%------------------------------------------------------------------------------
% File     : ITP139+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : float.ax [Gau19]
%          : HL4139+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  157 (  91 unt;   0 def)
%            Number of atoms       :  321 ( 126 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  194 (  30   ~;  10   |;  90   &)
%                                         (  20 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :  260 (  11 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  177 ( 177 usr;  96 con; 0-4 aty)
%            Number of variables   :  287 ( 277   !;  10   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

fof(reserved_2Eho_2Etruth,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).

fof(reserved_2Eho_2Enotfalse,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).

fof(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0] :
      ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).

fof(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        & p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).

fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
       => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a,V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
    <=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).

fof(reserved_2Equant_2E_21,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(reserved_2Equant_2E_3F,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2EFinite_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2EFinite_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__add_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__add_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Eieee_2Efloat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)),c_2Eieee_2Efloat__add_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__div_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__div_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Eieee_2Efloat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)),c_2Eieee_2Efloat__div_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__mul_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__mul_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Eieee_2Efloat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)),c_2Eieee_2Efloat__mul_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__sub_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__sub_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Eieee_2Efloat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Eieee_2Efloat)),c_2Eieee_2Efloat__sub_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2EInfinity_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2EInfinity_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2EIsdenormal_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2EIsdenormal_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2EIsdenormal_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2EIsnan_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2EIsnan_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2EIsnormal_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnormal_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2EIsnormal_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2EIszero_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),c_2Eieee_2EIszero_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2EVal_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Erealax_2Ereal),c_2Eieee_2EVal_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Efloat_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Eieee_2Efloat,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Eieee_2Efloat),c_2Eieee_2Efloat_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) ).

fof(arityeq3_2Ec_2Eieee_2Eround_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Eieee_2Eroundmode,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eieee_2Eroundmode,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Eround_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Eieee_2Eroundmode,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Edefloat_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Edefloat_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))) ).

fof(arityeq3_2Ec_2Eieee_2Ezerosign_2E3,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ezerosign_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),c_2Eieee_2Ezerosign_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X2_2E0))) ).

fof(arityeq1_2Ec_2Efloat_2Eerror_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Efloat_2Eerror_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Eexponent_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Eieee_2Eexponent_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Efraction_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Efraction_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Eieee_2Efraction_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Elargest_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Eieee_2Elargest_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Erealax_2Ereal),c_2Eieee_2Elargest_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Efloat_2Enormalizes_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Efloat_2Enormalizes_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ereal_2E_2F_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Erealax_2Ereal__add_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Erealax_2Ereal__mul_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ereal_2Ereal__sub_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__of__num_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Esign_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Eieee_2Esign_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Ethreshold_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Erealax_2Ereal),c_2Eieee_2Ethreshold_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq4_2Ec_2Eieee_2Eclosest_2E4_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Erealax_2Ereal,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))),c_2Eieee_2Eclosest_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Erealax_2Ereal,X3_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Eis__finite_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eieee_2Eis__finite_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Eis__valid_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eieee_2Eis__valid_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) ).

fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Eexpwidth_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Eexpwidth_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eieee_2Eexpwidth_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Efracwidth_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Efracwidth_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eieee_2Efracwidth_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Eemax_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Eemax_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eieee_2Eemax_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__eq_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__eq_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)),c_2Eieee_2Efloat__eq_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__ge_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__ge_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)),c_2Eieee_2Efloat__ge_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__gt_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__gt_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)),c_2Eieee_2Efloat__gt_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__le_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__le_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)),c_2Eieee_2Efloat__le_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Efloat__lt_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__lt_2E2(s(tyop_2Eieee_2Efloat,X0_2E0),s(tyop_2Eieee_2Efloat,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Efun(tyop_2Eieee_2Efloat,tyop_2Emin_2Ebool)),c_2Eieee_2Efloat__lt_2E0),s(tyop_2Eieee_2Efloat,X0_2E0))),s(tyop_2Eieee_2Efloat,X1_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Ebottomfloat_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ebottomfloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Ebottomfloat_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Eminus__infinity_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eminus__infinity_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Eminus__infinity_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Eminus__zero_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eminus__zero_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Eminus__zero_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Eplus__infinity_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eplus__infinity_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Eplus__infinity_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Eplus__zero_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eplus__zero_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Eplus__zero_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Etopfloat_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Etopfloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Eieee_2Etopfloat_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Ereal__ge_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal_2Ereal__ge_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Ereal__gt_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal_2Ereal__gt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Erealax_2Ereal__lt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Eabs_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Ereal_2Epow_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Ereal_2Ereal__lte_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq1_2Ec_2Eieee_2Ebias_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Ebias_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eieee_2Ebias_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) ).

fof(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Einv_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq2_2Ec_2Eieee_2Evalof_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Eieee_2Evalof_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal)),c_2Eieee_2Evalof_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq4_2Ec_2Eieee_2Eis__closest_2E4_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__closest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)))),c_2Eieee_2Eis__closest_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X3_2E0))) ).

fof(thm_2Efloat_2Eerror__def,axiom,
    ! [V0x_2E0] : s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))))),s(tyop_2Erealax_2Ereal,V0x_2E0))) ).

fof(thm_2Efloat_2Enormalizes__def,axiom,
    ! [V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Ebias_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) ) ) ).

fof(thm_2Efloat_2ESIGN,axiom,
    ! [V0a_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))) ).

fof(thm_2Efloat_2EEXPONENT,axiom,
    ! [V0a_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))))) ).

fof(thm_2Efloat_2EFRACTION,axiom,
    ! [V0a_2E0] : s(tyop_2Enum_2Enum,c_2Eieee_2Efraction_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))))) ).

fof(thm_2Efloat_2EIS__VALID,axiom,
    ! [V0X_2E0,V1a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Eieee_2Eexpwidth_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Efraction_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Eieee_2Efracwidth_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0)))))))) ) ) ).

fof(thm_2Efloat_2EVALOF,axiom,
    ! [F0_2E0] :
      ( ! [V1a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))))
        <=> s(tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) )
     => ! [V0X_2E0,V1a_2E0] : s(tyop_2Erealax_2Ereal,c_2Eieee_2Evalof_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Eieee_2Ebias_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Eieee_2Efraction_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Eieee_2Efracwidth_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Eieee_2Ebias_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Eieee_2Efraction_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Eieee_2Efracwidth_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))))))))) ) ).

fof(thm_2Efloat_2EIS__VALID__DEFLOAT,axiom,
    ! [V0a_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))))) ).

fof(thm_2Efloat_2EIS__FINITE__EXPLICIT,axiom,
    ! [V0a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Eexponent_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Efraction_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))))))))))))))))))))))))))))))))) ) ) ).

fof(thm_2Efloat_2EFLOAT__CASES,axiom,
    ! [V0a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsdenormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) ) ).

fof(thm_2Efloat_2EFLOAT__CASES__FINITE,axiom,
    ! [V0a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) ) ).

fof(thm_2Efloat_2EFLOAT__DISTINCT,axiom,
    ! [V0a_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsdenormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsdenormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsdenormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsdenormal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) ) ) ).

fof(thm_2Efloat_2EFLOAT__DISTINCT__FINITE,axiom,
    ! [V0a_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) ) ) ).

fof(thm_2Efloat_2EFLOAT__INFINITIES__SIGNED,axiom,
    ( s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EPlus__infinity_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
    & s(tyop_2Enum_2Enum,c_2Eieee_2Esign_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EMinus__infinity_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) ) ).

fof(thm_2Efloat_2EINFINITY__IS__INFINITY,axiom,
    ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EPlus__infinity_2E0))))
    & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EMinus__infinity_2E0)))) ) ).

fof(thm_2Efloat_2EZERO__IS__ZERO,axiom,
    ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EPlus__zero_2E0))))
    & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EMinus__zero_2E0)))) ) ).

fof(thm_2Efloat_2EINFINITY__NOT__NAN,axiom,
    ( ~ p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EPlus__infinity_2E0))))
    & ~ p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EMinus__infinity_2E0)))) ) ).

fof(thm_2Efloat_2EZERO__NOT__NAN,axiom,
    ( ~ p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EPlus__zero_2E0))))
    & ~ p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2EMinus__zero_2E0)))) ) ).

fof(thm_2Efloat_2EFLOAT__INFINITIES,axiom,
    ! [V0a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EInfinity_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__eq_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,c_2Eieee_2EPlus__infinity_2E0))))
        | p(s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__eq_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,c_2Eieee_2EMinus__infinity_2E0)))) ) ) ).

fof(thm_2Efloat_2EFLOAT__INFINITES__DISTINCT,axiom,
    ! [V0a_2E0] :
      ~ ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__eq_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,c_2Eieee_2EPlus__infinity_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__eq_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,c_2Eieee_2EMinus__infinity_2E0)))) ) ).

fof(thm_2Efloat_2EFLOAT__LT,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))) )
     => s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__lt_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))) ) ).

fof(thm_2Efloat_2EFLOAT__GT,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))) )
     => s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__gt_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))) ) ).

fof(thm_2Efloat_2EFLOAT__LE,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))) )
     => s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__le_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))) ) ).

fof(thm_2Efloat_2EFLOAT__GE,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))) )
     => s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__ge_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))) ) ).

fof(thm_2Efloat_2EFLOAT__EQ,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__eq_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))
      <=> s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))) = s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))) ) ) ).

fof(thm_2Efloat_2EFLOAT__EQ__REFL,axiom,
    ! [V0a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Efloat__eq_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V0a_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIsnan_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0)))) ) ).

fof(thm_2Efloat_2EIS__VALID__SPECIAL,axiom,
    ! [V0X_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eminus__infinity_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eplus__infinity_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Etopfloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ebottomfloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eplus__zero_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eminus__zero_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0)))))) ) ).

fof(thm_2Efloat_2EIS__CLOSEST__EXISTS,axiom,
    ! [V0v_2E0,V1x_2E0,V2s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0))))
     => ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
       => ? [V3a_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__closest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V3a_2E0)))) ) ) ).

fof(thm_2Efloat_2ECLOSEST__IS__EVERYTHING,axiom,
    ! [V0v_2E0,V1p_2E0,V2s_2E0,V3x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0))))
     => ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
       => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__closest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0))))))
          & ( ? [V4b_2E0] :
                ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__closest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4b_2E0))))
                & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V1p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4b_2E0)))) )
           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V1p_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Erealax_2Ereal,V3x_2E0)))))) ) ) ) ) ).

fof(thm_2Efloat_2ECLOSEST__IN__SET,axiom,
    ! [V0v_2E0,V1p_2E0,V2x_2E0,V3s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0))))
     => ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
       => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0)))) ) ) ).

fof(thm_2Efloat_2ECLOSEST__IS__CLOSEST,axiom,
    ! [V0v_2E0,V1p_2E0,V2x_2E0,V3s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0))))
     => ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)
       => p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__closest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0)))))) ) ) ).

fof(thm_2Efloat_2EIS__VALID__FINITE,axiom,
    ! [F0_2E0] :
      ( ! [V0X_2E0,V1a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0),s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0)))))
     => ! [V0X_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0)))))))) ) ).

fof(thm_2Efloat_2EIS__FINITE__FINITE,axiom,
    ! [F0_2E0] :
      ( ! [V0X_2E0,V1a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0),s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0)))))
     => ! [V0X_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0)))))))) ) ).

fof(thm_2Efloat_2EIS__VALID__NONEMPTY,axiom,
    ! [F0_2E0] :
      ( ! [V0X_2E0,V1a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0),s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0)))))
     => ! [V0X_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ) ).

fof(thm_2Efloat_2EIS__FINITE__NONEMPTY,axiom,
    ! [F0_2E0] :
      ( ! [V0X_2E0,V1a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0),s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V1a_2E0)))))
     => ! [V0X_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ) ).

fof(thm_2Efloat_2EIS__FINITE__CLOSEST,axiom,
    ! [F0_2E0] :
      ( ! [V0X_2E0,V4a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4a_2E0),s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4a_2E0)))))
     => ! [V0X_2E0,V1v_2E0,V2p_2E0,V3x_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V1v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))),s(tyop_2Erealax_2Ereal,V3x_2E0)))))) ) ).

fof(thm_2Efloat_2EIS__VALID__CLOSEST,axiom,
    ! [F0_2E0] :
      ( ! [V0X_2E0,V4a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4a_2E0),s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V4a_2E0)))))
     => ! [V0X_2E0,V1v_2E0,V2p_2E0,V3x_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eclosest_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Erealax_2Ereal),V1v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),V2p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0))))),s(tyop_2Erealax_2Ereal,V3x_2E0)))))) ) ).

fof(thm_2Efloat_2EIS__VALID__ROUND,axiom,
    ! [V0X_2E0,V1x_2E0] : p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__valid_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0X_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0)))))) ).

fof(thm_2Efloat_2EDEFLOAT__FLOAT__ROUND,axiom,
    ! [V0x_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) ).

fof(thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
    ! [V0x_2E0,V1b_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ezerosign_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ezerosign_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))) ).

fof(thm_2Efloat_2EVALOF__DEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
    ! [V0x_2E0,V1b_2E0] : s(tyop_2Erealax_2Ereal,c_2Eieee_2Evalof_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ezerosign_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))))))))) = s(tyop_2Erealax_2Ereal,c_2Eieee_2Evalof_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))) ).

fof(thm_2Efloat_2EISFINITE,axiom,
    ! [V0a_2E0] : s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))) = s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))) ).

fof(thm_2Efloat_2EVAL__FINITE,axiom,
    ! [V0a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Elargest_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) ) ).

fof(thm_2Efloat_2EFLOAT__THRESHOLD__EXPLICIT,axiom,
    s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).

fof(thm_2Efloat_2EFLOAT__LARGEST__EXPLICIT,axiom,
    s(tyop_2Erealax_2Ereal,c_2Eieee_2Elargest_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).

fof(thm_2Efloat_2EVAL__THRESHOLD,axiom,
    ! [V0a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) ) ).

fof(thm_2Efloat_2EERROR__IS__ZERO,axiom,
    ! [V0a_2E0,V1x_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))) = s(tyop_2Erealax_2Ereal,V1x_2E0) )
     => s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).

fof(thm_2Efloat_2EERROR__BOUND__NORM__STRONG,axiom,
    ! [V0x_2E0,V1j_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1j_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1j_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))))) ) ).

fof(thm_2Efloat_2EREAL__IN__BINADE,axiom,
    ! [V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))
     => ? [V1j_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Eieee_2Eemax_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))
          & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1j_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1j_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))) ) ) ).

fof(thm_2Efloat_2EERROR__BOUND__NORM__STRONG__NORMALIZE,axiom,
    ! [V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))
     => ? [V1j_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1j_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))))))))))) ) ).

fof(thm_2Efloat_2ERELATIVE__ERROR,axiom,
    ! [V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))
     => ? [V1e_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))
          & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V1e_2E0))))) ) ) ).

fof(thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND__FINITE,axiom,
    ! [V0b_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Eieee_2Eis__finite_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Edefloat_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Ezerosign_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eieee_2Eround_2E3(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0),s(tyop_2Eieee_2Eroundmode,c_2Eieee_2ETo__nearest_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))))))) ) ).

fof(thm_2Efloat_2EFLOAT__ADD,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__add_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__add_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))))) ) ) ).

fof(thm_2Efloat_2EFLOAT__SUB,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__sub_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__sub_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))))) ) ) ).

fof(thm_2Efloat_2EFLOAT__MUL,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__mul_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__mul_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))))) ) ) ).

fof(thm_2Efloat_2EFLOAT__DIV,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__div_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__div_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Efloat_2Eerror_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))))))) ) ) ).

fof(thm_2Efloat_2EFLOAT__ADD__FINITE,axiom,
    ! [V0b_2E0,V1a_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__add_2E2(s(tyop_2Eieee_2Efloat,V1a_2E0),s(tyop_2Eieee_2Efloat,V0b_2E0)))))) ) ).

fof(thm_2Efloat_2EFLOAT__SUB__FINITE,axiom,
    ! [V0b_2E0,V1a_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__sub_2E2(s(tyop_2Eieee_2Efloat,V1a_2E0),s(tyop_2Eieee_2Efloat,V0b_2E0)))))) ) ).

fof(thm_2Efloat_2EFLOAT__MUL__FINITE,axiom,
    ! [V0b_2E0,V1a_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Eieee_2Ethreshold_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eieee_2Efloat__format_2E0)))))) )
     => p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__mul_2E2(s(tyop_2Eieee_2Efloat,V1a_2E0),s(tyop_2Eieee_2Efloat,V0b_2E0)))))) ) ).

fof(thm_2Efloat_2EFLOAT__ADD__RELATIVE,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__add_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & ? [V2e_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))
            & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__add_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).

fof(thm_2Efloat_2EFLOAT__SUB__RELATIVE,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__sub_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & ? [V2e_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))
            & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__sub_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).

fof(thm_2Efloat_2EFLOAT__MUL__RELATIVE,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__mul_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & ? [V2e_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))
            & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__mul_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).

fof(thm_2Efloat_2EFLOAT__DIV__RELATIVE,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Eieee_2EIszero_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efloat_2Enormalizes_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0)))))))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Eieee_2EFinite_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__div_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))))
        & ? [V2e_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2e_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))))))))
            & s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,c_2Eieee_2Efloat__div_2E2(s(tyop_2Eieee_2Efloat,V0a_2E0),s(tyop_2Eieee_2Efloat,V1b_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Eieee_2EVal_2E1(s(tyop_2Eieee_2Efloat,V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Erealax_2Ereal,V2e_2E0))))) ) ) ) ).

fof(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
     => s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).

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