ITP001 Axioms: ITP139+5.ax


%------------------------------------------------------------------------------
% File     : ITP139+5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : float+2.ax [Gau20]
%          : HL4139+5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   68 (   4 unt;   0 def)
%            Number of atoms       :  316 (  33 equ)
%            Maximal formula atoms :   21 (   4 avg)
%            Number of connectives :  275 (  27   ~;   7   |;  97   &)
%                                         (  11 <=>; 133  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :  130 (   7 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 1-2 aty)
%            Number of functors    :   90 (  90 usr;  73 con; 0-2 aty)
%            Number of variables   :  112 ( 103   !;   9   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Efloat_2Eerror,axiom,
    mem(c_2Efloat_2Eerror,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).

fof(mem_c_2Efloat_2Enormalizes,axiom,
    mem(c_2Efloat_2Enormalizes,arr(ty_2Erealax_2Ereal,bool)) ).

fof(conj_thm_2Efloat_2ESIGN,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
     => ap(c_2Eieee_2Esign,V0a) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a) ) ).

fof(conj_thm_2Efloat_2EEXPONENT,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
     => ap(c_2Eieee_2Eexponent,V0a) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a)) ) ).

fof(conj_thm_2Efloat_2EFRACTION,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
     => ap(c_2Eieee_2Efraction,V0a) = ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a)) ) ).

fof(conj_thm_2Efloat_2EIS__VALID,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V1a] :
          ( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
         => ( p(ap(ap(c_2Eieee_2Eis__valid,V0X),V1a))
          <=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Esign,V1a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))
              & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Eexponent,V1a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Eexpwidth,V0X))))
              & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Efraction,V1a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Efracwidth,V0X)))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EVALOF,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V1a] :
          ( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
         => ap(ap(c_2Eieee_2Evalof,V0X),V1a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Eexponent,V1a)),c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Eieee_2Esign,V1a))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Eieee_2Efraction,V1a))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Efracwidth,V0X))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Eieee_2Esign,V1a))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Eexponent,V1a))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X))))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Eieee_2Efraction,V1a))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Efracwidth,V0X)))))) ) ) ).

fof(conj_thm_2Efloat_2EIS__VALID__DEFLOAT,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => p(ap(ap(c_2Eieee_2Eis__valid,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ).

fof(conj_thm_2Efloat_2EIS__FINITE__EXPLICIT,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
     => ( p(ap(ap(c_2Eieee_2Eis__finite,c_2Eieee_2Efloat__format),V0a))
      <=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Esign,V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))
          & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Eexponent,V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
          & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Efraction,V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))))))))))))))))) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__CASES,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( p(ap(c_2Eieee_2EIsnan,V0a))
        | p(ap(c_2Eieee_2EInfinity,V0a))
        | p(ap(c_2Eieee_2EIsnormal,V0a))
        | p(ap(c_2Eieee_2EIsdenormal,V0a))
        | p(ap(c_2Eieee_2EIszero,V0a)) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__CASES__FINITE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( p(ap(c_2Eieee_2EIsnan,V0a))
        | p(ap(c_2Eieee_2EInfinity,V0a))
        | p(ap(c_2Eieee_2EFinite,V0a)) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__DISTINCT,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
            & p(ap(c_2Eieee_2EInfinity,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
            & p(ap(c_2Eieee_2EIsnormal,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
            & p(ap(c_2Eieee_2EIsdenormal,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
            & p(ap(c_2Eieee_2EIszero,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
            & p(ap(c_2Eieee_2EIsnormal,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
            & p(ap(c_2Eieee_2EIsdenormal,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
            & p(ap(c_2Eieee_2EIszero,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EIsnormal,V0a))
            & p(ap(c_2Eieee_2EIsdenormal,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EIsnormal,V0a))
            & p(ap(c_2Eieee_2EIszero,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EIsdenormal,V0a))
            & p(ap(c_2Eieee_2EIszero,V0a)) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__DISTINCT__FINITE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
            & p(ap(c_2Eieee_2EInfinity,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
            & p(ap(c_2Eieee_2EFinite,V0a)) )
        & ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
            & p(ap(c_2Eieee_2EFinite,V0a)) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__INFINITIES__SIGNED,axiom,
    ( ap(c_2Eieee_2Esign,ap(c_2Eieee_2Edefloat,c_2Eieee_2EPlus__infinity)) = c_2Enum_2E0
    & ap(c_2Eieee_2Esign,ap(c_2Eieee_2Edefloat,c_2Eieee_2EMinus__infinity)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ).

fof(conj_thm_2Efloat_2EINFINITY__IS__INFINITY,axiom,
    ( p(ap(c_2Eieee_2EInfinity,c_2Eieee_2EPlus__infinity))
    & p(ap(c_2Eieee_2EInfinity,c_2Eieee_2EMinus__infinity)) ) ).

fof(conj_thm_2Efloat_2EZERO__IS__ZERO,axiom,
    ( p(ap(c_2Eieee_2EIszero,c_2Eieee_2EPlus__zero))
    & p(ap(c_2Eieee_2EIszero,c_2Eieee_2EMinus__zero)) ) ).

fof(conj_thm_2Efloat_2EINFINITY__NOT__NAN,axiom,
    ( ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EPlus__infinity))
    & ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EMinus__infinity)) ) ).

fof(conj_thm_2Efloat_2EZERO__NOT__NAN,axiom,
    ( ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EPlus__zero))
    & ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EMinus__zero)) ) ).

fof(conj_thm_2Efloat_2EFLOAT__INFINITIES,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( p(ap(c_2Eieee_2EInfinity,V0a))
      <=> ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EPlus__infinity))
          | p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EMinus__infinity)) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__INFINITES__DISTINCT,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ~ ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EPlus__infinity))
          & p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EMinus__infinity)) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__LT,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b)) )
           => ( p(ap(ap(c_2Eieee_2Efloat__lt,V0a),V1b))
            <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__GT,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b)) )
           => ( p(ap(ap(c_2Eieee_2Efloat__gt,V0a),V1b))
            <=> p(ap(ap(c_2Ereal_2Ereal__gt,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__LE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b)) )
           => ( p(ap(ap(c_2Eieee_2Efloat__le,V0a),V1b))
            <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__GE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b)) )
           => ( p(ap(ap(c_2Eieee_2Efloat__ge,V0a),V1b))
            <=> p(ap(ap(c_2Ereal_2Ereal__ge,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__EQ,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b)) )
           => ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),V1b))
            <=> ap(c_2Eieee_2EVal,V0a) = ap(c_2Eieee_2EVal,V1b) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__EQ__REFL,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),V0a))
      <=> ~ p(ap(c_2Eieee_2EIsnan,V0a)) ) ) ).

fof(conj_thm_2Efloat_2EIS__VALID__SPECIAL,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ( p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eminus__infinity,V0X)))
        & p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eplus__infinity,V0X)))
        & p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Etopfloat,V0X)))
        & p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Ebottomfloat,V0X)))
        & p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eplus__zero,V0X)))
        & p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eminus__zero,V0X))) ) ) ).

fof(conj_thm_2Efloat_2EIS__CLOSEST__EXISTS,axiom,
    ! [V0v] :
      ( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
     => ! [V1x] :
          ( mem(V1x,ty_2Erealax_2Ereal)
         => ! [V2s] :
              ( mem(V2s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
             => ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V2s))
               => ( V2s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
                 => ? [V3a] :
                      ( mem(V3a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
                      & p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V2s),V1x),V3a)) ) ) ) ) ) ) ).

fof(conj_thm_2Efloat_2ECLOSEST__IS__EVERYTHING,axiom,
    ! [V0v] :
      ( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
     => ! [V1p] :
          ( mem(V1p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
         => ! [V2s] :
              ( mem(V2s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
             => ! [V3x] :
                  ( mem(V3x,ty_2Erealax_2Ereal)
                 => ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V2s))
                   => ( V2s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
                     => ( p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V2s),V3x),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V2s),V3x)))
                        & ( ? [V4b] :
                              ( mem(V4b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
                              & p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V2s),V3x),V4b))
                              & p(ap(V1p,V4b)) )
                         => p(ap(V1p,ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V2s),V3x))) ) ) ) ) ) ) ) ) ).

fof(conj_thm_2Efloat_2ECLOSEST__IN__SET,axiom,
    ! [V0v] :
      ( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
     => ! [V1p] :
          ( mem(V1p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
         => ! [V2x] :
              ( mem(V2x,ty_2Erealax_2Ereal)
             => ! [V3s] :
                  ( mem(V3s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
                 => ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V3s))
                   => ( V3s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
                     => p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V3s),V2x)),V3s)) ) ) ) ) ) ) ).

fof(conj_thm_2Efloat_2ECLOSEST__IS__CLOSEST,axiom,
    ! [V0v] :
      ( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
     => ! [V1p] :
          ( mem(V1p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
         => ! [V2x] :
              ( mem(V2x,ty_2Erealax_2Ereal)
             => ! [V3s] :
                  ( mem(V3s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
                 => ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V3s))
                   => ( V3s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
                     => p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V3s),V2x),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V3s),V2x))) ) ) ) ) ) ) ).

fof(lameq_f3150,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V1a] : ap(f3150(V0X),V1a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V1a),ap(ap(c_2Eieee_2Eis__valid,V0X),V1a)) ) ).

fof(conj_thm_2Efloat_2EIS__VALID__FINITE,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3150(V0X)))) ) ).

fof(lameq_f3151,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V1a] : ap(f3151(V0X),V1a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V1a),ap(ap(c_2Eieee_2Eis__finite,V0X),V1a)) ) ).

fof(conj_thm_2Efloat_2EIS__FINITE__FINITE,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3151(V0X)))) ) ).

fof(conj_thm_2Efloat_2EIS__VALID__NONEMPTY,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3150(V0X)) != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ) ).

fof(conj_thm_2Efloat_2EIS__FINITE__NONEMPTY,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3151(V0X)) != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ) ).

fof(lameq_f3152,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V4a] : ap(f3152(V0X),V4a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V4a),ap(ap(c_2Eieee_2Eis__finite,V0X),V4a)) ) ).

fof(conj_thm_2Efloat_2EIS__FINITE__CLOSEST,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V1v] :
          ( mem(V1v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
         => ! [V2p] :
              ( mem(V2p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
             => ! [V3x] :
                  ( mem(V3x,ty_2Erealax_2Ereal)
                 => p(ap(ap(c_2Eieee_2Eis__finite,V0X),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V1v),V2p),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3152(V0X))),V3x))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EIS__VALID__CLOSEST,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V1v] :
          ( mem(V1v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
         => ! [V2p] :
              ( mem(V2p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
             => ! [V3x] :
                  ( mem(V3x,ty_2Erealax_2Ereal)
                 => p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V1v),V2p),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3152(V0X))),V3x))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EIS__VALID__ROUND,axiom,
    ! [V0X] :
      ( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
     => ! [V1x] :
          ( mem(V1x,ty_2Erealax_2Ereal)
         => p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(ap(ap(c_2Eieee_2Eround,V0X),c_2Eieee_2ETo__nearest),V1x))) ) ) ).

fof(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ROUND,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x))) = ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x) ) ).

fof(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1b] :
          ( mem(V1b,ty_2Enum_2Enum)
         => ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V1b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)))) = ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V1b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)) ) ) ).

fof(conj_thm_2Efloat_2EVALOF__DEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1b] :
          ( mem(V1b,ty_2Enum_2Enum)
         => ap(ap(c_2Eieee_2Evalof,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V1b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x))))) = ap(ap(c_2Eieee_2Evalof,c_2Eieee_2Efloat__format),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)) ) ) ).

fof(conj_thm_2Efloat_2EISFINITE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( p(ap(c_2Eieee_2EFinite,V0a))
      <=> p(ap(ap(c_2Eieee_2Eis__finite,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).

fof(conj_thm_2Efloat_2EVAL__FINITE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( p(ap(c_2Eieee_2EFinite,V0a))
       => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Eieee_2EVal,V0a))),ap(c_2Eieee_2Elargest,c_2Eieee_2Efloat__format))) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__THRESHOLD__EXPLICIT,axiom,
    ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).

fof(conj_thm_2Efloat_2EFLOAT__LARGEST__EXPLICIT,axiom,
    ap(c_2Eieee_2Elargest,c_2Eieee_2Efloat__format) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).

fof(conj_thm_2Efloat_2EVAL__THRESHOLD,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ( p(ap(c_2Eieee_2EFinite,V0a))
       => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(c_2Eieee_2EVal,V0a))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) ) ) ).

fof(ax_thm_2Efloat_2Eerror__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ap(c_2Efloat_2Eerror,V0x) = ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)))),V0x) ) ).

fof(conj_thm_2Efloat_2EERROR__IS__ZERO,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1x] :
          ( mem(V1x,ty_2Erealax_2Ereal)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & ap(c_2Eieee_2EVal,V0a) = V1x )
           => ap(c_2Efloat_2Eerror,V1x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ).

fof(conj_thm_2Efloat_2EERROR__BOUND__NORM__STRONG,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ! [V1j] :
          ( mem(V1j,ty_2Enum_2Enum)
         => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format)))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,V1j))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))) )
           => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Efloat_2Eerror,V0x))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1j)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ) ) ).

fof(ax_thm_2Efloat_2Enormalizes__def,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ( p(ap(c_2Efloat_2Enormalizes,V0x))
      <=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Ebias,c_2Eieee_2Efloat__format)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Eabs,V0x)))
          & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) ) ) ) ).

fof(conj_thm_2Efloat_2EREAL__IN__BINADE,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ( p(ap(c_2Efloat_2Enormalizes,V0x))
       => ? [V1j] :
            ( mem(V1j,ty_2Enum_2Enum)
            & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1j),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Eemax,c_2Eieee_2Efloat__format)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))
            & p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1j)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))),ap(c_2Ereal_2Eabs,V0x)))
            & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,V1j))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))) ) ) ) ).

fof(conj_thm_2Efloat_2EERROR__BOUND__NORM__STRONG__NORMALIZE,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ( p(ap(c_2Efloat_2Enormalizes,V0x))
       => ? [V1j] :
            ( mem(V1j,ty_2Enum_2Enum)
            & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Efloat_2Eerror,V0x))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1j)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ) ) ).

fof(conj_thm_2Efloat_2ERELATIVE__ERROR,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Erealax_2Ereal)
     => ( p(ap(c_2Efloat_2Enormalizes,V0x))
       => ? [V1e] :
            ( mem(V1e,ty_2Erealax_2Ereal)
            & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V1e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
            & ap(c_2Eieee_2EVal,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x))) = ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1e)) ) ) ) ).

fof(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND__FINITE,axiom,
    ! [V0b] :
      ( mem(V0b,ty_2Enum_2Enum)
     => ! [V1x] :
          ( mem(V1x,ty_2Erealax_2Ereal)
         => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V1x)),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format)))
           => p(ap(ap(c_2Eieee_2Eis__finite,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V0b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V1x)))))) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__ADD,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)))
              & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__SUB,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)))
              & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__MUL,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)))
              & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__DIV,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & ~ p(ap(c_2Eieee_2EIszero,V1b))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)))
              & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__ADD__FINITE,axiom,
    ! [V0b] :
      ( mem(V0b,ty_2Eieee_2Efloat)
     => ! [V1a] :
          ( mem(V1a,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V1a))
              & p(ap(c_2Eieee_2EFinite,V0b))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V1a)),ap(c_2Eieee_2EVal,V0b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
           => p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__add,V1a),V0b))) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__SUB__FINITE,axiom,
    ! [V0b] :
      ( mem(V0b,ty_2Eieee_2Efloat)
     => ! [V1a] :
          ( mem(V1a,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V1a))
              & p(ap(c_2Eieee_2EFinite,V0b))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V1a)),ap(c_2Eieee_2EVal,V0b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
           => p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__sub,V1a),V0b))) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__MUL__FINITE,axiom,
    ! [V0b] :
      ( mem(V0b,ty_2Eieee_2Efloat)
     => ! [V1a] :
          ( mem(V1a,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V1a))
              & p(ap(c_2Eieee_2EFinite,V0b))
              & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V1a)),ap(c_2Eieee_2EVal,V0b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
           => p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__mul,V1a),V0b))) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__ADD__RELATIVE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)))
              & ? [V2e] :
                  ( mem(V2e,ty_2Erealax_2Ereal)
                  & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
                  & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__SUB__RELATIVE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)))
              & ? [V2e] :
                  ( mem(V2e,ty_2Erealax_2Ereal)
                  & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
                  & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__MUL__RELATIVE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)))
              & ? [V2e] :
                  ( mem(V2e,ty_2Erealax_2Ereal)
                  & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
                  & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).

fof(conj_thm_2Efloat_2EFLOAT__DIV__RELATIVE,axiom,
    ! [V0a] :
      ( mem(V0a,ty_2Eieee_2Efloat)
     => ! [V1b] :
          ( mem(V1b,ty_2Eieee_2Efloat)
         => ( ( p(ap(c_2Eieee_2EFinite,V0a))
              & p(ap(c_2Eieee_2EFinite,V1b))
              & ~ p(ap(c_2Eieee_2EIszero,V1b))
              & p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
           => ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)))
              & ? [V2e] :
                  ( mem(V2e,ty_2Erealax_2Ereal)
                  & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
                  & ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).

%------------------------------------------------------------------------------