8323]) ).
thf(8510,plain,
! [SV1840: $i,SV1658: $i,SV1394: $i,SV1066: $i] :
( ( ( c_in @ ( c_append @ SV1066 @ SV1394 @ SV1658 ) @ ( c_List_Olists @ SV1840 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) )
= $false )
| ( ( c_in @ SV1066 @ ( c_List_Olists @ SV1840 @ SV1658 ) @ ( tc_List_Olist @ SV1658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8324]) ).
thf(8511,plain,
! [SV1841: $i,SV1659: $i,SV1395: $i,SV1067: $i] :
( ( ( c_in @ ( c_append @ SV1067 @ SV1395 @ SV1659 ) @ ( c_List_Olists @ SV1841 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) )
= $false )
| ( ( c_in @ SV1395 @ ( c_List_Olists @ SV1841 @ SV1659 ) @ ( tc_List_Olist @ SV1659 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8325]) ).
thf(8512,plain,
! [SV1842: $i,SV1660: $i,SV1396: $i,SV1068: $i] :
( ( ( c_in @ SV1068 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
= $false )
| ( ( ~ ( c_in @ SV1842 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
| ( c_in @ ( c_append @ SV1842 @ SV1068 @ SV1660 ) @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8326]) ).
thf(8513,plain,
! [SV1948: $i,SV1843: $i,SV1662: $i,SV1414: $i,SV1097: $i] :
( ( ( ~ ( c_in @ SV1097 @ ( c_Relation_OImage @ SV1414 @ ( c_insert @ SV1662 @ c_emptyset @ SV1843 ) @ SV1843 @ SV1948 ) @ SV1948 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1662 @ SV1097 @ SV1843 @ SV1948 ) @ SV1414 @ ( tc_prod @ SV1843 @ SV1948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8329]) ).
thf(8514,plain,
! [SV1949: $i,SV1844: $i,SV1663: $i,SV1415: $i,SV1098: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1098 @ SV1415 @ SV1663 @ SV1844 ) @ SV1949 @ ( tc_prod @ SV1663 @ SV1844 ) ) )
= $true )
| ( ( c_in @ SV1415 @ ( c_Relation_OImage @ SV1949 @ ( c_insert @ SV1098 @ c_emptyset @ SV1663 ) @ SV1663 @ SV1844 ) @ SV1844 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8330]) ).
thf(8515,plain,
! [SV1950: $i,SV1845: $i,SV1664: $i,SV1416: $i,SV1099: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1099 @ SV1416 @ SV1664 @ SV1845 ) @ ( c_Relation_Oconverse @ SV1950 @ SV1845 @ SV1664 ) @ ( tc_prod @ SV1664 @ SV1845 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1416 @ SV1099 @ SV1845 @ SV1664 ) @ SV1950 @ ( tc_prod @ SV1845 @ SV1664 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8331]) ).
thf(8516,plain,
! [SV1951: $i,SV1846: $i,SV1665: $i,SV1417: $i,SV1100: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1100 @ SV1417 @ SV1665 @ SV1846 ) @ SV1951 @ ( tc_prod @ SV1665 @ SV1846 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1417 @ SV1100 @ SV1846 @ SV1665 ) @ ( c_Relation_Oconverse @ SV1951 @ SV1665 @ SV1846 ) @ ( tc_prod @ SV1846 @ SV1665 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8332]) ).
thf(8517,plain,
! [SV1102: $i,SV1667: $i,SV1419: $i] :
( ( ( ~ ( c_in @ SV1419 @ ( c_SetInterval_OatLeast @ SV1667 @ SV1102 ) @ SV1102 ) )
= $true )
| ( ( c_lessequals @ SV1667 @ SV1419 @ SV1102 )
= $true )
| ( ( class_Orderings_Oord @ SV1102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8334]) ).
thf(8518,plain,
! [SV1103: $i,SV1668: $i,SV1420: $i] :
( ( ( ~ ( c_lessequals @ SV1420 @ SV1668 @ SV1103 ) )
= $true )
| ( ( c_in @ SV1668 @ ( c_SetInterval_OatLeast @ SV1420 @ SV1103 ) @ SV1103 )
= $true )
| ( ( class_Orderings_Oord @ SV1103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8335]) ).
thf(8519,plain,
! [SV1669: $i,SV1104: $i,SV1421: $i] :
( ( ( ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1421 @ SV1104 ) @ ( c_SetInterval_OatLeast @ SV1669 @ SV1104 ) @ ( tc_set @ SV1104 ) ) )
= $true )
| ( ( c_lessequals @ SV1669 @ SV1421 @ SV1104 )
= $true )
| ( ( class_Orderings_Oorder @ SV1104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8336]) ).
thf(8520,plain,
! [SV1105: $i,SV1670: $i,SV1422: $i] :
( ( ( ~ ( c_lessequals @ SV1422 @ SV1670 @ SV1105 ) )
= $true )
| ( ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1670 @ SV1105 ) @ ( c_SetInterval_OatLeast @ SV1422 @ SV1105 ) @ ( tc_set @ SV1105 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV1105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8337]) ).
thf(8521,plain,
! [SV1106: $i,SV1671: $i,SV1423: $i] :
( ( ( ~ ( c_in @ SV1423 @ ( c_SetInterval_OatMost @ SV1671 @ SV1106 ) @ SV1106 ) )
= $true )
| ( ( c_lessequals @ SV1423 @ SV1671 @ SV1106 )
= $true )
| ( ( class_Orderings_Oord @ SV1106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8338]) ).
thf(8522,plain,
! [SV1107: $i,SV1672: $i,SV1424: $i] :
( ( ( ~ ( c_lessequals @ SV1424 @ SV1672 @ SV1107 ) )
= $true )
| ( ( c_in @ SV1424 @ ( c_SetInterval_OatMost @ SV1672 @ SV1107 ) @ SV1107 )
= $true )
| ( ( class_Orderings_Oord @ SV1107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8339]) ).
thf(8523,plain,
! [SV1673: $i,SV1108: $i,SV1425: $i] :
( ( ( ~ ( c_lessequals @ ( c_SetInterval_OatMost @ SV1425 @ SV1108 ) @ ( c_SetInterval_OatMost @ SV1673 @ SV1108 ) @ ( tc_set @ SV1108 ) ) )
= $true )
| ( ( c_lessequals @ SV1425 @ SV1673 @ SV1108 )
= $true )
| ( ( class_Orderings_Oorder @ SV1108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8340]) ).
thf(8524,plain,
! [SV1109: $i,SV1674: $i,SV1426: $i] :
( ( ( ~ ( c_lessequals @ SV1426 @ SV1674 @ SV1109 ) )
= $true )
| ( ( c_lessequals @ ( c_SetInterval_OatMost @ SV1426 @ SV1109 ) @ ( c_SetInterval_OatMost @ SV1674 @ SV1109 ) @ ( tc_set @ SV1109 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV1109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8341]) ).
thf(8525,plain,
! [SV1110: $i,SV1675: $i,SV1427: $i] :
( ( ( ~ ( c_in @ SV1427 @ ( c_SetInterval_OgreaterThan @ SV1675 @ SV1110 ) @ SV1110 ) )
= $true )
| ( ( c_less @ SV1675 @ SV1427 @ SV1110 )
= $true )
| ( ( class_Orderings_Oord @ SV1110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8342]) ).
thf(8526,plain,
! [SV1111: $i,SV1676: $i,SV1428: $i] :
( ( ( ~ ( c_less @ SV1428 @ SV1676 @ SV1111 ) )
= $true )
| ( ( c_in @ SV1676 @ ( c_SetInterval_OgreaterThan @ SV1428 @ SV1111 ) @ SV1111 )
= $true )
| ( ( class_Orderings_Oord @ SV1111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8343]) ).
thf(8527,plain,
! [SV1677: $i,SV1112: $i,SV1429: $i] :
( ( ( ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1429 @ SV1112 ) @ ( c_SetInterval_OgreaterThan @ SV1677 @ SV1112 ) @ ( tc_set @ SV1112 ) ) )
= $true )
| ( ( c_lessequals @ SV1677 @ SV1429 @ SV1112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8344]) ).
thf(8528,plain,
! [SV1113: $i,SV1678: $i,SV1430: $i] :
( ( ( ~ ( c_lessequals @ SV1430 @ SV1678 @ SV1113 ) )
= $true )
| ( ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1678 @ SV1113 ) @ ( c_SetInterval_OgreaterThan @ SV1430 @ SV1113 ) @ ( tc_set @ SV1113 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV1113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8345]) ).
thf(8529,plain,
! [SV1114: $i,SV1679: $i,SV1431: $i] :
( ( ( ~ ( c_in @ SV1431 @ ( c_SetInterval_OlessThan @ SV1679 @ SV1114 ) @ SV1114 ) )
= $true )
| ( ( c_less @ SV1431 @ SV1679 @ SV1114 )
= $true )
| ( ( class_Orderings_Oord @ SV1114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8346]) ).
thf(8530,plain,
! [SV1115: $i,SV1680: $i,SV1432: $i] :
( ( ( ~ ( c_less @ SV1432 @ SV1680 @ SV1115 ) )
= $true )
| ( ( c_in @ SV1432 @ ( c_SetInterval_OlessThan @ SV1680 @ SV1115 ) @ SV1115 )
= $true )
| ( ( class_Orderings_Oord @ SV1115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8347]) ).
thf(8531,plain,
! [SV1681: $i,SV1116: $i,SV1433: $i] :
( ( ( ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1433 @ SV1116 ) @ ( c_SetInterval_OlessThan @ SV1681 @ SV1116 ) @ ( tc_set @ SV1116 ) ) )
= $true )
| ( ( c_lessequals @ SV1433 @ SV1681 @ SV1116 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8348]) ).
thf(8532,plain,
! [SV1117: $i,SV1682: $i,SV1434: $i] :
( ( ( ~ ( c_lessequals @ SV1434 @ SV1682 @ SV1117 ) )
= $true )
| ( ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1434 @ SV1117 ) @ ( c_SetInterval_OlessThan @ SV1682 @ SV1117 ) @ ( tc_set @ SV1117 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV1117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8349]) ).
thf(8533,plain,
! [SV1683: $i,SV1435: $i,SV1118: $i] :
( ( ( c_in @ SV1118 @ ( c_uminus @ SV1435 @ ( tc_set @ SV1683 ) ) @ SV1683 )
= $false )
| ( ( c_in @ SV1118 @ SV1435 @ SV1683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8350]) ).
thf(8534,plain,
! [SV1847: $i,SV1687: $i,SV1439: $i,SV1122: $i] :
( ( ( c_in @ SV1122 @ SV1439 @ SV1687 )
= $false )
| ( ( ~ ( c_in @ SV1122 @ ( c_minus @ SV1847 @ SV1439 @ ( tc_set @ SV1687 ) ) @ SV1687 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8353]) ).
thf(8535,plain,
! [SV1848: $i,SV1688: $i,SV1440: $i,SV1123: $i] :
( ( ( c_in @ SV1123 @ ( c_minus @ SV1440 @ SV1688 @ ( tc_set @ SV1848 ) ) @ SV1848 )
= $false )
| ( ( c_in @ SV1123 @ SV1440 @ SV1848 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8354]) ).
thf(8536,plain,
! [SV1849: $i,SV1689: $i,SV1441: $i,SV1124: $i] :
( ( ( c_in @ SV1124 @ SV1441 @ SV1689 )
= $false )
| ( ( ( c_in @ SV1124 @ SV1849 @ SV1689 )
| ( c_in @ SV1124 @ ( c_minus @ SV1441 @ SV1849 @ ( tc_set @ SV1689 ) ) @ SV1689 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8355]) ).
thf(8537,plain,
! [SV1850: $i,SV1690: $i,SV1442: $i,SV1125: $i] :
( ( ( c_in @ SV1125 @ ( c_inter @ SV1442 @ SV1690 @ SV1850 ) @ SV1850 )
= $false )
| ( ( c_in @ SV1125 @ SV1690 @ SV1850 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8356]) ).
thf(8538,plain,
! [SV1851: $i,SV1691: $i,SV1443: $i,SV1126: $i] :
( ( ( c_in @ SV1126 @ ( c_inter @ SV1443 @ SV1691 @ SV1851 ) @ SV1851 )
= $false )
| ( ( c_in @ SV1126 @ SV1443 @ SV1851 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8357]) ).
thf(8539,plain,
! [SV1852: $i,SV1692: $i,SV1444: $i,SV1127: $i] :
( ( ( c_in @ SV1127 @ SV1444 @ SV1692 )
= $false )
| ( ( ~ ( c_in @ SV1127 @ SV1852 @ SV1692 )
| ( c_in @ SV1127 @ ( c_inter @ SV1852 @ SV1444 @ SV1692 ) @ SV1692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8358]) ).
thf(8540,plain,
! [SV1853: $i,SV1693: $i,SV1445: $i,SV1128: $i] :
( ( ( c_in @ SV1128 @ SV1445 @ ( tc_set @ SV1693 ) )
= $false )
| ( ( ~ ( c_in @ SV1853 @ ( c_Inter @ SV1445 @ SV1693 ) @ SV1693 )
| ( c_in @ SV1853 @ SV1128 @ SV1693 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8359]) ).
thf(8541,plain,
! [SV1854: $i,SV1696: $i,SV1448: $i,SV1131: $i] :
( ( ( c_in @ SV1131 @ SV1448 @ SV1696 )
= $false )
| ( ( c_in @ SV1131 @ ( c_union @ SV1854 @ SV1448 @ SV1696 ) @ SV1696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8362]) ).
thf(8542,plain,
! [SV1855: $i,SV1697: $i,SV1449: $i,SV1132: $i] :
( ( ( c_in @ SV1132 @ SV1449 @ SV1697 )
= $false )
| ( ( c_in @ SV1132 @ ( c_union @ SV1449 @ SV1855 @ SV1697 ) @ SV1697 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8363]) ).
thf(8543,plain,
! [SV1856: $i,SV1698: $i,SV1450: $i,SV1133: $i] :
( ( ( c_in @ SV1133 @ ( c_union @ SV1450 @ SV1698 @ SV1856 ) @ SV1856 )
= $false )
| ( ( ( c_in @ SV1133 @ SV1698 @ SV1856 )
| ( c_in @ SV1133 @ SV1450 @ SV1856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8364]) ).
thf(8544,plain,
! [SV1857: $i,SV1699: $i,SV1451: $i,SV1135: $i] :
( ( ( c_in @ SV1135 @ SV1451 @ SV1699 )
= $false )
| ( ( ~ ( c_in @ SV1451 @ SV1857 @ ( tc_set @ SV1699 ) )
| ( c_in @ SV1135 @ ( c_Union @ SV1857 @ SV1699 ) @ SV1699 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8365]) ).
thf(8545,plain,
! [SV1858: $i,SV1700: $i,SV1453: $i,SV1137: $i] :
( ( ( c_in @ SV1137 @ SV1453 @ SV1700 )
= $false )
| ( ( c_in @ SV1137 @ ( c_insert @ SV1858 @ SV1453 @ SV1700 ) @ SV1700 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8366]) ).
thf(8546,plain,
! [SV1859: $i,SV1702: $i,SV1455: $i,SV1139: $i] :
( ( ( c_in @ SV1139 @ ( c_insert @ SV1455 @ SV1702 @ SV1859 ) @ SV1859 )
= $false )
| ( ( ( c_in @ SV1139 @ SV1702 @ SV1859 )
| ( SV1139 = SV1455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8367]) ).
thf(8547,plain,
! [SV1860: $i,SV1705: $i,SV1461: $i,SV1145: $i] :
( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1145 @ SV1461 @ SV1705 @ SV1705 ) @ SV1860 @ ( tc_prod @ SV1705 @ SV1705 ) ) @ SV1705 )
= $false )
| ( ( c_Wellfounded__Recursion_Oacyclic @ SV1860 @ SV1705 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8370]) ).
thf(8548,plain,
! [SV1861: $i,SV1706: $i,SV1462: $i,SV1146: $i] :
( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1146 @ SV1462 @ SV1706 @ SV1706 ) @ SV1861 @ ( tc_prod @ SV1706 @ SV1706 ) ) @ SV1706 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1462 @ SV1146 @ SV1706 @ SV1706 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1706 ) @ ( tc_prod @ SV1706 @ SV1706 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8371]) ).
thf(8549,plain,
! [SV1862: $i,SV1707: $i,SV1463: $i,SV1147: $i] :
( ( ( c_Wellfounded__Recursion_Oacyclic @ SV1147 @ SV1463 )
= $false )
| ( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1707 @ SV1862 @ SV1463 @ SV1463 ) @ SV1147 @ ( tc_prod @ SV1463 @ SV1463 ) ) @ SV1463 )
| ( c_in @ ( c_Pair @ SV1862 @ SV1707 @ SV1463 @ SV1463 ) @ ( c_Transitive__Closure_Ortrancl @ SV1147 @ SV1463 ) @ ( tc_prod @ SV1463 @ SV1463 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8372]) ).
thf(8550,plain,
! [SV1863: $i,SV1708: $i,SV1464: $i,SV1148: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1148 @ SV1464 @ SV1708 @ SV1708 ) @ SV1863 @ ( tc_prod @ SV1708 @ SV1708 ) ) @ SV1708 )
= $false )
| ( ( c_Wellfounded__Recursion_Owf @ SV1863 @ SV1708 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8373]) ).
thf(8551,plain,
! [SV1864: $i,SV1709: $i,SV1465: $i,SV1149: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1149 @ SV1465 @ SV1709 @ SV1709 ) @ SV1864 @ ( tc_prod @ SV1709 @ SV1709 ) ) @ SV1709 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1465 @ SV1149 @ SV1709 @ SV1709 ) @ ( c_Transitive__Closure_Ortrancl @ SV1864 @ SV1709 ) @ ( tc_prod @ SV1709 @ SV1709 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8374]) ).
thf(8552,plain,
! [SV1865: $i,SV1710: $i,SV1466: $i,SV1150: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ SV1150 @ SV1466 )
= $false )
| ( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1710 @ SV1865 @ SV1466 @ SV1466 ) @ SV1150 @ ( tc_prod @ SV1466 @ SV1466 ) ) @ SV1466 )
| ( c_in @ ( c_Pair @ SV1865 @ SV1710 @ SV1466 @ SV1466 ) @ ( c_Transitive__Closure_Ortrancl @ SV1150 @ SV1466 ) @ ( tc_prod @ SV1466 @ SV1466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8375]) ).
thf(8553,plain,
! [SV1473: $i,SV1715: $i,SV1157: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1157 ) ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV1473 @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1157 @ SV1473 ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8380]) ).
thf(8554,plain,
! [SV1477: $i,SV1716: $i,SV1161: $i] :
( ( ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1716 ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV1161 @ ( c_Message_Oparts @ SV1477 ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV1161 @ ( c_Message_Oparts @ ( c_union @ SV1477 @ SV1716 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8381]) ).
thf(8555,plain,
! [SV1866: $i,SV1720: $i,SV1483: $i,SV1168: $i] :
( ( ( c_lessequals @ SV1168 @ SV1483 @ ( tc_set @ SV1720 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1866 @ SV1168 @ ( tc_set @ SV1720 ) )
| ( c_lessequals @ SV1866 @ SV1483 @ ( tc_set @ SV1720 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8383]) ).
thf(8556,plain,
! [SV1868: $i,SV1722: $i,SV1485: $i,SV1170: $i] :
( ( ( ( c_Message_Omsg_OCrypt @ SV1170 @ SV1485 )
= ( c_Message_Omsg_OCrypt @ SV1722 @ SV1868 ) )
= $false )
| ( ( SV1170 = SV1722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8385]) ).
thf(8557,plain,
! [SV1952: $i,SV1869: $i,SV1723: $i,SV1487: $i,SV1172: $i] :
( ( ( ( c_append @ SV1172 @ ( c_List_Olist_OCons @ SV1487 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 )
!= ( c_append @ SV1869 @ ( c_List_Olist_OCons @ SV1952 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 ) )
= $true )
| ( ( SV1487 = SV1952 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8386]) ).
thf(8558,plain,
! [SV1953: $i,SV1870: $i,SV1724: $i,SV1488: $i,SV1173: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1173 @ SV1488 @ SV1724 @ SV1870 )
= ( c_Datatype__Universe_ONumb @ SV1953 @ SV1724 @ SV1870 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8387]) ).
thf(8559,plain,
! [SV1871: $i,SV1725: $i,SV1491: $i,SV1176: $i] :
( ( ( ( c_Datatype__Universe_OLeaf @ SV1176 @ SV1491 @ SV1725 )
= ( c_Datatype__Universe_OLeaf @ SV1871 @ SV1491 @ SV1725 ) )
= $false )
| ( ( SV1176 = SV1871 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8388]) ).
thf(8560,plain,
! [SV1873: $i,SV1727: $i,SV1494: $i,SV1180: $i] :
( ( ( ( c_Datatype__Universe_ONumb @ SV1180 @ SV1494 @ SV1727 )
= ( c_Datatype__Universe_ONumb @ SV1873 @ SV1494 @ SV1727 ) )
= $false )
| ( ( SV1180 = SV1873 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8390]) ).
thf(8561,plain,
! [SV1874: $i,SV1729: $i,SV1497: $i,SV1184: $i] :
( ( ( ( c_Message_Omsg_OMPair @ SV1184 @ SV1497 )
= ( c_Message_Omsg_OMPair @ SV1729 @ SV1874 ) )
= $false )
| ( ( SV1184 = SV1729 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8392]) ).
thf(8562,plain,
! [SV1954: $i,SV1875: $i,SV1730: $i,SV1498: $i,SV1185: $i] :
( ( ( ( c_List_Olist_OCons @ SV1185 @ SV1498 @ SV1730 )
!= ( c_List_Olist_OCons @ SV1875 @ SV1954 @ SV1730 ) )
= $true )
| ( ( SV1498 = SV1954 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8393]) ).
thf(8563,plain,
! [SV1955: $i,SV1877: $i,SV1732: $i,SV1501: $i,SV1188: $i] :
( ( ( ( c_append @ SV1188 @ ( c_List_Olist_OCons @ SV1501 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 )
!= ( c_append @ SV1877 @ ( c_List_Olist_OCons @ SV1955 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 ) )
= $true )
| ( ( SV1188 = SV1877 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8395]) ).
thf(8564,plain,
! [SV1878: $i,SV1733: $i,SV1502: $i,SV1189: $i] :
( ( ( ( c_Datatype__Universe_OAtom @ SV1189 @ SV1502 @ SV1733 )
= ( c_Datatype__Universe_OAtom @ SV1878 @ SV1502 @ SV1733 ) )
= $false )
| ( ( SV1189 = SV1878 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8396]) ).
thf(8565,plain,
! [SV1879: $i,SV1735: $i,SV1504: $i,SV1192: $i] :
( ( ( ( c_Datatype__Universe_OIn1 @ SV1192 @ SV1504 @ SV1735 )
= ( c_Datatype__Universe_OIn1 @ SV1879 @ SV1504 @ SV1735 ) )
= $false )
| ( ( SV1192 = SV1879 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8398]) ).
thf(8566,plain,
! [SV1737: $i,SV1194: $i,SV1506: $i] :
( ( ( ( c_SetInterval_OlessThan @ SV1506 @ SV1194 )
!= ( c_SetInterval_OlessThan @ SV1737 @ SV1194 ) )
= $true )
| ( ( SV1506 = SV1737 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8400]) ).
thf(8567,plain,
! [SV1975: $i,SV1956: $i,SV1880: $i,SV1738: $i,SV1507: $i,SV1195: $i] :
( ( ( ( c_Pair @ SV1195 @ SV1507 @ SV1738 @ SV1880 )
!= ( c_Pair @ SV1956 @ SV1975 @ SV1738 @ SV1880 ) )
| ( SV1195 = SV1956 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8401]) ).
thf(8568,plain,
! [SV1881: $i,SV1740: $i,SV1510: $i,SV1198: $i] :
( ( ( ( c_List_Ochar_OChar @ SV1198 @ SV1510 )
= ( c_List_Ochar_OChar @ SV1740 @ SV1881 ) )
= $false )
| ( ( SV1510 = SV1881 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8402]) ).
thf(8569,plain,
! [SV1957: $i,SV1882: $i,SV1741: $i,SV1512: $i,SV1200: $i] :
( ( ( c_Datatype__Universe_OLeaf @ SV1200 @ SV1512 @ SV1741 )
= ( c_Datatype__Universe_OScons @ SV1882 @ SV1957 @ SV1512 @ SV1741 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8403]) ).
thf(8570,plain,
! [SV1883: $i,SV1743: $i,SV1514: $i,SV1202: $i] :
( ( ( ( c_append @ SV1202 @ SV1514 @ SV1743 )
= ( c_append @ SV1202 @ SV1883 @ SV1743 ) )
= $false )
| ( ( SV1514 = SV1883 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8405]) ).
thf(8571,plain,
! [SV1884: $i,SV1745: $i,SV1516: $i,SV1205: $i] :
( ( ( ( c_Datatype__Universe_OIn0 @ SV1205 @ SV1516 @ SV1745 )
= ( c_Datatype__Universe_OIn0 @ SV1884 @ SV1516 @ SV1745 ) )
= $false )
| ( ( SV1205 = SV1884 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8407]) ).
thf(8572,plain,
! [SV1976: $i,SV1958: $i,SV1885: $i,SV1746: $i,SV1517: $i,SV1206: $i] :
( ( ( ( c_Pair @ SV1206 @ SV1517 @ SV1746 @ SV1885 )
!= ( c_Pair @ SV1958 @ SV1976 @ SV1746 @ SV1885 ) )
| ( SV1517 = SV1976 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8408]) ).
thf(8573,plain,
! [SV1959: $i,SV1886: $i,SV1747: $i,SV1518: $i,SV1207: $i] :
( ( ( c_Datatype__Universe_OAtom @ SV1207 @ SV1518 @ SV1747 )
= ( c_Datatype__Universe_OScons @ SV1886 @ SV1959 @ SV1518 @ SV1747 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8409]) ).
thf(8574,plain,
! [SV1887: $i,SV1748: $i,SV1519: $i,SV1209: $i] :
( ( ( ( c_List_Orev @ SV1209 @ SV1519 )
= ( c_List_Olist_OCons @ SV1748 @ SV1887 @ SV1519 ) )
= $false )
| ( ( SV1209
= ( c_append @ ( c_List_Orev @ SV1887 @ SV1519 ) @ ( c_List_Olist_OCons @ SV1748 @ c_List_Olist_ONil @ SV1519 ) @ SV1519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8410]) ).
thf(8575,plain,
! [SV1749: $i,SV1210: $i,SV1520: $i] :
( ( ( ( c_SetInterval_OatLeast @ SV1520 @ SV1210 )
!= ( c_SetInterval_OatLeast @ SV1749 @ SV1210 ) )
= $true )
| ( ( SV1520 = SV1749 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8411]) ).
thf(8576,plain,
! [SV1960: $i,SV1888: $i,SV1751: $i,SV1522: $i,SV1212: $i] :
( ( ( c_Datatype__Universe_ONumb @ SV1212 @ SV1522 @ SV1751 )
= ( c_Datatype__Universe_OScons @ SV1888 @ SV1960 @ SV1522 @ SV1751 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8413]) ).
thf(8577,plain,
! [SV1889: $i,SV1752: $i,SV1523: $i,SV1213: $i] :
( ( ( ( c_insert @ SV1213 @ c_emptyset @ SV1523 )
= ( c_insert @ SV1752 @ SV1889 @ SV1523 ) )
= $false )
| ( ( SV1752 = SV1213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8414]) ).
thf(8578,plain,
! [SV1757: $i,SV1221: $i,SV1530: $i] :
( ( ( ( c_SetInterval_OgreaterThan @ SV1530 @ SV1221 )
!= ( c_SetInterval_OgreaterThan @ SV1757 @ SV1221 ) )
= $true )
| ( ( SV1530 = SV1757 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8419]) ).
thf(8579,plain,
! [SV1890: $i,SV1758: $i,SV1531: $i,SV1222: $i] :
( ( ( ( c_Message_Omsg_OCrypt @ SV1222 @ SV1531 )
= ( c_Message_Omsg_OCrypt @ SV1758 @ SV1890 ) )
= $false )
| ( ( SV1531 = SV1890 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8420]) ).
thf(8580,plain,
! [SV1961: $i,SV1892: $i,SV1764: $i,SV1543: $i,SV1234: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1234 @ SV1543 @ SV1764 @ SV1892 )
= ( c_Datatype__Universe_OLeaf @ SV1961 @ SV1764 @ SV1892 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8426]) ).
thf(8581,plain,
! [SV1962: $i,SV1893: $i,SV1765: $i,SV1544: $i,SV1235: $i] :
( ( ( ( c_List_Olist_OCons @ SV1235 @ SV1544 @ SV1765 )
!= ( c_List_Olist_OCons @ SV1893 @ SV1962 @ SV1765 ) )
= $true )
| ( ( SV1235 = SV1893 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8427]) ).
thf(8582,plain,
! [SV1895: $i,SV1768: $i,SV1549: $i,SV1240: $i] :
( ( ( ( c_Sum__Type_OInl @ SV1240 @ SV1549 @ SV1768 )
= ( c_Sum__Type_OInl @ SV1895 @ SV1549 @ SV1768 ) )
= $false )
| ( ( SV1240 = SV1895 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8429]) ).
thf(8583,plain,
! [SV1977: $i,SV1963: $i,SV1896: $i,SV1769: $i,SV1550: $i,SV1241: $i] :
( ( ( ( c_Datatype__Universe_OScons @ SV1241 @ SV1550 @ SV1769 @ SV1896 )
!= ( c_Datatype__Universe_OScons @ SV1963 @ SV1977 @ SV1769 @ SV1896 ) )
| ( SV1241 = SV1963 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8430]) ).
thf(8584,plain,
! [SV1897: $i,SV1770: $i,SV1551: $i,SV1242: $i] :
( ( ( ( c_append @ SV1242 @ SV1551 @ SV1770 )
= ( c_append @ SV1897 @ SV1551 @ SV1770 ) )
= $false )
| ( ( SV1242 = SV1897 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8431]) ).
thf(8585,plain,
! [SV1964: $i,SV1898: $i,SV1771: $i,SV1553: $i,SV1244: $i] :
( ( ( c_Datatype__Universe_OScons @ SV1244 @ SV1553 @ SV1771 @ SV1898 )
= ( c_Datatype__Universe_OAtom @ SV1964 @ SV1771 @ SV1898 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8432]) ).
thf(8586,plain,
! [SV1900: $i,SV1773: $i,SV1555: $i,SV1246: $i] :
( ( ( ( c_List_Ochar_OChar @ SV1246 @ SV1555 )
= ( c_List_Ochar_OChar @ SV1773 @ SV1900 ) )
= $false )
| ( ( SV1246 = SV1773 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8434]) ).
thf(8587,plain,
! [SV1978: $i,SV1965: $i,SV1901: $i,SV1775: $i,SV1557: $i,SV1248: $i] :
( ( ( ( c_Datatype__Universe_OScons @ SV1248 @ SV1557 @ SV1775 @ SV1901 )
!= ( c_Datatype__Universe_OScons @ SV1965 @ SV1978 @ SV1775 @ SV1901 ) )
| ( SV1557 = SV1978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8436]) ).
thf(8588,plain,
! [SV1776: $i,SV1249: $i,SV1558: $i] :
( ( ( ( c_SetInterval_OatMost @ SV1558 @ SV1249 )
!= ( c_SetInterval_OatMost @ SV1776 @ SV1249 ) )
= $true )
| ( ( SV1558 = SV1776 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8437]) ).
thf(8589,plain,
! [SV1902: $i,SV1778: $i,SV1561: $i,SV1252: $i] :
( ( ( ( c_Message_Omsg_OMPair @ SV1252 @ SV1561 )
= ( c_Message_Omsg_OMPair @ SV1778 @ SV1902 ) )
= $false )
| ( ( SV1561 = SV1902 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8439]) ).
thf(8590,plain,
! [SV1903: $i,SV1779: $i,SV1562: $i,SV1253: $i] :
( ( ( ( c_insert @ SV1253 @ c_emptyset @ SV1562 )
= ( c_insert @ SV1779 @ SV1903 @ SV1562 ) )
= $false )
| ( ( c_lessequals @ SV1903 @ ( c_insert @ SV1253 @ c_emptyset @ SV1562 ) @ ( tc_set @ SV1562 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8440]) ).
thf(8591,plain,
! [SV1904: $i,SV1780: $i,SV1564: $i,SV1255: $i] :
( ( ( ( c_Sum__Type_OInr @ SV1255 @ SV1564 @ SV1780 )
= ( c_Sum__Type_OInr @ SV1904 @ SV1564 @ SV1780 ) )
= $false )
| ( ( SV1255 = SV1904 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8441]) ).
thf(8592,plain,
! [SV1905: $i,SV1781: $i,SV1565: $i,SV1256: $i] :
( ( ( ( c_insert @ SV1256 @ SV1565 @ SV1781 )
= ( c_insert @ SV1905 @ c_emptyset @ SV1781 ) )
= $false )
| ( ( c_lessequals @ SV1565 @ ( c_insert @ SV1905 @ c_emptyset @ SV1781 ) @ ( tc_set @ SV1781 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8442]) ).
thf(8593,plain,
! [SV1906: $i,SV1782: $i,SV1566: $i,SV1257: $i] :
( ( ( ( c_insert @ SV1257 @ SV1566 @ SV1782 )
= ( c_insert @ SV1906 @ c_emptyset @ SV1782 ) )
= $false )
| ( ( SV1257 = SV1906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8443]) ).
thf(8594,plain,
! [SV1907: $i,SV1783: $i,SV1567: $i,SV1258: $i,SV1: $i] :
( ( ( c_in @ SV1 @ ( c_Datatype__Universe_Odprod @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) ) )
= $false )
| ( ( SV1
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( c_Main_OdprodE__2 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ SV1783 @ SV1907 ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ ( c_Main_OdprodE__4 @ SV1 @ SV1258 @ SV1567 @ SV1783 @ SV1907 ) @ SV1783 @ SV1907 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1783 @ SV1907 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8444]) ).
thf(8595,plain,
! [SV1908: $i,SV1784: $i,SV1568: $i,SV1259: $i,SV2: $i] :
( ( ( c_in @ SV2 @ ( c_Datatype__Universe_Odprod @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( c_Main_OdprodE__4 @ SV2 @ SV1259 @ SV1568 @ SV1784 @ SV1908 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) @ SV1568 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1784 @ SV1908 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8445]) ).
thf(8596,plain,
! [SV1909: $i,SV1785: $i,SV1569: $i,SV1260: $i,SV3: $i] :
( ( ( c_in @ SV3 @ ( c_Datatype__Universe_Odprod @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( c_Main_OdprodE__3 @ SV3 @ SV1260 @ SV1569 @ SV1785 @ SV1909 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) @ SV1260 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1785 @ SV1909 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8446]) ).
thf(8597,plain,
! [SV1979: $i,SV1966: $i,SV1910: $i,SV1786: $i,SV1570: $i,SV1261: $i,SV4: $i] :
( ( ! [SY3420: $i] :
( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SV1966 @ SV1979 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SY3420 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1966 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SV1979 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SY3420 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8447]) ).
thf(8598,plain,
! [SV1911: $i,SV1787: $i,SV1571: $i,SV1262: $i,SV5: $i] :
( ( ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SV1262 @ SV1571 @ SV1787 @ SV1911 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
= $false )
| ( ( ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
| ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8448]) ).
thf(8599,plain,
! [SV1912: $i,SV1788: $i,SV1572: $i,SV1263: $i,SV6: $i] :
( ( ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SV1263 @ SV1572 @ SV1788 @ SV1912 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( c_Main_OdsumE__4 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) @ SV1572 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
| ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8449]) ).
thf(8600,plain,
! [SV1913: $i,SV1789: $i,SV1573: $i,SV1264: $i,SV7: $i] :
( ( ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1264 @ SV1573 @ SV1789 @ SV1913 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( c_Main_OdsumE__2 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) @ SV1264 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
| ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8450]) ).
thf(8601,plain,
! [SV1914: $i,SV1790: $i,SV1574: $i,SV1265: $i,SV8: $i] :
( ( ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1265 @ SV1574 @ SV1790 @ SV1914 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__2 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1265 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__4 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1574 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8451]) ).
thf(8602,plain,
! [SV1967: $i,SV1915: $i,SV1791: $i,SV1575: $i,SV1266: $i,SV9: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV9 @ SV1266 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ SV1915 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SV1575 @ SV1791 ) @ ( c_Datatype__Universe_OIn0 @ SV1266 @ SV1575 @ SV1791 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1915 @ SV1967 @ SV1575 @ SV1791 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8452]) ).
thf(8603,plain,
! [SV1968: $i,SV1916: $i,SV1792: $i,SV1576: $i,SV1267: $i,SV10: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV10 @ SV1267 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ SV1916 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SV1576 @ SV1792 ) @ ( c_Datatype__Universe_OIn1 @ SV1267 @ SV1576 @ SV1792 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1968 @ SV1916 @ SV1576 @ SV1792 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8453]) ).
thf(8604,plain,
! [SV1917: $i,SV1793: $i,SV1577: $i,SV1268: $i,SV11: $i] :
( ( ( c_in @ SV11 @ ( c_Datatype__Universe_Ouprod @ SV1268 @ SV1577 @ SV1793 @ SV1917 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1793 @ SV1917 ) ) )
= $false )
| ( ( SV11
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SV1917 ) @ ( c_Main_OuprodE__2 @ SV1268 @ SV1577 @ SV11 @ SV1793 @ SV1917 ) @ SV1793 @ SV1917 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8454]) ).
thf(8605,plain,
! [SV1918: $i,SV1794: $i,SV1578: $i,SV1269: $i,SV12: $i] :
( ( ( c_in @ SV12 @ ( c_Datatype__Universe_Ouprod @ SV1269 @ SV1578 @ SV1794 @ SV1918 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SV1918 ) ) )
= $false )
| ( ( c_in @ ( c_Main_OuprodE__2 @ SV1269 @ SV1578 @ SV12 @ SV1794 @ SV1918 ) @ SV1578 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1794 @ SV1918 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8455]) ).
thf(8606,plain,
! [SV1919: $i,SV1795: $i,SV1579: $i,SV1270: $i,SV13: $i] :
( ( ( c_in @ SV13 @ ( c_Datatype__Universe_Ouprod @ SV1270 @ SV1579 @ SV1795 @ SV1919 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SV1919 ) ) )
= $false )
| ( ( c_in @ ( c_Main_OuprodE__1 @ SV1270 @ SV1579 @ SV13 @ SV1795 @ SV1919 ) @ SV1270 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1795 @ SV1919 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8456]) ).
thf(8607,plain,
! [SV1969: $i,SV1920: $i,SV1796: $i,SV1580: $i,SV1271: $i,SV14: $i] :
( ( ( ~ ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1920 @ SV1969 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SV1920 @ SV14 @ SV1580 @ SV1796 ) @ ( c_Datatype__Universe_Ouprod @ SV1969 @ SV1271 @ SV1580 @ SV1796 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8457]) ).
thf(8608,plain,
! [SV1921: $i,SV1797: $i,SV1581: $i,SV1272: $i,SV15: $i] :
( ( ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SV1272 @ SV1581 @ SV1797 @ SV1921 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1797 @ SV1921 ) ) )
= $false )
| ( ( ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1272 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) )
| ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1581 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8458]) ).
thf(8609,plain,
! [SV1922: $i,SV1798: $i,SV1582: $i,SV1273: $i,SV16: $i] :
( ( ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SV1273 @ SV1582 @ SV1798 @ SV1922 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) )
= $false )
| ( ( ( c_in @ ( c_Main_OusumE__2 @ SV1582 @ SV16 @ SV1798 @ SV1922 ) @ SV1582 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) )
| ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1273 @ SV16 @ SV1798 @ SV1922 ) @ SV1798 @ SV1922 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8459]) ).
thf(8610,plain,
! [SV1923: $i,SV1799: $i,SV1583: $i,SV1274: $i,SV17: $i] :
( ( ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1274 @ SV1583 @ SV1799 @ SV1923 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) )
= $false )
| ( ( ( c_in @ ( c_Main_OusumE__1 @ SV1274 @ SV17 @ SV1799 @ SV1923 ) @ SV1274 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) )
| ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1583 @ SV17 @ SV1799 @ SV1923 ) @ SV1799 @ SV1923 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8460]) ).
thf(8611,plain,
! [SV1924: $i,SV1800: $i,SV1584: $i,SV1275: $i,SV18: $i] :
( ( ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1275 @ SV1584 @ SV1800 @ SV1924 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
= $false )
| ( ( ( c_in @ ( c_Main_OusumE__1 @ SV1275 @ SV18 @ SV1800 @ SV1924 ) @ SV1275 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
| ( c_in @ ( c_Main_OusumE__2 @ SV1584 @ SV18 @ SV1800 @ SV1924 ) @ SV1584 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8461]) ).
thf(8612,plain,
! [SV1925: $i,SV1801: $i,SV1585: $i,SV1276: $i,SV19: $i] :
( ( ( c_in @ SV19 @ SV1276 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) )
= $false )
| ( ( c_in @ ( c_Datatype__Universe_OIn0 @ SV19 @ SV1585 @ SV1801 ) @ ( c_Datatype__Universe_Ousum @ SV1276 @ SV1925 @ SV1585 @ SV1801 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1585 @ SV1801 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8462]) ).
thf(8613,plain,
! [SV1926: $i,SV1802: $i,SV1586: $i,SV1277: $i,SV20: $i] :
( ( ( c_in @ SV20 @ SV1277 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) )
= $false )
| ( ( c_in @ ( c_Datatype__Universe_OIn1 @ SV20 @ SV1586 @ SV1802 ) @ ( c_Datatype__Universe_Ousum @ SV1926 @ SV1277 @ SV1586 @ SV1802 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1586 @ SV1802 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8463]) ).
thf(8614,plain,
! [SV1803: $i,SV1287: $i,SV33: $i,SV1590: $i] :
( ( ( ~ ( c_in @ SV1590 @ SV33 @ SV1287 ) )
= $true )
| ( ( ~ ( c_in @ SV1803 @ SV33 @ SV1287 )
| ( SV1590 = SV1803 ) )
= $true )
| ( ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8465]) ).
thf(8615,plain,
! [SV1294: $i,SV1591: $i,SV42: $i,SV1804: $i] :
( ( ( ~ ( c_in @ SV1804 @ ( c_List_Oset @ SV42 @ SV1591 ) @ SV1591 ) )
= $true )
| ( ( c_in @ SV1804 @ SV1294 @ SV1591 )
= $true )
| ( ( c_in @ SV42 @ ( c_List_Olists @ SV1294 @ SV1591 ) @ ( tc_List_Olist @ SV1591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8466]) ).
thf(8616,plain,
! [SV1927: $i,SV1805: $i,SV1594: $i,SV1298: $i,SV46: $i] :
( ( ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV46 @ SV1298 @ SV1594 ) @ SV1805 @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) @ ( c_List_Olistrel @ SV1927 @ SV1594 ) @ ( tc_prod @ ( tc_List_Olist @ SV1594 ) @ ( tc_List_Olist @ SV1594 ) ) )
= $false )
| ( ( SV1805
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ SV1927 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ ( c_Main_Olistrel__Cons1__2 @ SV1927 @ SV1805 @ SV46 @ SV1298 @ SV1594 ) @ SV1594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8467]) ).
thf(8617,plain,
! [SV1928: $i,SV1806: $i,SV1595: $i,SV1299: $i,SV47: $i] :
( ( ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV47 @ SV1299 @ SV1595 ) @ SV1806 @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SV1928 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1299 @ ( c_Main_Olistrel__Cons1__2 @ SV1928 @ SV1806 @ SV47 @ SV1299 @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) @ ( c_List_Olistrel @ SV1928 @ SV1595 ) @ ( tc_prod @ ( tc_List_Olist @ SV1595 ) @ ( tc_List_Olist @ SV1595 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8468]) ).
thf(8618,plain,
! [SV1929: $i,SV1807: $i,SV1596: $i,SV1300: $i,SV48: $i] :
( ( ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ SV48 @ SV1300 @ SV1596 ) @ SV1807 @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) @ ( c_List_Olistrel @ SV1929 @ SV1596 ) @ ( tc_prod @ ( tc_List_Olist @ SV1596 ) @ ( tc_List_Olist @ SV1596 ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV48 @ ( c_Main_Olistrel__Cons1__1 @ SV1929 @ SV1807 @ SV48 @ SV1300 @ SV1596 ) @ SV1596 @ SV1596 ) @ SV1929 @ ( tc_prod @ SV1596 @ SV1596 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8469]) ).
thf(8619,plain,
! [SV1930: $i,SV1808: $i,SV1597: $i,SV1301: $i,SV49: $i] :
( ( ( c_in @ ( c_Pair @ SV49 @ ( c_List_Olist_OCons @ SV1301 @ SV1597 @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) @ ( c_List_Olistrel @ SV1930 @ SV1808 ) @ ( tc_prod @ ( tc_List_Olist @ SV1808 ) @ ( tc_List_Olist @ SV1808 ) ) )
= $false )
| ( ( SV49
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ SV1930 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ ( c_Main_Olistrel__Cons2__2 @ SV1930 @ SV49 @ SV1301 @ SV1597 @ SV1808 ) @ SV1808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8470]) ).
thf(8620,plain,
! [SV1931: $i,SV1809: $i,SV1598: $i,SV1302: $i,SV50: $i] :
( ( ( c_in @ ( c_Pair @ SV50 @ ( c_List_Olist_OCons @ SV1302 @ SV1598 @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SV1931 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ SV1931 @ SV50 @ SV1302 @ SV1598 @ SV1809 ) @ SV1598 @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) @ ( c_List_Olistrel @ SV1931 @ SV1809 ) @ ( tc_prod @ ( tc_List_Olist @ SV1809 ) @ ( tc_List_Olist @ SV1809 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8471]) ).
thf(8621,plain,
! [SV1932: $i,SV1810: $i,SV1599: $i,SV1303: $i,SV51: $i] :
( ( ( c_in @ ( c_Pair @ SV51 @ ( c_List_Olist_OCons @ SV1303 @ SV1599 @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) @ ( c_List_Olistrel @ SV1932 @ SV1810 ) @ ( tc_prod @ ( tc_List_Olist @ SV1810 ) @ ( tc_List_Olist @ SV1810 ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ SV1932 @ SV51 @ SV1303 @ SV1599 @ SV1810 ) @ SV1303 @ SV1810 @ SV1810 ) @ SV1932 @ ( tc_prod @ SV1810 @ SV1810 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8472]) ).
thf(8622,plain,
! [SV56: $i,SV1604: $i,SV1308: $i,SV1813: $i] :
( ( ( ~ ( c_in @ SV1813 @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) ) )
= $true )
| ( ( c_in @ ( c_List_Olist_OCons @ SV56 @ SV1813 @ SV1604 ) @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) )
= $true )
| ( ( c_in @ SV56 @ SV1308 @ SV1604 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8475]) ).
thf(8623,plain,
! [SV1933: $i,SV1815: $i,SV1606: $i,SV1314: $i,SV66: $i] :
( ( ( c_in @ ( c_Pair @ SV66 @ SV1314 @ SV1606 @ SV1815 ) @ SV1933 @ ( tc_prod @ SV1606 @ SV1815 ) )
= $false )
| ( ( c_in @ SV66 @ ( c_Relation_ODomain @ SV1933 @ SV1606 @ SV1815 ) @ SV1606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8477]) ).
thf(8624,plain,
! [SV1934: $i,SV1816: $i,SV1607: $i,SV1316: $i,SV68: $i] :
( ( ( c_in @ SV68 @ ( c_Relation_OImage @ SV1316 @ SV1607 @ SV1816 @ SV1934 ) @ SV1934 )
= $false )
| ( ( c_in @ ( c_Main_OImageE__1 @ SV1607 @ SV68 @ SV1316 @ SV1816 @ SV1934 ) @ SV1607 @ SV1816 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8478]) ).
thf(8625,plain,
! [SV1935: $i,SV1817: $i,SV1608: $i,SV1317: $i,SV69: $i] :
( ( ( c_in @ SV69 @ ( c_Relation_OImage @ SV1317 @ SV1608 @ SV1817 @ SV1935 ) @ SV1935 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ SV1608 @ SV69 @ SV1317 @ SV1817 @ SV1935 ) @ SV69 @ SV1817 @ SV1935 ) @ SV1317 @ ( tc_prod @ SV1817 @ SV1935 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8479]) ).
thf(8626,plain,
! [SV1970: $i,SV1936: $i,SV1818: $i,SV1609: $i,SV1318: $i,SV70: $i] :
( ( ( ~ ( c_in @ SV70 @ SV1318 @ SV1609 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1818 @ SV1609 @ SV1936 ) @ SV1970 @ ( tc_prod @ SV1609 @ SV1936 ) )
| ( c_in @ SV1818 @ ( c_Relation_OImage @ SV1970 @ SV1318 @ SV1609 @ SV1936 ) @ SV1936 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8480]) ).
thf(8627,plain,
! [SV1937: $i,SV1820: $i,SV1611: $i,SV1320: $i,SV72: $i] :
( ( ( c_in @ ( c_Pair @ SV72 @ SV1320 @ SV1611 @ SV1820 ) @ SV1937 @ ( tc_prod @ SV1611 @ SV1820 ) )
= $false )
| ( ( c_in @ SV1320 @ ( c_Relation_ORange @ SV1937 @ SV1611 @ SV1820 ) @ SV1820 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8482]) ).
thf(8628,plain,
! [SV1971: $i,SV1938: $i,SV1823: $i,SV1617: $i,SV1326: $i,SV78: $i] :
( ( ( ~ ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SV1326 @ SV1617 @ SV1823 @ SV1938 @ SV1971 ) @ ( tc_prod @ SV1971 @ SV1938 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SV1971 ) @ ( c_Main_Orel__compE__3 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SV1971 ) @ SV1823 @ SV1938 ) @ SV1326 @ ( tc_prod @ SV1823 @ SV1938 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8485]) ).
thf(8629,plain,
! [SV1972: $i,SV1939: $i,SV1824: $i,SV1618: $i,SV1327: $i,SV79: $i] :
( ( ( ~ ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SV1327 @ SV1618 @ SV1824 @ SV1939 @ SV1972 ) @ ( tc_prod @ SV1972 @ SV1939 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SV1972 ) @ ( c_Main_Orel__compE__2 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SV1972 ) @ SV1972 @ SV1824 ) @ SV1618 @ ( tc_prod @ SV1972 @ SV1824 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8486]) ).
thf(8630,plain,
! [SV1973: $i,SV1940: $i,SV1825: $i,SV1619: $i,SV1328: $i,SV80: $i] :
( ( ( ~ ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SV1328 @ SV1619 @ SV1825 @ SV1940 @ SV1973 ) @ ( tc_prod @ SV1973 @ SV1940 ) ) )
= $true )
| ( ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SV1973 ) @ ( c_Main_Orel__compE__3 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SV1973 ) @ SV1973 @ SV1940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8487]) ).
thf(8631,plain,
! [SV1980: $i,SV1974: $i,SV1941: $i,SV1826: $i,SV1620: $i,SV1329: $i,SV81: $i] :
( ( ! [SY3421: $i] :
( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) )
| ~ ( c_in @ ( c_Pair @ SV1974 @ SV81 @ SV1980 @ SV1620 ) @ SY3421 @ ( tc_prod @ SV1980 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SV1974 @ SV1329 @ SV1980 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SY3421 @ SV1620 @ SV1826 @ SV1980 ) @ ( tc_prod @ SV1980 @ SV1826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8488]) ).
thf(8632,plain,
! [SV103: $i,SV1629: $i,SV1827: $i,SV1349: $i] :
( ( ( ~ ( c_lessequals @ SV1349 @ SV1827 @ ( tc_set @ SV1629 ) ) )
= $true )
| ( ( c_in @ SV103 @ SV1827 @ SV1629 )
= $true )
| ( ( c_in @ SV103 @ SV1349 @ SV1629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8491]) ).
thf(8633,plain,
! [SV1632: $i,SV106: $i,SV1352: $i] :
( ( ( c_lessequals @ SV1352 @ SV106 @ ( tc_set @ SV1632 ) )
= $false )
| ( ( SV1352 = SV106 )
= $true )
| ( ( c_lessequals @ SV106 @ SV1352 @ ( tc_set @ SV1632 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8492]) ).
thf(8634,plain,
! [SV1942: $i,SV1828: $i,SV1633: $i,SV1354: $i,SV108: $i] :
( ( ( c_in @ SV108 @ SV1354 @ SV1633 )
= $false )
| ( ( c_in @ ( c_Sum__Type_OInl @ SV108 @ SV1633 @ SV1828 ) @ ( c_Sum__Type_OPlus @ SV1354 @ SV1942 @ SV1633 @ SV1828 ) @ ( tc_sum @ SV1633 @ SV1828 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8493]) ).
thf(8635,plain,
! [SV1943: $i,SV1829: $i,SV1634: $i,SV1355: $i,SV109: $i] :
( ( ( c_in @ SV109 @ SV1355 @ SV1634 )
= $false )
| ( ( c_in @ ( c_Sum__Type_OInr @ SV109 @ SV1634 @ SV1829 ) @ ( c_Sum__Type_OPlus @ SV1943 @ SV1355 @ SV1829 @ SV1634 ) @ ( tc_sum @ SV1829 @ SV1634 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8494]) ).
thf(8636,plain,
! [SV1944: $i,SV1830: $i,SV1635: $i,SV1356: $i,SV110: $i] :
( ( ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SV1356 @ SV1635 @ SV1830 @ SV1944 ) @ ( tc_sum @ SV1830 @ SV1944 ) )
= $false )
| ( ( ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1356 @ SV110 @ SV1830 @ SV1944 ) @ SV1830 @ SV1944 ) )
| ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1635 @ SV110 @ SV1944 @ SV1830 ) @ SV1944 @ SV1830 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8495]) ).
thf(8637,plain,
! [SV1945: $i,SV1831: $i,SV1636: $i,SV1357: $i,SV111: $i] :
( ( ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SV1357 @ SV1636 @ SV1831 @ SV1945 ) @ ( tc_sum @ SV1831 @ SV1945 ) )
= $false )
| ( ( ( c_in @ ( c_Main_OPlusE__2 @ SV1636 @ SV111 @ SV1945 @ SV1831 ) @ SV1636 @ SV1945 )
| ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1357 @ SV111 @ SV1831 @ SV1945 ) @ SV1831 @ SV1945 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8496]) ).
thf(8638,plain,
! [SV1946: $i,SV1832: $i,SV1637: $i,SV1358: $i,SV112: $i] :
( ( ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SV1358 @ SV1637 @ SV1832 @ SV1946 ) @ ( tc_sum @ SV1832 @ SV1946 ) )
= $false )
| ( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1358 @ SV112 @ SV1832 @ SV1946 ) @ SV1358 @ SV1832 )
| ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1637 @ SV112 @ SV1946 @ SV1832 ) @ SV1946 @ SV1832 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8497]) ).
thf(8639,plain,
! [SV1947: $i,SV1833: $i,SV1638: $i,SV1359: $i,SV113: $i] :
( ( ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SV1359 @ SV1638 @ SV1833 @ SV1947 ) @ ( tc_sum @ SV1833 @ SV1947 ) )
= $false )
| ( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1359 @ SV113 @ SV1833 @ SV1947 ) @ SV1359 @ SV1833 )
| ( c_in @ ( c_Main_OPlusE__2 @ SV1638 @ SV113 @ SV1947 @ SV1833 ) @ SV1638 @ SV1947 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8498]) ).
thf(8640,plain,
! [SV1364: $i,SV119: $i,SV1836: $i,SV1643: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV1643 @ SV1836 ) )
= $true )
| ( ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1643 @ SV119 @ SV1836 @ SV1364 ) @ ( tc_prod @ SV1836 @ SV1364 ) )
= $true )
| ( ( c_Relation_Otrans @ SV119 @ SV1364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8501]) ).
thf(8641,plain,
! [SV1365: $i,SV120: $i,SV1837: $i,SV1644: $i] :
( ( ( ~ ( c_Wellfounded__Recursion_Owf @ SV1644 @ SV1837 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1644 @ SV120 @ SV1837 @ SV1365 ) @ ( tc_prod @ SV1837 @ SV1365 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Owf @ SV120 @ SV1365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8502]) ).
thf(8642,plain,
! [SV1051: $i,SV1382: $i,SV1650: $i] :
( ( ( c_in @ SV1650 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
= $false )
| ( ( c_in @ ( c_union @ SV1650 @ SV1051 @ SV1382 ) @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
= $true )
| ( ( c_in @ SV1051 @ c_Finite__Set_OFinites @ ( tc_set @ SV1382 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8508]) ).
thf(8643,plain,
! [SV1387: $i,SV1655: $i,SV1056: $i] :
( ( ( c_Divides_Oop_Advd @ SV1056 @ SV1655 @ tc_nat )
= $false )
| ( ( c_Divides_Oop_Advd @ SV1056 @ ( c_GCD_Ogcd @ ( c_Pair @ SV1655 @ SV1387 @ tc_nat @ tc_nat ) ) @ tc_nat )
= $true )
| ( ( c_Divides_Oop_Advd @ SV1056 @ SV1387 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8509]) ).
thf(8644,plain,
! [SV1068: $i,SV1660: $i,SV1396: $i,SV1842: $i] :
( ( ( ~ ( c_in @ SV1842 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) ) )
= $true )
| ( ( c_in @ ( c_append @ SV1842 @ SV1068 @ SV1660 ) @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
= $true )
| ( ( c_in @ SV1068 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8512]) ).
thf(8645,plain,
! [SV1948: $i,SV1843: $i,SV1662: $i,SV1414: $i,SV1097: $i] :
( ( ( c_in @ SV1097 @ ( c_Relation_OImage @ SV1414 @ ( c_insert @ SV1662 @ c_emptyset @ SV1843 ) @ SV1843 @ SV1948 ) @ SV1948 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1662 @ SV1097 @ SV1843 @ SV1948 ) @ SV1414 @ ( tc_prod @ SV1843 @ SV1948 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8513]) ).
thf(8646,plain,
! [SV1949: $i,SV1844: $i,SV1663: $i,SV1415: $i,SV1098: $i] :
( ( ( c_in @ ( c_Pair @ SV1098 @ SV1415 @ SV1663 @ SV1844 ) @ SV1949 @ ( tc_prod @ SV1663 @ SV1844 ) )
= $false )
| ( ( c_in @ SV1415 @ ( c_Relation_OImage @ SV1949 @ ( c_insert @ SV1098 @ c_emptyset @ SV1663 ) @ SV1663 @ SV1844 ) @ SV1844 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8514]) ).
thf(8647,plain,
! [SV1950: $i,SV1845: $i,SV1664: $i,SV1416: $i,SV1099: $i] :
( ( ( c_in @ ( c_Pair @ SV1099 @ SV1416 @ SV1664 @ SV1845 ) @ ( c_Relation_Oconverse @ SV1950 @ SV1845 @ SV1664 ) @ ( tc_prod @ SV1664 @ SV1845 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1416 @ SV1099 @ SV1845 @ SV1664 ) @ SV1950 @ ( tc_prod @ SV1845 @ SV1664 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8515]) ).
thf(8648,plain,
! [SV1951: $i,SV1846: $i,SV1665: $i,SV1417: $i,SV1100: $i] :
( ( ( c_in @ ( c_Pair @ SV1100 @ SV1417 @ SV1665 @ SV1846 ) @ SV1951 @ ( tc_prod @ SV1665 @ SV1846 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1417 @ SV1100 @ SV1846 @ SV1665 ) @ ( c_Relation_Oconverse @ SV1951 @ SV1665 @ SV1846 ) @ ( tc_prod @ SV1846 @ SV1665 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8516]) ).
thf(8649,plain,
! [SV1102: $i,SV1667: $i,SV1419: $i] :
( ( ( c_in @ SV1419 @ ( c_SetInterval_OatLeast @ SV1667 @ SV1102 ) @ SV1102 )
= $false )
| ( ( c_lessequals @ SV1667 @ SV1419 @ SV1102 )
= $true )
| ( ( class_Orderings_Oord @ SV1102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8517]) ).
thf(8650,plain,
! [SV1103: $i,SV1668: $i,SV1420: $i] :
( ( ( c_lessequals @ SV1420 @ SV1668 @ SV1103 )
= $false )
| ( ( c_in @ SV1668 @ ( c_SetInterval_OatLeast @ SV1420 @ SV1103 ) @ SV1103 )
= $true )
| ( ( class_Orderings_Oord @ SV1103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8518]) ).
thf(8651,plain,
! [SV1669: $i,SV1104: $i,SV1421: $i] :
( ( ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1421 @ SV1104 ) @ ( c_SetInterval_OatLeast @ SV1669 @ SV1104 ) @ ( tc_set @ SV1104 ) )
= $false )
| ( ( c_lessequals @ SV1669 @ SV1421 @ SV1104 )
= $true )
| ( ( class_Orderings_Oorder @ SV1104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8519]) ).
thf(8652,plain,
! [SV1105: $i,SV1670: $i,SV1422: $i] :
( ( ( c_lessequals @ SV1422 @ SV1670 @ SV1105 )
= $false )
| ( ( c_lessequals @ ( c_SetInterval_OatLeast @ SV1670 @ SV1105 ) @ ( c_SetInterval_OatLeast @ SV1422 @ SV1105 ) @ ( tc_set @ SV1105 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV1105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8520]) ).
thf(8653,plain,
! [SV1106: $i,SV1671: $i,SV1423: $i] :
( ( ( c_in @ SV1423 @ ( c_SetInterval_OatMost @ SV1671 @ SV1106 ) @ SV1106 )
= $false )
| ( ( c_lessequals @ SV1423 @ SV1671 @ SV1106 )
= $true )
| ( ( class_Orderings_Oord @ SV1106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8521]) ).
thf(8654,plain,
! [SV1107: $i,SV1672: $i,SV1424: $i] :
( ( ( c_lessequals @ SV1424 @ SV1672 @ SV1107 )
= $false )
| ( ( c_in @ SV1424 @ ( c_SetInterval_OatMost @ SV1672 @ SV1107 ) @ SV1107 )
= $true )
| ( ( class_Orderings_Oord @ SV1107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8522]) ).
thf(8655,plain,
! [SV1673: $i,SV1108: $i,SV1425: $i] :
( ( ( c_lessequals @ ( c_SetInterval_OatMost @ SV1425 @ SV1108 ) @ ( c_SetInterval_OatMost @ SV1673 @ SV1108 ) @ ( tc_set @ SV1108 ) )
= $false )
| ( ( c_lessequals @ SV1425 @ SV1673 @ SV1108 )
= $true )
| ( ( class_Orderings_Oorder @ SV1108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8523]) ).
thf(8656,plain,
! [SV1109: $i,SV1674: $i,SV1426: $i] :
( ( ( c_lessequals @ SV1426 @ SV1674 @ SV1109 )
= $false )
| ( ( c_lessequals @ ( c_SetInterval_OatMost @ SV1426 @ SV1109 ) @ ( c_SetInterval_OatMost @ SV1674 @ SV1109 ) @ ( tc_set @ SV1109 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV1109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8524]) ).
thf(8657,plain,
! [SV1110: $i,SV1675: $i,SV1427: $i] :
( ( ( c_in @ SV1427 @ ( c_SetInterval_OgreaterThan @ SV1675 @ SV1110 ) @ SV1110 )
= $false )
| ( ( c_less @ SV1675 @ SV1427 @ SV1110 )
= $true )
| ( ( class_Orderings_Oord @ SV1110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8525]) ).
thf(8658,plain,
! [SV1111: $i,SV1676: $i,SV1428: $i] :
( ( ( c_less @ SV1428 @ SV1676 @ SV1111 )
= $false )
| ( ( c_in @ SV1676 @ ( c_SetInterval_OgreaterThan @ SV1428 @ SV1111 ) @ SV1111 )
= $true )
| ( ( class_Orderings_Oord @ SV1111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8526]) ).
thf(8659,plain,
! [SV1677: $i,SV1112: $i,SV1429: $i] :
( ( ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1429 @ SV1112 ) @ ( c_SetInterval_OgreaterThan @ SV1677 @ SV1112 ) @ ( tc_set @ SV1112 ) )
= $false )
| ( ( c_lessequals @ SV1677 @ SV1429 @ SV1112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8527]) ).
thf(8660,plain,
! [SV1113: $i,SV1678: $i,SV1430: $i] :
( ( ( c_lessequals @ SV1430 @ SV1678 @ SV1113 )
= $false )
| ( ( c_lessequals @ ( c_SetInterval_OgreaterThan @ SV1678 @ SV1113 ) @ ( c_SetInterval_OgreaterThan @ SV1430 @ SV1113 ) @ ( tc_set @ SV1113 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV1113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8528]) ).
thf(8661,plain,
! [SV1114: $i,SV1679: $i,SV1431: $i] :
( ( ( c_in @ SV1431 @ ( c_SetInterval_OlessThan @ SV1679 @ SV1114 ) @ SV1114 )
= $false )
| ( ( c_less @ SV1431 @ SV1679 @ SV1114 )
= $true )
| ( ( class_Orderings_Oord @ SV1114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8529]) ).
thf(8662,plain,
! [SV1115: $i,SV1680: $i,SV1432: $i] :
( ( ( c_less @ SV1432 @ SV1680 @ SV1115 )
= $false )
| ( ( c_in @ SV1432 @ ( c_SetInterval_OlessThan @ SV1680 @ SV1115 ) @ SV1115 )
= $true )
| ( ( class_Orderings_Oord @ SV1115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8530]) ).
thf(8663,plain,
! [SV1681: $i,SV1116: $i,SV1433: $i] :
( ( ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1433 @ SV1116 ) @ ( c_SetInterval_OlessThan @ SV1681 @ SV1116 ) @ ( tc_set @ SV1116 ) )
= $false )
| ( ( c_lessequals @ SV1433 @ SV1681 @ SV1116 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8531]) ).
thf(8664,plain,
! [SV1117: $i,SV1682: $i,SV1434: $i] :
( ( ( c_lessequals @ SV1434 @ SV1682 @ SV1117 )
= $false )
| ( ( c_lessequals @ ( c_SetInterval_OlessThan @ SV1434 @ SV1117 ) @ ( c_SetInterval_OlessThan @ SV1682 @ SV1117 ) @ ( tc_set @ SV1117 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV1117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8532]) ).
thf(8665,plain,
! [SV1687: $i,SV1439: $i,SV1847: $i,SV1122: $i] :
( ( ( c_in @ SV1122 @ ( c_minus @ SV1847 @ SV1439 @ ( tc_set @ SV1687 ) ) @ SV1687 )
= $false )
| ( ( c_in @ SV1122 @ SV1439 @ SV1687 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8534]) ).
thf(8666,plain,
! [SV1441: $i,SV1689: $i,SV1849: $i,SV1124: $i] :
( ( ( c_in @ SV1124 @ SV1849 @ SV1689 )
= $true )
| ( ( c_in @ SV1124 @ ( c_minus @ SV1441 @ SV1849 @ ( tc_set @ SV1689 ) ) @ SV1689 )
= $true )
| ( ( c_in @ SV1124 @ SV1441 @ SV1689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8536]) ).
thf(8667,plain,
! [SV1444: $i,SV1692: $i,SV1852: $i,SV1127: $i] :
( ( ( ~ ( c_in @ SV1127 @ SV1852 @ SV1692 ) )
= $true )
| ( ( c_in @ SV1127 @ ( c_inter @ SV1852 @ SV1444 @ SV1692 ) @ SV1692 )
= $true )
| ( ( c_in @ SV1127 @ SV1444 @ SV1692 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8539]) ).
thf(8668,plain,
! [SV1128: $i,SV1693: $i,SV1445: $i,SV1853: $i] :
( ( ( ~ ( c_in @ SV1853 @ ( c_Inter @ SV1445 @ SV1693 ) @ SV1693 ) )
= $true )
| ( ( c_in @ SV1853 @ SV1128 @ SV1693 )
= $true )
| ( ( c_in @ SV1128 @ SV1445 @ ( tc_set @ SV1693 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8540]) ).
thf(8669,plain,
! [SV1450: $i,SV1856: $i,SV1698: $i,SV1133: $i] :
( ( ( c_in @ SV1133 @ SV1698 @ SV1856 )
= $true )
| ( ( c_in @ SV1133 @ SV1450 @ SV1856 )
= $true )
| ( ( c_in @ SV1133 @ ( c_union @ SV1450 @ SV1698 @ SV1856 ) @ SV1856 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8543]) ).
thf(8670,plain,
! [SV1135: $i,SV1699: $i,SV1857: $i,SV1451: $i] :
( ( ( ~ ( c_in @ SV1451 @ SV1857 @ ( tc_set @ SV1699 ) ) )
= $true )
| ( ( c_in @ SV1135 @ ( c_Union @ SV1857 @ SV1699 ) @ SV1699 )
= $true )
| ( ( c_in @ SV1135 @ SV1451 @ SV1699 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8544]) ).
thf(8671,plain,
! [SV1455: $i,SV1859: $i,SV1702: $i,SV1139: $i] :
( ( ( c_in @ SV1139 @ SV1702 @ SV1859 )
= $true )
| ( ( SV1139 = SV1455 )
= $true )
| ( ( c_in @ SV1139 @ ( c_insert @ SV1455 @ SV1702 @ SV1859 ) @ SV1859 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8546]) ).
thf(8672,plain,
! [SV1861: $i,SV1706: $i,SV1146: $i,SV1462: $i] :
( ( ( c_in @ ( c_Pair @ SV1462 @ SV1146 @ SV1706 @ SV1706 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1706 ) @ ( tc_prod @ SV1706 @ SV1706 ) )
= $false )
| ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1146 @ SV1462 @ SV1706 @ SV1706 ) @ SV1861 @ ( tc_prod @ SV1706 @ SV1706 ) ) @ SV1706 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8548]) ).
thf(8673,plain,
! [SV1147: $i,SV1463: $i,SV1862: $i,SV1707: $i] :
( ( ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ SV1707 @ SV1862 @ SV1463 @ SV1463 ) @ SV1147 @ ( tc_prod @ SV1463 @ SV1463 ) ) @ SV1463 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1862 @ SV1707 @ SV1463 @ SV1463 ) @ ( c_Transitive__Closure_Ortrancl @ SV1147 @ SV1463 ) @ ( tc_prod @ SV1463 @ SV1463 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Oacyclic @ SV1147 @ SV1463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8549]) ).
thf(8674,plain,
! [SV1864: $i,SV1709: $i,SV1149: $i,SV1465: $i] :
( ( ( c_in @ ( c_Pair @ SV1465 @ SV1149 @ SV1709 @ SV1709 ) @ ( c_Transitive__Closure_Ortrancl @ SV1864 @ SV1709 ) @ ( tc_prod @ SV1709 @ SV1709 ) )
= $false )
| ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1149 @ SV1465 @ SV1709 @ SV1709 ) @ SV1864 @ ( tc_prod @ SV1709 @ SV1709 ) ) @ SV1709 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8551]) ).
thf(8675,plain,
! [SV1150: $i,SV1466: $i,SV1865: $i,SV1710: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ SV1710 @ SV1865 @ SV1466 @ SV1466 ) @ SV1150 @ ( tc_prod @ SV1466 @ SV1466 ) ) @ SV1466 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1865 @ SV1710 @ SV1466 @ SV1466 ) @ ( c_Transitive__Closure_Ortrancl @ SV1150 @ SV1466 ) @ ( tc_prod @ SV1466 @ SV1466 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Owf @ SV1150 @ SV1466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8552]) ).
thf(8676,plain,
! [SV1473: $i,SV1715: $i,SV1157: $i] :
( ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ SV1157 ) ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV1473 @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1157 @ SV1473 ) @ ( c_Message_Oanalz @ SV1715 ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8553]) ).
thf(8677,plain,
! [SV1483: $i,SV1720: $i,SV1168: $i,SV1866: $i] :
( ( ( ~ ( c_lessequals @ SV1866 @ SV1168 @ ( tc_set @ SV1720 ) ) )
= $true )
| ( ( c_lessequals @ SV1866 @ SV1483 @ ( tc_set @ SV1720 ) )
= $true )
| ( ( c_lessequals @ SV1168 @ SV1483 @ ( tc_set @ SV1720 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8555]) ).
thf(8678,plain,
! [SV1952: $i,SV1869: $i,SV1723: $i,SV1487: $i,SV1172: $i] :
( ( ( ( c_append @ SV1172 @ ( c_List_Olist_OCons @ SV1487 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 )
= ( c_append @ SV1869 @ ( c_List_Olist_OCons @ SV1952 @ c_List_Olist_ONil @ SV1723 ) @ SV1723 ) )
= $false )
| ( ( SV1487 = SV1952 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8557]) ).
thf(8679,plain,
! [SV1954: $i,SV1875: $i,SV1730: $i,SV1498: $i,SV1185: $i] :
( ( ( ( c_List_Olist_OCons @ SV1185 @ SV1498 @ SV1730 )
= ( c_List_Olist_OCons @ SV1875 @ SV1954 @ SV1730 ) )
= $false )
| ( ( SV1498 = SV1954 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8562]) ).
thf(8680,plain,
! [SV1955: $i,SV1877: $i,SV1732: $i,SV1501: $i,SV1188: $i] :
( ( ( ( c_append @ SV1188 @ ( c_List_Olist_OCons @ SV1501 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 )
= ( c_append @ SV1877 @ ( c_List_Olist_OCons @ SV1955 @ c_List_Olist_ONil @ SV1732 ) @ SV1732 ) )
= $false )
| ( ( SV1188 = SV1877 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8563]) ).
thf(8681,plain,
! [SV1737: $i,SV1194: $i,SV1506: $i] :
( ( ( ( c_SetInterval_OlessThan @ SV1506 @ SV1194 )
= ( c_SetInterval_OlessThan @ SV1737 @ SV1194 ) )
= $false )
| ( ( SV1506 = SV1737 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8566]) ).
thf(8682,plain,
! [SV1975: $i,SV1956: $i,SV1880: $i,SV1738: $i,SV1507: $i,SV1195: $i] :
( ( ( ( c_Pair @ SV1195 @ SV1507 @ SV1738 @ SV1880 )
!= ( c_Pair @ SV1956 @ SV1975 @ SV1738 @ SV1880 ) )
= $true )
| ( ( SV1195 = SV1956 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8567]) ).
thf(8683,plain,
! [SV1976: $i,SV1958: $i,SV1885: $i,SV1746: $i,SV1517: $i,SV1206: $i] :
( ( ( ( c_Pair @ SV1206 @ SV1517 @ SV1746 @ SV1885 )
!= ( c_Pair @ SV1958 @ SV1976 @ SV1746 @ SV1885 ) )
= $true )
| ( ( SV1517 = SV1976 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8572]) ).
thf(8684,plain,
! [SV1749: $i,SV1210: $i,SV1520: $i] :
( ( ( ( c_SetInterval_OatLeast @ SV1520 @ SV1210 )
= ( c_SetInterval_OatLeast @ SV1749 @ SV1210 ) )
= $false )
| ( ( SV1520 = SV1749 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8575]) ).
thf(8685,plain,
! [SV1757: $i,SV1221: $i,SV1530: $i] :
( ( ( ( c_SetInterval_OgreaterThan @ SV1530 @ SV1221 )
= ( c_SetInterval_OgreaterThan @ SV1757 @ SV1221 ) )
= $false )
| ( ( SV1530 = SV1757 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8578]) ).
thf(8686,plain,
! [SV1962: $i,SV1893: $i,SV1765: $i,SV1544: $i,SV1235: $i] :
( ( ( ( c_List_Olist_OCons @ SV1235 @ SV1544 @ SV1765 )
= ( c_List_Olist_OCons @ SV1893 @ SV1962 @ SV1765 ) )
= $false )
| ( ( SV1235 = SV1893 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8581]) ).
thf(8687,plain,
! [SV1977: $i,SV1963: $i,SV1896: $i,SV1769: $i,SV1550: $i,SV1241: $i] :
( ( ( ( c_Datatype__Universe_OScons @ SV1241 @ SV1550 @ SV1769 @ SV1896 )
!= ( c_Datatype__Universe_OScons @ SV1963 @ SV1977 @ SV1769 @ SV1896 ) )
= $true )
| ( ( SV1241 = SV1963 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8583]) ).
thf(8688,plain,
! [SV1978: $i,SV1965: $i,SV1901: $i,SV1775: $i,SV1557: $i,SV1248: $i] :
( ( ( ( c_Datatype__Universe_OScons @ SV1248 @ SV1557 @ SV1775 @ SV1901 )
!= ( c_Datatype__Universe_OScons @ SV1965 @ SV1978 @ SV1775 @ SV1901 ) )
= $true )
| ( ( SV1557 = SV1978 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8587]) ).
thf(8689,plain,
! [SV1776: $i,SV1249: $i,SV1558: $i] :
( ( ( ( c_SetInterval_OatMost @ SV1558 @ SV1249 )
= ( c_SetInterval_OatMost @ SV1776 @ SV1249 ) )
= $false )
| ( ( SV1558 = SV1776 )
= $true )
| ( ( class_Orderings_Olinorder @ SV1249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8588]) ).
thf(8690,plain,
! [SV1981: $i,SV1979: $i,SV1966: $i,SV1910: $i,SV1786: $i,SV1570: $i,SV1261: $i,SV4: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ~ ( c_in @ ( c_Pair @ SV1966 @ SV1979 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1981 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1966 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SV1979 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV1981 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8597]) ).
thf(8691,plain,
! [SV1571: $i,SV1911: $i,SV1787: $i,SV1262: $i,SV5: $i] :
( ( ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1262 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
= $true )
| ( ( SV5
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1571 @ SV5 @ SV1787 @ SV1911 ) @ SV1787 @ SV1911 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
= $true )
| ( ( c_in @ SV5 @ ( c_Datatype__Universe_Odsum @ SV1262 @ SV1571 @ SV1787 @ SV1911 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1787 @ SV1911 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8598]) ).
thf(8692,plain,
! [SV1263: $i,SV1912: $i,SV1788: $i,SV6: $i,SV1572: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( c_Main_OdsumE__4 @ SV1572 @ SV6 @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) @ SV1572 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
= $true )
| ( ( SV6
= ( c_Pair @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__1 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( c_Datatype__Universe_OIn0 @ ( c_Main_OdsumE__2 @ SV1263 @ SV6 @ SV1788 @ SV1912 ) @ SV1788 @ SV1912 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
= $true )
| ( ( c_in @ SV6 @ ( c_Datatype__Universe_Odsum @ SV1263 @ SV1572 @ SV1788 @ SV1912 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1788 @ SV1912 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8599]) ).
thf(8693,plain,
! [SV1573: $i,SV1913: $i,SV1789: $i,SV7: $i,SV1264: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( c_Main_OdsumE__2 @ SV1264 @ SV7 @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) @ SV1264 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
= $true )
| ( ( SV7
= ( c_Pair @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__3 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( c_Datatype__Universe_OIn1 @ ( c_Main_OdsumE__4 @ SV1573 @ SV7 @ SV1789 @ SV1913 ) @ SV1789 @ SV1913 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
= $true )
| ( ( c_in @ SV7 @ ( c_Datatype__Universe_Odsum @ SV1264 @ SV1573 @ SV1789 @ SV1913 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1789 @ SV1913 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8600]) ).
thf(8694,plain,
! [SV1574: $i,SV1914: $i,SV1790: $i,SV8: $i,SV1265: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__1 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__2 @ SV1265 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1265 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Main_OdsumE__3 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( c_Main_OdsumE__4 @ SV1574 @ SV8 @ SV1790 @ SV1914 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) @ SV1574 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
= $true )
| ( ( c_in @ SV8 @ ( c_Datatype__Universe_Odsum @ SV1265 @ SV1574 @ SV1790 @ SV1914 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1790 @ SV1914 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8601]) ).
thf(8695,plain,
! [SV1967: $i,SV1915: $i,SV1791: $i,SV1575: $i,SV1266: $i,SV9: $i] :
( ( ( c_in @ ( c_Pair @ SV9 @ SV1266 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ SV1915 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ SV9 @ SV1575 @ SV1791 ) @ ( c_Datatype__Universe_OIn0 @ SV1266 @ SV1575 @ SV1791 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1915 @ SV1967 @ SV1575 @ SV1791 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1575 @ SV1791 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8602]) ).
thf(8696,plain,
! [SV1968: $i,SV1916: $i,SV1792: $i,SV1576: $i,SV1267: $i,SV10: $i] :
( ( ( c_in @ ( c_Pair @ SV10 @ SV1267 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ SV1916 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ SV10 @ SV1576 @ SV1792 ) @ ( c_Datatype__Universe_OIn1 @ SV1267 @ SV1576 @ SV1792 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) @ ( c_Datatype__Universe_Odsum @ SV1968 @ SV1916 @ SV1576 @ SV1792 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1576 @ SV1792 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8603]) ).
thf(8697,plain,
! [SV1969: $i,SV1920: $i,SV1796: $i,SV1580: $i,SV1271: $i,SV14: $i] :
( ( ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
= $false )
| ( ( ~ ( c_in @ SV1920 @ SV1969 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ SV1920 @ SV14 @ SV1580 @ SV1796 ) @ ( c_Datatype__Universe_Ouprod @ SV1969 @ SV1271 @ SV1580 @ SV1796 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8607]) ).
thf(8698,plain,
! [SV1581: $i,SV1921: $i,SV1797: $i,SV1272: $i,SV15: $i] :
( ( ( SV15
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1272 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) )
= $true )
| ( ( SV15
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1581 @ SV15 @ SV1797 @ SV1921 ) @ SV1797 @ SV1921 ) )
= $true )
| ( ( c_in @ SV15 @ ( c_Datatype__Universe_Ousum @ SV1272 @ SV1581 @ SV1797 @ SV1921 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1797 @ SV1921 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8608]) ).
thf(8699,plain,
! [SV1273: $i,SV1922: $i,SV1798: $i,SV16: $i,SV1582: $i] :
( ( ( c_in @ ( c_Main_OusumE__2 @ SV1582 @ SV16 @ SV1798 @ SV1922 ) @ SV1582 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) )
= $true )
| ( ( SV16
= ( c_Datatype__Universe_OIn0 @ ( c_Main_OusumE__1 @ SV1273 @ SV16 @ SV1798 @ SV1922 ) @ SV1798 @ SV1922 ) )
= $true )
| ( ( c_in @ SV16 @ ( c_Datatype__Universe_Ousum @ SV1273 @ SV1582 @ SV1798 @ SV1922 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1798 @ SV1922 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8609]) ).
thf(8700,plain,
! [SV1583: $i,SV1923: $i,SV1799: $i,SV17: $i,SV1274: $i] :
( ( ( c_in @ ( c_Main_OusumE__1 @ SV1274 @ SV17 @ SV1799 @ SV1923 ) @ SV1274 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) )
= $true )
| ( ( SV17
= ( c_Datatype__Universe_OIn1 @ ( c_Main_OusumE__2 @ SV1583 @ SV17 @ SV1799 @ SV1923 ) @ SV1799 @ SV1923 ) )
= $true )
| ( ( c_in @ SV17 @ ( c_Datatype__Universe_Ousum @ SV1274 @ SV1583 @ SV1799 @ SV1923 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1799 @ SV1923 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8610]) ).
thf(8701,plain,
! [SV1584: $i,SV1924: $i,SV1800: $i,SV18: $i,SV1275: $i] :
( ( ( c_in @ ( c_Main_OusumE__1 @ SV1275 @ SV18 @ SV1800 @ SV1924 ) @ SV1275 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
= $true )
| ( ( c_in @ ( c_Main_OusumE__2 @ SV1584 @ SV18 @ SV1800 @ SV1924 ) @ SV1584 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
= $true )
| ( ( c_in @ SV18 @ ( c_Datatype__Universe_Ousum @ SV1275 @ SV1584 @ SV1800 @ SV1924 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1800 @ SV1924 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8611]) ).
thf(8702,plain,
! [SV1803: $i,SV1287: $i,SV33: $i,SV1590: $i] :
( ( ( c_in @ SV1590 @ SV33 @ SV1287 )
= $false )
| ( ( ~ ( c_in @ SV1803 @ SV33 @ SV1287 )
| ( SV1590 = SV1803 ) )
= $true )
| ( ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8614]) ).
thf(8703,plain,
! [SV1294: $i,SV1591: $i,SV42: $i,SV1804: $i] :
( ( ( c_in @ SV1804 @ ( c_List_Oset @ SV42 @ SV1591 ) @ SV1591 )
= $false )
| ( ( c_in @ SV1804 @ SV1294 @ SV1591 )
= $true )
| ( ( c_in @ SV42 @ ( c_List_Olists @ SV1294 @ SV1591 ) @ ( tc_List_Olist @ SV1591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8615]) ).
thf(8704,plain,
! [SV56: $i,SV1604: $i,SV1308: $i,SV1813: $i] :
( ( ( c_in @ SV1813 @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) )
= $false )
| ( ( c_in @ ( c_List_Olist_OCons @ SV56 @ SV1813 @ SV1604 ) @ ( c_List_Olists @ SV1308 @ SV1604 ) @ ( tc_List_Olist @ SV1604 ) )
= $true )
| ( ( c_in @ SV56 @ SV1308 @ SV1604 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8622]) ).
thf(8705,plain,
! [SV1970: $i,SV1936: $i,SV1818: $i,SV1609: $i,SV1318: $i,SV70: $i] :
( ( ( c_in @ SV70 @ SV1318 @ SV1609 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1818 @ SV1609 @ SV1936 ) @ SV1970 @ ( tc_prod @ SV1609 @ SV1936 ) )
| ( c_in @ SV1818 @ ( c_Relation_OImage @ SV1970 @ SV1318 @ SV1609 @ SV1936 ) @ SV1936 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8626]) ).
thf(8706,plain,
! [SV1971: $i,SV1938: $i,SV1823: $i,SV1617: $i,SV1326: $i,SV78: $i] :
( ( ( c_in @ SV78 @ ( c_Relation_Orel__comp @ SV1326 @ SV1617 @ SV1823 @ SV1938 @ SV1971 ) @ ( tc_prod @ SV1971 @ SV1938 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SV1971 ) @ ( c_Main_Orel__compE__3 @ SV1326 @ SV1617 @ SV78 @ SV1823 @ SV1938 @ SV1971 ) @ SV1823 @ SV1938 ) @ SV1326 @ ( tc_prod @ SV1823 @ SV1938 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8628]) ).
thf(8707,plain,
! [SV1972: $i,SV1939: $i,SV1824: $i,SV1618: $i,SV1327: $i,SV79: $i] :
( ( ( c_in @ SV79 @ ( c_Relation_Orel__comp @ SV1327 @ SV1618 @ SV1824 @ SV1939 @ SV1972 ) @ ( tc_prod @ SV1972 @ SV1939 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SV1972 ) @ ( c_Main_Orel__compE__2 @ SV1327 @ SV1618 @ SV79 @ SV1824 @ SV1939 @ SV1972 ) @ SV1972 @ SV1824 ) @ SV1618 @ ( tc_prod @ SV1972 @ SV1824 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8629]) ).
thf(8708,plain,
! [SV1973: $i,SV1940: $i,SV1825: $i,SV1619: $i,SV1328: $i,SV80: $i] :
( ( ( c_in @ SV80 @ ( c_Relation_Orel__comp @ SV1328 @ SV1619 @ SV1825 @ SV1940 @ SV1973 ) @ ( tc_prod @ SV1973 @ SV1940 ) )
= $false )
| ( ( SV80
= ( c_Pair @ ( c_Main_Orel__compE__1 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SV1973 ) @ ( c_Main_Orel__compE__3 @ SV1328 @ SV1619 @ SV80 @ SV1825 @ SV1940 @ SV1973 ) @ SV1973 @ SV1940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8630]) ).
thf(8709,plain,
! [SV1982: $i,SV1980: $i,SV1974: $i,SV1941: $i,SV1826: $i,SV1620: $i,SV1329: $i,SV81: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) )
| ~ ( c_in @ ( c_Pair @ SV1974 @ SV81 @ SV1980 @ SV1620 ) @ SV1982 @ ( tc_prod @ SV1980 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SV1974 @ SV1329 @ SV1980 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SV1982 @ SV1620 @ SV1826 @ SV1980 ) @ ( tc_prod @ SV1980 @ SV1826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8631]) ).
thf(8710,plain,
! [SV103: $i,SV1629: $i,SV1827: $i,SV1349: $i] :
( ( ( c_lessequals @ SV1349 @ SV1827 @ ( tc_set @ SV1629 ) )
= $false )
| ( ( c_in @ SV103 @ SV1827 @ SV1629 )
= $true )
| ( ( c_in @ SV103 @ SV1349 @ SV1629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8632]) ).
thf(8711,plain,
! [SV1635: $i,SV1944: $i,SV1830: $i,SV1356: $i,SV110: $i] :
( ( ( SV110
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1356 @ SV110 @ SV1830 @ SV1944 ) @ SV1830 @ SV1944 ) )
= $true )
| ( ( SV110
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1635 @ SV110 @ SV1944 @ SV1830 ) @ SV1944 @ SV1830 ) )
= $true )
| ( ( c_in @ SV110 @ ( c_Sum__Type_OPlus @ SV1356 @ SV1635 @ SV1830 @ SV1944 ) @ ( tc_sum @ SV1830 @ SV1944 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8636]) ).
thf(8712,plain,
! [SV1357: $i,SV1831: $i,SV1945: $i,SV111: $i,SV1636: $i] :
( ( ( c_in @ ( c_Main_OPlusE__2 @ SV1636 @ SV111 @ SV1945 @ SV1831 ) @ SV1636 @ SV1945 )
= $true )
| ( ( SV111
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ SV1357 @ SV111 @ SV1831 @ SV1945 ) @ SV1831 @ SV1945 ) )
= $true )
| ( ( c_in @ SV111 @ ( c_Sum__Type_OPlus @ SV1357 @ SV1636 @ SV1831 @ SV1945 ) @ ( tc_sum @ SV1831 @ SV1945 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8637]) ).
thf(8713,plain,
! [SV1637: $i,SV1946: $i,SV1832: $i,SV112: $i,SV1358: $i] :
( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1358 @ SV112 @ SV1832 @ SV1946 ) @ SV1358 @ SV1832 )
= $true )
| ( ( SV112
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ SV1637 @ SV112 @ SV1946 @ SV1832 ) @ SV1946 @ SV1832 ) )
= $true )
| ( ( c_in @ SV112 @ ( c_Sum__Type_OPlus @ SV1358 @ SV1637 @ SV1832 @ SV1946 ) @ ( tc_sum @ SV1832 @ SV1946 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8638]) ).
thf(8714,plain,
! [SV1638: $i,SV1947: $i,SV1833: $i,SV113: $i,SV1359: $i] :
( ( ( c_in @ ( c_Main_OPlusE__1 @ SV1359 @ SV113 @ SV1833 @ SV1947 ) @ SV1359 @ SV1833 )
= $true )
| ( ( c_in @ ( c_Main_OPlusE__2 @ SV1638 @ SV113 @ SV1947 @ SV1833 ) @ SV1638 @ SV1947 )
= $true )
| ( ( c_in @ SV113 @ ( c_Sum__Type_OPlus @ SV1359 @ SV1638 @ SV1833 @ SV1947 ) @ ( tc_sum @ SV1833 @ SV1947 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8639]) ).
thf(8715,plain,
! [SV1364: $i,SV119: $i,SV1836: $i,SV1643: $i] :
( ( ( c_Relation_Otrans @ SV1643 @ SV1836 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ SV1643 @ SV119 @ SV1836 @ SV1364 ) @ ( tc_prod @ SV1836 @ SV1364 ) )
= $true )
| ( ( c_Relation_Otrans @ SV119 @ SV1364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8640]) ).
thf(8716,plain,
! [SV1365: $i,SV120: $i,SV1837: $i,SV1644: $i] :
( ( ( c_Wellfounded__Recursion_Owf @ SV1644 @ SV1837 )
= $false )
| ( ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ SV1644 @ SV120 @ SV1837 @ SV1365 ) @ ( tc_prod @ SV1837 @ SV1365 ) )
= $true )
| ( ( c_Wellfounded__Recursion_Owf @ SV120 @ SV1365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8641]) ).
thf(8717,plain,
! [SV1068: $i,SV1660: $i,SV1396: $i,SV1842: $i] :
( ( ( c_in @ SV1842 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
= $false )
| ( ( c_in @ ( c_append @ SV1842 @ SV1068 @ SV1660 ) @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
= $true )
| ( ( c_in @ SV1068 @ ( c_List_Olists @ SV1396 @ SV1660 ) @ ( tc_List_Olist @ SV1660 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8644]) ).
thf(8718,plain,
! [SV1444: $i,SV1692: $i,SV1852: $i,SV1127: $i] :
( ( ( c_in @ SV1127 @ SV1852 @ SV1692 )
= $false )
| ( ( c_in @ SV1127 @ ( c_inter @ SV1852 @ SV1444 @ SV1692 ) @ SV1692 )
= $true )
| ( ( c_in @ SV1127 @ SV1444 @ SV1692 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8667]) ).
thf(8719,plain,
! [SV1128: $i,SV1693: $i,SV1445: $i,SV1853: $i] :
( ( ( c_in @ SV1853 @ ( c_Inter @ SV1445 @ SV1693 ) @ SV1693 )
= $false )
| ( ( c_in @ SV1853 @ SV1128 @ SV1693 )
= $true )
| ( ( c_in @ SV1128 @ SV1445 @ ( tc_set @ SV1693 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8668]) ).
thf(8720,plain,
! [SV1135: $i,SV1699: $i,SV1857: $i,SV1451: $i] :
( ( ( c_in @ SV1451 @ SV1857 @ ( tc_set @ SV1699 ) )
= $false )
| ( ( c_in @ SV1135 @ ( c_Union @ SV1857 @ SV1699 ) @ SV1699 )
= $true )
| ( ( c_in @ SV1135 @ SV1451 @ SV1699 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8670]) ).
thf(8721,plain,
! [SV1483: $i,SV1720: $i,SV1168: $i,SV1866: $i] :
( ( ( c_lessequals @ SV1866 @ SV1168 @ ( tc_set @ SV1720 ) )
= $false )
| ( ( c_lessequals @ SV1866 @ SV1483 @ ( tc_set @ SV1720 ) )
= $true )
| ( ( c_lessequals @ SV1168 @ SV1483 @ ( tc_set @ SV1720 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8677]) ).
thf(8722,plain,
! [SV1975: $i,SV1956: $i,SV1880: $i,SV1738: $i,SV1507: $i,SV1195: $i] :
( ( ( ( c_Pair @ SV1195 @ SV1507 @ SV1738 @ SV1880 )
= ( c_Pair @ SV1956 @ SV1975 @ SV1738 @ SV1880 ) )
= $false )
| ( ( SV1195 = SV1956 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8682]) ).
thf(8723,plain,
! [SV1976: $i,SV1958: $i,SV1885: $i,SV1746: $i,SV1517: $i,SV1206: $i] :
( ( ( ( c_Pair @ SV1206 @ SV1517 @ SV1746 @ SV1885 )
= ( c_Pair @ SV1958 @ SV1976 @ SV1746 @ SV1885 ) )
= $false )
| ( ( SV1517 = SV1976 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8683]) ).
thf(8724,plain,
! [SV1977: $i,SV1963: $i,SV1896: $i,SV1769: $i,SV1550: $i,SV1241: $i] :
( ( ( ( c_Datatype__Universe_OScons @ SV1241 @ SV1550 @ SV1769 @ SV1896 )
= ( c_Datatype__Universe_OScons @ SV1963 @ SV1977 @ SV1769 @ SV1896 ) )
= $false )
| ( ( SV1241 = SV1963 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8687]) ).
thf(8725,plain,
! [SV1978: $i,SV1965: $i,SV1901: $i,SV1775: $i,SV1557: $i,SV1248: $i] :
( ( ( ( c_Datatype__Universe_OScons @ SV1248 @ SV1557 @ SV1775 @ SV1901 )
= ( c_Datatype__Universe_OScons @ SV1965 @ SV1978 @ SV1775 @ SV1901 ) )
= $false )
| ( ( SV1557 = SV1978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8688]) ).
thf(8726,plain,
! [SV1981: $i,SV1979: $i,SV1966: $i,SV1910: $i,SV1786: $i,SV1570: $i,SV1261: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV1979 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1981 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1966 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SV1979 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV1981 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8690]) ).
thf(8727,plain,
! [SV1271: $i,SV14: $i,SV1796: $i,SV1580: $i,SV1969: $i,SV1920: $i] :
( ( ( ~ ( c_in @ SV1920 @ SV1969 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) ) )
= $true )
| ( ( c_in @ ( c_Datatype__Universe_OScons @ SV1920 @ SV14 @ SV1580 @ SV1796 ) @ ( c_Datatype__Universe_Ouprod @ SV1969 @ SV1271 @ SV1580 @ SV1796 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
= $true )
| ( ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8697]) ).
thf(8728,plain,
! [SV1590: $i,SV1287: $i,SV33: $i,SV1803: $i] :
( ( ( ~ ( c_in @ SV1803 @ SV33 @ SV1287 ) )
= $true )
| ( ( SV1590 = SV1803 )
= $true )
| ( ( c_in @ SV1590 @ SV33 @ SV1287 )
= $false )
| ( ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8702]) ).
thf(8729,plain,
! [SV1318: $i,SV1970: $i,SV1936: $i,SV1609: $i,SV1818: $i,SV70: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV70 @ SV1818 @ SV1609 @ SV1936 ) @ SV1970 @ ( tc_prod @ SV1609 @ SV1936 ) ) )
= $true )
| ( ( c_in @ SV1818 @ ( c_Relation_OImage @ SV1970 @ SV1318 @ SV1609 @ SV1936 ) @ SV1936 )
= $true )
| ( ( c_in @ SV70 @ SV1318 @ SV1609 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8705]) ).
thf(8730,plain,
! [SV1982: $i,SV1980: $i,SV1974: $i,SV1941: $i,SV1826: $i,SV1620: $i,SV1329: $i,SV81: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1974 @ SV81 @ SV1980 @ SV1620 ) @ SV1982 @ ( tc_prod @ SV1980 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SV1974 @ SV1329 @ SV1980 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SV1982 @ SV1620 @ SV1826 @ SV1980 ) @ ( tc_prod @ SV1980 @ SV1826 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8709]) ).
thf(8731,plain,
! [SV1981: $i,SV1979: $i,SV1966: $i,SV1910: $i,SV1786: $i,SV1570: $i,SV1261: $i,SV4: $i] :
( ( ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV1979 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1981 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1966 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SV1979 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV1981 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8726]) ).
thf(8732,plain,
! [SV1271: $i,SV14: $i,SV1796: $i,SV1580: $i,SV1969: $i,SV1920: $i] :
( ( ( c_in @ SV1920 @ SV1969 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
= $false )
| ( ( c_in @ ( c_Datatype__Universe_OScons @ SV1920 @ SV14 @ SV1580 @ SV1796 ) @ ( c_Datatype__Universe_Ouprod @ SV1969 @ SV1271 @ SV1580 @ SV1796 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
= $true )
| ( ( c_in @ SV14 @ SV1271 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1580 @ SV1796 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8727]) ).
thf(8733,plain,
! [SV1590: $i,SV1287: $i,SV33: $i,SV1803: $i] :
( ( ( c_in @ SV1803 @ SV33 @ SV1287 )
= $false )
| ( ( SV1590 = SV1803 )
= $true )
| ( ( c_in @ SV1590 @ SV33 @ SV1287 )
= $false )
| ( ( c_Infinite__Set_Oatmost__one @ SV33 @ SV1287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8728]) ).
thf(8734,plain,
! [SV1318: $i,SV1970: $i,SV1936: $i,SV1609: $i,SV1818: $i,SV70: $i] :
( ( ( c_in @ ( c_Pair @ SV70 @ SV1818 @ SV1609 @ SV1936 ) @ SV1970 @ ( tc_prod @ SV1609 @ SV1936 ) )
= $false )
| ( ( c_in @ SV1818 @ ( c_Relation_OImage @ SV1970 @ SV1318 @ SV1609 @ SV1936 ) @ SV1936 )
= $true )
| ( ( c_in @ SV70 @ SV1318 @ SV1609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8729]) ).
thf(8735,plain,
! [SV1982: $i,SV1980: $i,SV1974: $i,SV1941: $i,SV1826: $i,SV1620: $i,SV1329: $i,SV81: $i] :
( ( ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1974 @ SV81 @ SV1980 @ SV1620 ) @ SV1982 @ ( tc_prod @ SV1980 @ SV1620 ) )
| ( c_in @ ( c_Pair @ SV1974 @ SV1329 @ SV1980 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SV1982 @ SV1620 @ SV1826 @ SV1980 ) @ ( tc_prod @ SV1980 @ SV1826 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8730]) ).
thf(8736,plain,
! [SV1910: $i,SV1261: $i,SV4: $i,SV1981: $i,SV1786: $i,SV1570: $i,SV1979: $i,SV1966: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1966 @ SV1979 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1981 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1966 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SV1979 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV1981 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8731]) ).
thf(8737,plain,
! [SV1941: $i,SV1826: $i,SV1329: $i,SV1982: $i,SV1620: $i,SV1980: $i,SV81: $i,SV1974: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1974 @ SV81 @ SV1980 @ SV1620 ) @ SV1982 @ ( tc_prod @ SV1980 @ SV1620 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1974 @ SV1329 @ SV1980 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SV1982 @ SV1620 @ SV1826 @ SV1980 ) @ ( tc_prod @ SV1980 @ SV1826 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8735]) ).
thf(8738,plain,
! [SV1910: $i,SV1261: $i,SV4: $i,SV1981: $i,SV1786: $i,SV1570: $i,SV1979: $i,SV1966: $i] :
( ( ( c_in @ ( c_Pair @ SV1966 @ SV1979 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1981 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ SV1966 @ SV4 @ SV1570 @ SV1786 ) @ ( c_Datatype__Universe_OScons @ SV1979 @ SV1261 @ SV1570 @ SV1786 ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ ( c_Datatype__Universe_Odprod @ SV1981 @ SV1910 @ SV1570 @ SV1786 ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV4 @ SV1261 @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) @ SV1910 @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ SV1570 @ SV1786 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8736]) ).
thf(8739,plain,
! [SV1941: $i,SV1826: $i,SV1329: $i,SV1982: $i,SV1620: $i,SV1980: $i,SV81: $i,SV1974: $i] :
( ( ( c_in @ ( c_Pair @ SV1974 @ SV81 @ SV1980 @ SV1620 ) @ SV1982 @ ( tc_prod @ SV1980 @ SV1620 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1974 @ SV1329 @ SV1980 @ SV1826 ) @ ( c_Relation_Orel__comp @ SV1941 @ SV1982 @ SV1620 @ SV1826 @ SV1980 ) @ ( tc_prod @ SV1980 @ SV1826 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV81 @ SV1329 @ SV1620 @ SV1826 ) @ SV1941 @ ( tc_prod @ SV1620 @ SV1826 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8737]) ).
thf(8740,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[2789,8739,8738,8734,8733,8732,8725,8724,8723,8722,8721,8720,8719,8718,8717,8716,8715,8714,8713,8712,8711,8710,8708,8707,8706,8704,8703,8701,8700,8699,8698,8696,8695,8694,8693,8692,8691,8689,8686,8685,8684,8681,8680,8679,8678,8676,8675,8674,8673,8672,8671,8669,8666,8665,8664,8663,8662,8661,8660,8659,8658,8657,8656,8655,8654,8653,8652,8651,8650,8649,8648,8647,8646,8645,8643,8642,8635,8634,8633,8627,8625,8624,8623,8621,8620,8619,8618,8617,8616,8613,8612,8606,8605,8604,8596,8595,8594,8593,8592,8591,8590,8589,8586,8585,8584,8582,8580,8579,8577,8576,8574,8573,8571,8570,8569,8568,8565,8564,8561,8560,8559,8558,8556,8554,8550,8547,8545,8542,8541,8538,8537,8535,8533,8511,8510,8507,8506,8505,8504,8503,8500,8499,8490,8489,8484,8483,8481,8476,8474,8473,8464,8438,8435,8433,8428,8425,8424,8423,8422,8421,8418,8417,8416,8415,8412,8406,8404,8399,8397,8394,8391,8389,8384,8382,8379,8378,8377,8376,8369,8368,8361,8360,8352,8351,8333,8328,8327,8322,8321,8320,8319,8317,8316,8313,8305,8297,8295,8293,8291,8290,8289,8284,8283,8282,8269,8268,8261,8257,8256,8255,8254,8230,8226,8219,8215,8214,8212,8209,8207,8205,8204,8201,8199,8193,8179,8177,8176,8168,8164,8161,8158,8155,8151,8150,8147,8146,8145,8139,8138,8131,8130,8110,8086,8085,8083,8082,8081,8080,8076,8075,8074,8073,8072,8071,8062,8061,8041,8032,8017,8014,8013,8012,7999,7933,7895,7887,7886,7861,7859,7857,7817,7816,7815,7814,7813,7805,7804,7796,7781,7780,7779,7777,7776,7775,7774,7773,7772,7771,7770,7769,7768,7767,7766,7765,7764,7763,7762,7761,7760,7759,7758,7757,7756,7755,7754,7753,7752,7751,7750,7749,7748,7747,7746,7745,7744,7743,7742,7741,7740,7739,7738,7737,7736,7735,7734,7733,7732,7731,7730,7729,7728,7727,7726,7725,7724,7723,7722,7721,7720,7719,7718,7717,7716,7715,7714,7713,7712,7711,7710,7709,7708,7707,7706,7705,7704,7703,7702,7701,7700,7699,7698,7697,7696,7695,7694,7693,7692,7691,7690,7689,7688,7687,7686,7685,7684,7683,7682,7681,7680,7679,7678,7677,7676,7675,7674,7673,7672,7671,7670,7669,7668,7667,7666,7665,7664,7663,7662,7661,7660,7659,7658,7657,7656,7655,7654,7653,7652,7651,7650,7649,7648,7647,7646,7645,7644,7643,7642,7641,7640,7639,7638,7637,7636,7635,7634,7633,7632,7631,7630,7629,7628,7627,7626,7625,7624,7623,7622,7621,7620,7619,7618,7617,7616,7615,7614,7613,7612,7611,7610,7609,7608,7607,7606,7605,7604,7603,7602,7601,7600,7599,7598,7597,7596,7595,7594,7593,7592,7591,7590,7589,7588,7587,7586,7585,7584,7583,7582,7581,7580,7579,7578,7577,7576,7575,7574,7573,7572,7571,7570,7569,7568,7567,7566,7565,7564,7563,7562,7561,7560,7559,7558,7557,7556,7555,7554,7553,7552,7551,7550,7549,7548,7547,7546,7545,7544,7543,7542,7541,7540,7539,7538,7537,7536,7535,7534,7533,7532,7531,7530,7529,7528,7527,7526,7525,7524,7523,7522,7521,7520,7519,7518,7517,7516,7515,7514,7513,7512,7511,7510,7509,7508,7507,7506,7505,7504,7503,7502,7501,7500,7499,7498,7497,7496,7495,7494,7493,7492,7491,7490,7489,7488,7487,7486,7485,7484,7483,7482,7481,7480,7479,7478,7477,7476,7475,7474,7473,7472,7471,7470,7469,7468,7467,7466,7465,7464,7463,7462,7461,7460,7459,7458,7457,7456,7455,7454,7453,7452,7451,7450,7449,7448,7447,7446,7445,7444,7443,7442,7441,7440,7439,7438,7437,7436,7435,7434,7433,7432,7431,7430,7429,7428,7427,7426,7425,7424,7423,7422,7421,7420,7419,7418,7417,7416,7415,7414,7413,7412,7411,7410,7409,7408,7407,7406,7405,7404,7403,7402,7401,7400,7399,7398,7397,7396,7395,7394,7393,7392,7391,7390,7389,7388,7387,7386,7385,7384,7383,7382,7381,7380,7379,7378,7377,7376,7375,7374,7373,7372,7371,7370,7369,7368,7367,7366,7365,7364,7363,7362,7361,7360,7359,7358,7357,7356,7355,7354,7353,7352,7351,7350,7349,7348,7347,7346,7345,7344,7343,7342,7341,7340,7339,7338,7337,7336,7335,7334,7333,7332,7331,7330,7329,7328,7327,7326,7325,7324,7323,7322,7321,7320,7319,7318,7317,7316,7315,7314,7313,7312,7311,7310,7309,7308,7307,7306,7305,7304,7303,7302,7301,7300,7299,7298,7297,7296,7295,7294,7293,7292,7291,7290,7289,7288,7287,7286,7285,7284,7283,7282,7281,7280,7279,7278,7277,7276,7275,7274,7273,7272,7271,7270,7269,7268,7267,7266,7265,7264,7263,7262,7261,7260,7259,7258,7257,7256,7255,7254,7253,7252,7251,7250,7249,7248,7247,7246,7245,7244,7243,7242,7241,7240,7239,7238,7237,7236,7235,7234,7233,7232,7231,7230,7229,7228,7227,7226,7225,7224,7223,7222,7221,7220,7219,7218,7217,7216,7215,7214,7213,7212,7211,7210,7209,7208,7207,7206,7205,7204,7203,7202,7201,7200,7199,7198,7197,7196,7195,7194,7193,7192,7191,7190,7189,7188,7187,7186,7185,7184,7183,7182,7181,7180,7179,7178,7177,7176,7175,7174,7173,7172,7171,7170,7169,7168,7167,7166,7165,7164,7163,7162,7161,7160,7159,7158,7157,7156,7155,7154,7153,7152,7151,7150,7149,7148,7147,7146,7145,7144,7143,7142,7141,7140,7139,7138,7137,7136,7135,7134,7133,7132,7131,7130,7129,7128,7127,7126,7125,7124,7123,7122,7121,7120,7119,7118,7117,7116,7115,7114,7113,7112,7111,7110,7109,7108,7107,7106,7105,7104,7103,7102,7101,7100,7099,7098,7097,7096,7095,7094,7093,7092,7091,7090,7089,7088,7087,7086,7085,7084,7083,7082,7081,7080,7079,7078,7077,7076,7075,7074,7073,7072,7071,7070,7069,7068,7067,7066,7065,7064,7063,7062,7061,7060,7059,7058,7057,7056,7055,7054,7053,7052,7051,7050,7049,7048,7047,7046,7045,7044,7043,7042,7041,7040,7039,7038,7037,7036,7035,7034,7033,7032,7031,7030,7029,7028,7027,7026,7025,7024,7023,7022,7021,7020,7019,7018,7017,7016,7015,7014,7013,7012,7011,7010,7009,7008,7007,7006,7005,7004,7003,7002,7001,7000,6999,6998,6997,6996,6995,6994,6993,6992,6991,6990,6989,6988,6987,6986,6985,6984,6983,6982,6981,6980,6979,6978,6977,6976,6975,6974,6973,6972,6971,6970,6969,6968,6967,6966,6965,6964,6963,6962,6961,6960,6959,6958,6957,6956,6955,6954,6953,6952,6951,6950,6949,6948,6947,6946,6945,6944,6943,6942,6941,6940,6939,6938,6937,6936,6935,6934,6933,6932,6931,6930,6929,6928,6927,6926,6925,6924,6923,6922,6921,6920,6919,6918,6917,6916,6915,6914,6913,6912,6911,6910,6909,6908,6907,6906,6905,6904,6903,6902,6901,6900,6899,6898,6897,6896,6895,6894,6893,6892,6891,6890,6889,6888,6887,6886,6885,6884,6883,6882,6881,6880,6879,6878,6877,6876,6875,6874,6873,6872,6871,6869,6866,6861,6781,6739,6731,6727,6713,6704,6702,6687,6620,6618,6615,6604,6603,6600,6599,6598,6575,6574,6570,5658,5643,5638,5633,5630,5627,5626,5625,5624,5623,5622,5621,5620,5601,5598,5586,5582,5581,5580,5579,5578,5577,5575,5574,5568,5567,5509,5492,5481,5472,5471,5462,5461,5449,5414,5371,5359,5358,5355,5351,5348,5343,5342,5335,4407,4405,4404,4403,4396,4369,4364,4341,4339,4338,4315,4314,4303,4300,4299,4065,4063,4061,4059,3998,3974,3036,3035,3034,3033,3032,3031,3030,3029,3028,3027,3026,3025,3024,3023,3022,3021,3020,3019,3018,3017,3016,3015,3014,3013,3012,3011,3010,3009,3008,3007,3006,3005,3004,3003,3002,3001,3000,2999,2998,2997,2996,2995,2994,2993,2992,2991,2990,2989,2986,2985,2984,2983,2982,2981,2980,2979,2978,2977,2976,2975,2974,2973,2972,2971,2970,2969,2968,2967,2966,2965,2964,2963,2962,2961,2960,2959,2958,2957,2956,2955,2954,2953,2952,2951,2950,2949,2948,2947,2946,2945,2944,2943,2942,2941,2940,2939,2938,2937,2936,2935,2934,2933,2932,2931,2930,2929,2928,2927,2926,2925,2924,2923,2922,2921,2920,2917,2915,2790]) ).
thf(8741,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[8740]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV242-1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 16:24:28 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 214.71/43.14 ..........
% 214.71/43.14
% 214.71/43.14 No.of.Axioms: 1392
% 214.71/43.14
% 214.71/43.14 Length.of.Defs: 0
% 214.71/43.14
% 214.71/43.14 Contains.Choice.Funs: false
% 214.71/43.14 ............................................................................................................................................................................................
% 214.71/43.14
% 214.71/43.14 ********************************
% 214.71/43.14 * All subproblems solved! *
% 214.71/43.14 ********************************
% 214.71/43.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1392,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8740,loop_count:0,foatp_calls:1,translation:fof_full)
% 214.71/43.14
% 214.71/43.14 %**** Beginning of derivation protocol ****
% 214.71/43.14 % SZS output start CNFRefutation
% See solution above
% 214.71/43.18
% 214.71/43.18 %**** End of derivation protocol ****
% 214.71/43.18 %**** no. of clauses in derivation: 8741 ****
% 214.71/43.18 %**** clause counter: 8740 ****
% 214.71/43.18
% 214.71/43.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1392,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8740,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------