%------------------------------------------------------------------------------
% File     : ITP134+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    : binary_ieee.ax [Gau19]
%          : HL4134+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  721 ( 490 unt;   0 def)
%            Number of atoms       : 1835 (1389 equ)
%            Maximal formula atoms :   37 (   2 avg)
%            Number of connectives : 1286 ( 172   ~;  72   |; 590   &)
%                                         ( 173 <=>; 279  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   42 (   6 avg)
%            Maximal term depth    :   31 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  394 ( 394 usr; 203 con; 0-8 aty)
%            Number of variables   : 4077 (3942   !; 135   ?)
% 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_2Emin_2E_40_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger_2EABS_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2EABS_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Einteger_2ENum_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum),c_2Einteger_2ENum_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2EFloat_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__value),c_2Ebinary__ieee_2EFloat_2E0),s(tyop_2Erealax_2Ereal,X0_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(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_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(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_2Ewords_2EINT__MAX_2E1_2Emono_2EA_27w,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27w),tyop_2Enum_2Enum),c_2Ewords_2EINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27w),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_2Efcp_2Edimindex_2E1_2Emono_2EA_27t,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27t),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(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(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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ecombin_2EI_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecombin_2EI_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2EA_27w,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Enum_2Enum),c_2Ewords_2Ew2n_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0),s(tyop_2Einteger_2Eint,X2_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))),s(tyop_2Einteger_2Eint,X2_2E0))) ).

fof(arityeq1_2Ec_2Eintreal_2EINT__CEILING_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),c_2Eintreal_2EINT__CEILING_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq1_2Ec_2Eintreal_2EINT__FLOOR_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),c_2Eintreal_2EINT__FLOOR_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))) ).

fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ESOME_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),c_2Eoption_2ESOME_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq5_2Ec_2Ebinary__ieee_2Erounding__CASE_2E5_2Emono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(tyop_2Einteger_2Eint,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0),s(tyop_2Einteger_2Eint,X2_2E0),s(tyop_2Einteger_2Eint,X3_2E0),s(tyop_2Einteger_2Eint,X4_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))),c_2Ebinary__ieee_2Erounding__CASE_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))),s(tyop_2Einteger_2Eint,X2_2E0))),s(tyop_2Einteger_2Eint,X3_2E0))),s(tyop_2Einteger_2Eint,X4_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0),s(tyop_2Ebool_2Eitself(A_27t),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)))),c_2Epair_2E_2C_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))),s(tyop_2Ebool_2Eitself(A_27t),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2EULP_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2EULP_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ebinary__ieee_2Efloat__Exponent_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27w,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_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_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_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(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Enum_2Enum),c_2Ewords_2Ew2n_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Echeck__for__signalling_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Echeck__for__signalling_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eclosest__such_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Eclosest__such_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Ebinary__ieee_2Eclosest__such_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27w,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27w),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__DivideByZero_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Eflags__DivideByZero_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Precision__fupd_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) ).

fof(arityeq6_2Ec_2Ebinary__ieee_2Erecordtype_2Eflags_2E6,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0,X5_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0),s(tyop_2Emin_2Ebool,X3_2E0),s(tyop_2Emin_2Ebool,X4_2E0),s(tyop_2Emin_2Ebool,X5_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Ebinary__ieee_2Eflags)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Ebinary__ieee_2Eflags))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Ebinary__ieee_2Eflags)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Ebinary__ieee_2Eflags))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Ebinary__ieee_2Eflags)))))),c_2Ebinary__ieee_2Erecordtype_2Eflags_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))),s(tyop_2Emin_2Ebool,X3_2E0))),s(tyop_2Emin_2Ebool,X4_2E0))),s(tyop_2Emin_2Ebool,X5_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__InvalidOp_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Eflags__InvalidOp_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Overflow_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Eflags__Overflow_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Precision_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Eflags__Precision_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Precision__fupd_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eflags__size_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Eflags__size_2E1(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Enum_2Enum),c_2Ebinary__ieee_2Eflags__size_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ebinary__ieee_2Efloat__Exponent_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__some__qnan_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__some__qnan_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent_2E1_2Emono_2EA_27g_20mono_2EA_27h,axiom,
    ! [A_27g,A_27h,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h)),c_2Ebinary__ieee_2Efloat__Exponent_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27g_20mono_2EA_27h,axiom,
    ! [A_27g,A_27h,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__bottom_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__bottom_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__infinity_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__minus__infinity_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__minus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__minus__zero_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__infinity_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__plus__infinity_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__plus__zero_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__top_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__top_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Erecordtype_2Efloat_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X2_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent_2E1_2Emono_2EA_27t_20mono_2EA_27x,axiom,
    ! [A_27t,A_27x,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27w_20mono_2EA_27x,axiom,
    ! [A_27t,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent_2E1_2Emono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27u,A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ebinary__ieee_2Efloat__Exponent_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27t,A_27u,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27w_20mono_2EA_27y,axiom,
    ! [A_27t,A_27w,A_27y,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27y_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27x_29,axiom,
    ! [A_27w,A_27x,A_27y,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Sign_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27e_20mono_2EA_27f,axiom,
    ! [A_27e,A_27f,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Sign_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27e_20mono_2EA_27f,axiom,
    ! [A_27e,A_27f,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Sign_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27t_20mono_2EA_27x,axiom,
    ! [A_27t,A_27x,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Sign_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27u,A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Sign_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ebinary__ieee_2Efloat__Significand_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ebinary__ieee_2Efloat__Significand_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__some__qnan_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__some__qnan_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand_2E1_2Emono_2EA_27i_20mono_2EA_27j,axiom,
    ! [A_27i,A_27j,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),c_2Ebinary__ieee_2Efloat__Significand_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27i_20mono_2EA_27j,axiom,
    ! [A_27i,A_27j,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ebinary__ieee_2Efloat__Significand_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand_2E1_2Emono_2EA_27t_20mono_2EA_27x,axiom,
    ! [A_27t,A_27x,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ebinary__ieee_2Efloat__Significand_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand_2E1_2Emono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27u,A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ebinary__ieee_2Efloat__Significand_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27v_20mono_2EA_27w,axiom,
    ! [A_27t,A_27v,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27v_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27u_29,axiom,
    ! [A_27t,A_27u,A_27v,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__abs_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__abs_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__abs_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__compare2num_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Enum_2Enum),c_2Ebinary__ieee_2Efloat__compare2num_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Enum2float__compare_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ebinary__ieee_2Efloat__compare),c_2Ebinary__ieee_2Enum2float__compare_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__compare__size_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare__size_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Enum_2Enum),c_2Ebinary__ieee_2Efloat__compare__size_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__finite_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27m_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27m_29,axiom,
    ! [A_27m,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27n_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27n_29,axiom,
    ! [A_27n,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27n_20mono_2EA_27m_20mono_2EA_27m,axiom,
    ! [A_27m,A_27n,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27n_20mono_2EA_27m,axiom,
    ! [A_27m,A_27n,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27n_20mono_2EA_27n_20mono_2EA_27m,axiom,
    ! [A_27m,A_27n,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27n_20mono_2EA_27m,axiom,
    ! [A_27m,A_27n,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__finite_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__finite_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__infinite_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__infinite_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27e_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27e_29,axiom,
    ! [A_27e,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27f_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27f_29,axiom,
    ! [A_27f,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27f_20mono_2EA_27e_20mono_2EA_27e,axiom,
    ! [A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27f_20mono_2EA_27e,axiom,
    ! [A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27f_20mono_2EA_27f_20mono_2EA_27e,axiom,
    ! [A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__infinite_2E1_2Emono_2EA_27f_20mono_2EA_27e,axiom,
    ! [A_27e,A_27f,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__infinite_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__infinite_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__infinite_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__integral_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__integral_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__integral_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__integral_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__nan_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__nan_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__nan_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__nan_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__nan_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__nan_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__normal_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__normal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27g_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27g_29,axiom,
    ! [A_27g,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27h_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27h_29,axiom,
    ! [A_27h,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27h_20mono_2EA_27g_20mono_2EA_27g,axiom,
    ! [A_27g,A_27h,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27h_20mono_2EA_27g,axiom,
    ! [A_27g,A_27h,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27h_20mono_2EA_27h_20mono_2EA_27g,axiom,
    ! [A_27g,A_27h,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__normal_2E1_2Emono_2EA_27h_20mono_2EA_27g,axiom,
    ! [A_27g,A_27h,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__normal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__normal_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__normal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__signalling_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__signalling_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__signalling_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29,axiom,
    ! [A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27d_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27d_29,axiom,
    ! [A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27c,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27d_20mono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__signalling_2E1_2Emono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27c,A_27d,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__signalling_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__signalling_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__signalling_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__signalling_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__signalling_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__subnormal_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__subnormal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27i_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27i_29,axiom,
    ! [A_27i,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27j_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27j_29,axiom,
    ! [A_27j,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27j_20mono_2EA_27i_20mono_2EA_27i,axiom,
    ! [A_27i,A_27j,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27j_20mono_2EA_27i,axiom,
    ! [A_27i,A_27j,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27j_20mono_2EA_27j_20mono_2EA_27i,axiom,
    ! [A_27i,A_27j,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__subnormal_2E1_2Emono_2EA_27j_20mono_2EA_27i,axiom,
    ! [A_27i,A_27j,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__subnormal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__subnormal_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__subnormal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__zero_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27k_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27k_29,axiom,
    ! [A_27k,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27l_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27l_29,axiom,
    ! [A_27l,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27l_20mono_2EA_27k_20mono_2EA_27k,axiom,
    ! [A_27k,A_27l,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27l_20mono_2EA_27k,axiom,
    ! [A_27k,A_27l,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27l_20mono_2EA_27l_20mono_2EA_27k,axiom,
    ! [A_27k,A_27l,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27l_20mono_2EA_27k,axiom,
    ! [A_27k,A_27l,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__zero_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__zero_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__some__qnan_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__some__qnan_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27w_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__value_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat__value),c_2Ebinary__ieee_2Efloat__value_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__value_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat__value),c_2Ebinary__ieee_2Efloat__value_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__value__size_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__value__size_2E1(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Enum_2Enum),c_2Ebinary__ieee_2Efloat__value__size_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eis__integral_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eis__integral_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Eis__integral_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Elargest_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Elargest_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27d,axiom,
    ! [A_27d,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27f,axiom,
    ! [A_27f,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27g,axiom,
    ! [A_27g,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27i,axiom,
    ! [A_27i,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27j,axiom,
    ! [A_27j,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27k,axiom,
    ! [A_27k,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27l,axiom,
    ! [A_27l,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27t,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Enum2rounding_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Ebinary__ieee_2Erounding,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ebinary__ieee_2Erounding),c_2Ebinary__ieee_2Enum2rounding_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Erounding2num_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Enum_2Enum),c_2Ebinary__ieee_2Erounding2num_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Ereal__to__float_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Ereal__to__float_2E1(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Ereal__to__float_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Ereal__to__float__with__flags_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Ereal__to__float__with__flags_2E1(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Ebinary__ieee_2Ereal__to__float__with__flags_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Erounding__size_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Enum_2Enum),c_2Ebinary__ieee_2Erounding__size_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Ethreshold_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__1comp_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__1comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ewords_2Eword__1comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__2comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ewords_2Eword__2comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27e,axiom,
    ! [A_27e,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27e,axiom,
    ! [A_27e,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),c_2Ewords_2Eword__2comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27g,axiom,
    ! [A_27g,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),c_2Ewords_2Eword__2comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27m,axiom,
    ! [A_27m,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27m,axiom,
    ! [A_27m,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),c_2Ewords_2Eword__2comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27t,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ewords_2Eword__2comp_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__lsb_2E1_2Emono_2EA_27t,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__lsb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Emin_2Ebool),c_2Ewords_2Eword__lsb_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__msb_2E1_2Emono_2EA_27d,axiom,
    ! [A_27d,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Emin_2Ebool),c_2Ewords_2Eword__msb_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Eword__msb_2E1_2Emono_2EA_27t,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Emin_2Ebool),c_2Ewords_2Eword__msb_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = 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_2Ecombin_2EK_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27u_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29,axiom,
    ! [A_27t,A_27u,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27x_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29,axiom,
    ! [A_27w,A_27x,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x))),c_2Ecombin_2EK_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27u_20mono_2EA_27w_20mono_2EA_27x,axiom,
    ! [A_27u,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27u_20mono_2EA_27x,axiom,
    ! [A_27u,A_27x,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2EFP__Sqrt_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),c_2Ebinary__ieee_2EFP__Sqrt_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Add_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Div_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Div_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Mul_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Sub_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Sub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2EFP__MulAdd_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),c_2Ebinary__ieee_2EFP__MulAdd_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2EFP__MulSub_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),c_2Ebinary__ieee_2EFP__MulSub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ebinary__ieee_2Efp__op_28A_27t_2CA_27w_29_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2EbasicSize_2Ebool__size_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Enum_2Enum),c_2EbasicSize_2Ebool__size_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__size_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Enum_2Enum))),c_2Ebinary__ieee_2Efloat__size_2E0),s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Add_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)))),c_2Ebinary__ieee_2EFP__Add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Div_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)))),c_2Ebinary__ieee_2EFP__Div_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Mul_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)))),c_2Ebinary__ieee_2EFP__Mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Sub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)))),c_2Ebinary__ieee_2EFP__Sub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27c_2CA_27d_29,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27c_2CA_27d_29,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)))),c_2Elist_2ECONS_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Add_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)))),c_2Ebinary__ieee_2EFP__Add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Echeck__for__signalling_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Echeck__for__signalling_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),X0_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Div_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)))),c_2Ebinary__ieee_2EFP__Div_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Mul_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)))),c_2Ebinary__ieee_2EFP__Mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Sub_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d)))),c_2Ebinary__ieee_2EFP__Sub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Emin_2Ebool,X1_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_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_2Ewords_2EUINT__MAX_2E1_2Emono_2EA_27w,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27w),tyop_2Enum_2Enum),c_2Ewords_2EUINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27t,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27t),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Enum_2Enum),c_2Ewords_2Edimword_2E0),s(tyop_2Ebool_2Eitself(A_27t),X0_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(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_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_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(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_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(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__xor_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__xor_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone))),c_2Ewords_2Eword__xor_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Eround_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq1_2Ec_2Eintreal_2Ereal__of__int_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Eintreal_2Ereal__of__int_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Erealax_2Ereal),c_2Eintreal_2Ereal__of__int_2E0),s(tyop_2Einteger_2Eint,X0_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Efloat__round_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_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(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,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(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2EA_27t,axiom,
    ! [A_27t,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Enum_2Enum),c_2Ewords_2Ew2n_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Ebinary__ieee_2Efloat__compare,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Ebinary__ieee_2Erounding,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Enum_2Enum),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29_29_20mono_2Etyop_2Ebinary__ieee_2Eflags,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29_29_29_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Erounding_2Ctyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29_29_29_29_20mono_2Etyop_2Ebinary__ieee_2Efp__op_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Ebinary__ieee_2Efloat__value,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),X1_2E0))) ).

fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29_20mono_2Etyop_2Erealax_2Ereal,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eexponent__boundary_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eexponent__boundary_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Ebinary__ieee_2Eexponent__boundary_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__CASE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(A_27a,c_2Ebinary__ieee_2Eflags__CASE_2E2(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),A_27a)),c_2Ebinary__ieee_2Eflags__CASE_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27a,A_27t,A_27w,X0_2E0,X1_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__CASE_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),A_27a)),c_2Ebinary__ieee_2Efloat__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27w_20mono_2EA_27y,axiom,
    ! [A_27t,A_27w,A_27y,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27x_20mono_2EA_27y,axiom,
    ! [A_27t,A_27x,A_27y,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27w,axiom,
    ! [A_27w,X0_2E0,X1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X1_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w))),c_2Ewords_2Eword__sub_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27x,axiom,
    ! [A_27t,A_27x,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E2_2Emono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27u,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27u_20mono_2EA_27x,axiom,
    ! [A_27t,A_27u,A_27x,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27t_20mono_2EA_27v_20mono_2EA_27w,axiom,
    ! [A_27t,A_27v,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E2_2Emono_2EA_27u_20mono_2EA_27v_20mono_2EA_27w,axiom,
    ! [A_27u,A_27v,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__compare_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__compare_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat__compare)),c_2Ebinary__ieee_2Efloat__compare_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__equal_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__equal_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Ebinary__ieee_2Efloat__equal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__equal_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__greater__equal_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Ebinary__ieee_2Efloat__greater__equal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__greater__than_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__greater__than_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Ebinary__ieee_2Efloat__greater__than_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__equal_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__less__equal_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Ebinary__ieee_2Efloat__less__equal_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__less__than_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__less__than_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Ebinary__ieee_2Efloat__less__than_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__round_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__round_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Ebinary__ieee_2Efloat__round_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__round__to__integral_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__round__to__integral_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Efloat__round__to__integral_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__round__to__integral_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round__to__integral_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Efloat__round__to__integral_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__round__with__flags_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Efloat__round__with__flags_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))))),c_2Ebinary__ieee_2Efloat__round__with__flags_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__sqrt_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Efloat__sqrt_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__to__int_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__to__int_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),c_2Ebinary__ieee_2Efloat__to__int_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eintegral__round_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eintegral__round_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Eintegral__round_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Eflags,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Eflags,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27a,A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27w_20mono_2EA_27x,axiom,
    ! [A_27t,A_27w,A_27x,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27a,A_27t,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27y_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27a,A_27t,A_27w,A_27y,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27t,A_27u,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27a,A_27t,A_27u,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27u,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27v_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27a,A_27t,A_27v,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27x,axiom,
    ! [A_27t,A_27x,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29,axiom,
    ! [A_27a,A_27t,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29,axiom,
    ! [A_27t,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27x_20mono_2EA_27y,axiom,
    ! [A_27t,A_27x,A_27y,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27y_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29,axiom,
    ! [A_27a,A_27t,A_27x,A_27y,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27y_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29,axiom,
    ! [A_27t,A_27w,A_27x,A_27y,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E1_2Emono_2EA_27t_20mono_2EA_27u_20mono_2EA_27x,axiom,
    ! [A_27t,A_27u,A_27x,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29,axiom,
    ! [A_27a,A_27t,A_27u,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27x_29,axiom,
    ! [A_27t,A_27u,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign__fupd_2E1_2Emono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27u,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29,axiom,
    ! [A_27a,A_27u,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29,axiom,
    ! [A_27t,A_27u,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1_2Emono_2EA_27u_20mono_2EA_27w_20mono_2EA_27x,axiom,
    ! [A_27u,A_27w,A_27x,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29,axiom,
    ! [A_27a,A_27u,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27x_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29,axiom,
    ! [A_27t,A_27u,A_27w,A_27x,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Significand__fupd_2E1_2Emono_2EA_27u_20mono_2EA_27v_20mono_2EA_27w,axiom,
    ! [A_27u,A_27v,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w))),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27v_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29,axiom,
    ! [A_27a,A_27u,A_27v,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27v_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27u_2CA_27w_29,axiom,
    ! [A_27t,A_27u,A_27v,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Erealax_2Ereal,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),tyop_2Erealax_2Ereal)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat__value_20mono_2Etyop_2Ebinary__ieee_2Efloat__value,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat__compare_20mono_2Etyop_2Ebinary__ieee_2Efloat__value_20mono_2Etyop_2Ebinary__ieee_2Efloat__value,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)),X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)),tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)),tyop_2Ebinary__ieee_2Efloat__compare)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29_20mono_2Etyop_2Ebinary__ieee_2Efloat__value_20mono_2Etyop_2Ebinary__ieee_2Efloat__value,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X1_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_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(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(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29,axiom,
    ! [A_27a,A_27t,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Ebool_2Eitself(A_27t),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)))),c_2Epair_2E_2C_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Ebool_2Eitself(A_27t),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2EULP_2E1_2Emono_2EA_27t_20mono_2EA_27a,axiom,
    ! [A_27a,A_27t,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2EULP_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2EINT__MIN_2E1_2Emono_2EA_27w,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27w),tyop_2Enum_2Enum),c_2Ewords_2EINT__MIN_2E0),s(tyop_2Ebool_2Eitself(A_27w),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(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_2Ebinary__ieee_2Eround_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a))),c_2Ebinary__ieee_2Eround_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__ls_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__ls_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),c_2Ewords_2Eword__ls_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Exponent_2E1_2Emono_2EA_27t_20mono_2Etyop_2Esum_2Esum_28A_27w_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone))),c_2Ebinary__ieee_2Efloat__Exponent_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),X0_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27t_20mono_2Etyop_2Esum_2Esum_28A_27w_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone))))),c_2Ebinary__ieee_2Efloat__round_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27w_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27w,X0_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone))),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq2_2Ec_2Ewords_2Eword__ls_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27w_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__ls_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool)),c_2Ewords_2Eword__ls_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),X1_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),X0_2E0))) ).

fof(arityeq2_2Ec_2Ebinary__ieee_2Eclosest_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebinary__ieee_2Eclosest_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),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(arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest__such_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Ebinary__ieee_2Eclosest__such_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ebinary__ieee_2Efloat__compare,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X1_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Ebinary__ieee_2Efloat__compare)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Ebinary__ieee_2Efloat__compare))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ebinary__ieee_2Efloat__value,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X2_2E0))) ).

fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Elist_2ECONS_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ebinary__ieee_2Echeck__for__signalling_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Echeck__for__signalling_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__value__CASE_2E4_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X2_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),c_2Ebinary__ieee_2Efloat__value__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X2_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X3_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round__with__flags_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__round__with__flags_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),X1_2E0))) ).

fof(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),X2_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),c_2Epair_2E_2C_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),c_2Epair_2E_2C_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),X1_2E0))) ).

fof(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),X2_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Erounding_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),X1_2E0))) ).

fof(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Erounding_2Ctyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29_29_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),X2_2E0))) ).

fof(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Erealax_2Ereal,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Eclosest__such_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Ebinary__ieee_2Eclosest__such_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__add_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))))),c_2Ebinary__ieee_2Efloat__add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__add_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))))),c_2Ebinary__ieee_2Efloat__add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__add_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__div_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))))),c_2Ebinary__ieee_2Efloat__div_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__div_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))))),c_2Ebinary__ieee_2Efloat__div_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__div_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__div_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))))),c_2Ebinary__ieee_2Efloat__mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))))),c_2Ebinary__ieee_2Efloat__mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a)))),c_2Ebinary__ieee_2Efloat__round_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__round__with__flags_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Erealax_2Ereal,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))))),c_2Ebinary__ieee_2Efloat__round__with__flags_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Erealax_2Ereal,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) ).

fof(arityeq1_2Ec_2Etransc_2Esqrt_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Etransc_2Esqrt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__sub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))))),c_2Ebinary__ieee_2Efloat__sub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__sub_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d))))),c_2Ebinary__ieee_2Efloat__sub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__sub_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__sub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Efp__op__size_2E3_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Enum_2Enum))),c_2Ebinary__ieee_2Efp__op__size_2E0),s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Eis__closest_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eis__closest_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Ebinary__ieee_2Eis__closest_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Erecordtype_2Efloat_2E3_2Emono_2EA_27u_20mono_2EA_27w,axiom,
    ! [A_27u,A_27w,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)))),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebinary__ieee_2Erecordtype_2Efloat_2E3_2Emono_2EA_27t_20mono_2EA_27x,axiom,
    ! [A_27t,A_27x,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),X1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)))),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),X1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),X2_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__add_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul__add_2E4(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),c_2Ebinary__ieee_2Efloat__mul__add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__sub_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul__sub_2E4(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),c_2Ebinary__ieee_2Efloat__mul__sub_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__value__CASE_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Ebinary__ieee_2Efloat__value__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__value__CASE_2E4_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0),s(tyop_2Emin_2Ebool,X3_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2Ebinary__ieee_2Efloat__value__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))),s(tyop_2Emin_2Ebool,X3_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__value__CASE_2E4_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Ebinary__ieee_2Efloat__value__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__value__CASE_2E4_2Emono_2Etyop_2Ebinary__ieee_2Efloat__compare,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X2_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X3_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Ebinary__ieee_2Efloat__compare)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Ebinary__ieee_2Efloat__compare))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Ebinary__ieee_2Efloat__compare)))),c_2Ebinary__ieee_2Efloat__value__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,X3_2E0))) ).

fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__value__CASE_2E4_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Einteger_2Eint_29,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X2_2E0),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X3_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))))),c_2Ebinary__ieee_2Efloat__value__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X2_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X3_2E0))) ).

fof(arityeq5_2Ec_2Ebinary__ieee_2Efloat__compare__CASE_2E5_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0),s(A_27a,X4_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))))),c_2Ebinary__ieee_2Efloat__compare__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))),s(A_27a,X4_2E0))) ).

fof(arityeq5_2Ec_2Ebinary__ieee_2Efloat__compare__CASE_2E5_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0),s(tyop_2Emin_2Ebool,X3_2E0),s(tyop_2Emin_2Ebool,X4_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),c_2Ebinary__ieee_2Efloat__compare__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))),s(tyop_2Emin_2Ebool,X3_2E0))),s(tyop_2Emin_2Ebool,X4_2E0))) ).

fof(arityeq5_2Ec_2Ebinary__ieee_2Erounding__CASE_2E5_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0),s(A_27a,X4_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))))),c_2Ebinary__ieee_2Erounding__CASE_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))),s(A_27a,X4_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))) ).

fof(arityeq5_2Ec_2Ebinary__ieee_2Erounding__CASE_2E5_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,
    ! [A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X4_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),c_2Ebinary__ieee_2Erounding__CASE_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X4_2E0))) ).

fof(arityeq8_2Ec_2Ebinary__ieee_2Efp__op__CASE_2E8_2Emono_2EA_27a_20mono_2EA_27t_20mono_2EA_27w,axiom,
    ! [A_27a,A_27t,A_27w,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0,X5_2E0,X6_2E0,X7_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),X6_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),X7_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),A_27a)))))))),c_2Ebinary__ieee_2Efp__op__CASE_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X3_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X4_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),X5_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),X6_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),X7_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__TY__DEF,axiom,
    ! [A_27t,A_27w,F1_2E0,F0_2E0] :
      ( ! [V7n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),F1_2E0),s(tyop_2Enum_2Enum,V7n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),c_2Eind__type_2EBOTTOM_2E0)
     => ( ! [V1a0_27_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),V1a0_27_2E0))))
          <=> ! [V2_27float_27_2E0] :
                ( ! [V3a0_27_2E0] :
                    ( ? [V4a0_2E0,V5a1_2E0,V6a2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V5a1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V6a2_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),F1_2E0)))
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),tyop_2Emin_2Ebool),V2_27float_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),V3a0_27_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),tyop_2Emin_2Ebool),V2_27float_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),V1a0_27_2E0)))) ) )
       => ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t))))),V0rep_2E0)))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__case__def,axiom,
    ! [A_27a,A_27t,A_27w,V0a0_2E0,V1a1_2E0,V2a2_2E0,V3f_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__CASE_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0a0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1a1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2a2_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V3f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V3f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0a0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1a1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2a2_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__size__def,axiom,
    ! [A_27t,A_27w,V0f_2E0,V1f1_2E0,V2a0_2E0,V3a1_2E0,V4a2_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V1f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V2a0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3a1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V4a2_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_2Ebinary__ieee_2Efloat__Sign,axiom,
    ! [A_27t,A_27w,V0c_2E0,V1c0_2E0,V2c1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2c1_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c_2E0) ).

fof(thm_2Ebinary__ieee_2Efloat__Exponent,axiom,
    ! [A_27t,A_27w,V0c_2E0,V1c0_2E0,V2c1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2c1_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1c0_2E0) ).

fof(thm_2Ebinary__ieee_2Efloat__Significand,axiom,
    ! [A_27t,A_27w,V0c_2E0,V1c0_2E0,V2c1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2c1_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2c1_2E0) ).

fof(thm_2Ebinary__ieee_2Efloat__Sign__fupd,axiom,
    ! [A_27t,A_27w,V0f_2E0,V1c_2E0,V2c0_2E0,V3c1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__Exponent__fupd,axiom,
    ! [A_27t,A_27w,A_27x,V0f_2E0,V1c_2E0,V2c0_2E0,V3c1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V0f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V0f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__Significand__fupd,axiom,
    ! [A_27t,A_27u,A_27w,V0f_2E0,V1c_2E0,V2c0_2E0,V3c1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V0f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V0f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))))) ).

fof(thm_2Ebinary__ieee_2Efloat__value__TY__DEF,axiom,
    ! [F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V7n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),F3_2E0),s(tyop_2Enum_2Enum,V7n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),c_2Eind__type_2EBOTTOM_2E0)
     => ( ! [V6n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),F2_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),c_2Eind__type_2EBOTTOM_2E0)
       => ( ! [V5n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),F1_2E0),s(tyop_2Enum_2Enum,V5n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),c_2Eind__type_2EBOTTOM_2E0)
         => ( ! [V1a0_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),V1a0_2E0))))
              <=> ! [V2_27float__value_27_2E0] :
                    ( ! [V3a0_2E0] :
                        ( ( ? [V4a_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Erealax_2Ereal,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),F1_2E0)))
                          | s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),F2_2E0)))
                          | s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),F3_2E0))) )
                       => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),V2_27float__value_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),V3a0_2E0)))) )
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),V2_27float__value_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),V1a0_2E0)))) ) )
           => ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Eind__type_2Erecspace(tyop_2Erealax_2Ereal)),V0rep_2E0)))) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__case__def,axiom,
    ! [A_27a] :
      ( ! [V0a_2E0,V1f_2E0,V2v_2E0,V3v1_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V0a_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V1f_2E0),s(A_27a,V2v_2E0),s(A_27a,V3v1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V1f_2E0),s(tyop_2Erealax_2Ereal,V0a_2E0)))
      & ! [V4f_2E0,V5v_2E0,V6v1_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V4f_2E0),s(A_27a,V5v_2E0),s(A_27a,V6v1_2E0))) = s(A_27a,V5v_2E0)
      & ! [V7f_2E0,V8v_2E0,V9v1_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V7f_2E0),s(A_27a,V8v_2E0),s(A_27a,V9v1_2E0))) = s(A_27a,V9v1_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__size__def,axiom,
    ( ! [V0a_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__value__size_2E1(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V0a_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_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__value__size_2E1(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
    & s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__value__size_2E1(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__to__real__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V0x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ! [V0x_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),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_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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_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_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_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_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__def,axiom,
    ! [A_27t,A_27w,F0_2E0,F1_2E0] :
      ( ! [V0x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0) )
     => ( ! [V0x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
          <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
       => ! [V0x_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__nan__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1v1_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V1v1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
     => ! [V0x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__signalling__def,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__signalling_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0)))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__infinite__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1v1_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V1v1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
     => ! [V0x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__normal__def,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__subnormal__def,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__zero__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V1r_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V1r_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ! [V0x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__finite__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1v1_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V1v1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
     => ! [V0x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eis__integral__def,axiom,
    ! [V0r_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eis__integral_2E1(s(tyop_2Erealax_2Ereal,V0r_2E0))))
    <=> ? [V1n_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0r_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__integral__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1r_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V1r_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eis__integral_2E1(s(tyop_2Erealax_2Ereal,V1r_2E0)))
     => ! [V0x_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__negate__def,axiom,
    ! [A_27t,A_27w,V0x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__1comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__abs__def,axiom,
    ! [A_27t,A_27w,V0x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__abs_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__plus__infinity__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2Efloat__plus__zero__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2Efloat__top__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_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_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2Eword__T_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2Efloat__plus__min__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_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_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2Efloat__minus__infinity__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Ebinary__ieee_2Efloat__minus__zero__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Ebinary__ieee_2Efloat__bottom__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Ebinary__ieee_2Efloat__minus__min__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Ebinary__ieee_2Eflags__TY__DEF,axiom,
    ! [F1_2E0,F0_2E0] :
      ( ! [V10n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),F1_2E0),s(tyop_2Enum_2Enum,V10n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),c_2Eind__type_2EBOTTOM_2E0)
     => ( ! [V1a0_27_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),V1a0_27_2E0))))
          <=> ! [V2_27flags_27_2E0] :
                ( ! [V3a0_27_2E0] :
                    ( ? [V4a0_2E0,V5a1_2E0,V6a2_2E0,V7a3_2E0,V8a4_2E0,V9a5_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,V4a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,V5a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,V6a2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,V7a3_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,V8a4_2E0),s(tyop_2Emin_2Ebool,V9a5_2E0))))))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),F1_2E0)))
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),tyop_2Emin_2Ebool),V2_27flags_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),V3a0_27_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),tyop_2Emin_2Ebool),V2_27flags_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),V1a0_27_2E0)))) ) )
       => ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),V0rep_2E0)))) ) ) ).

fof(thm_2Ebinary__ieee_2Eflags__case__def,axiom,
    ! [A_27a,V0a0_2E0,V1a1_2E0,V2a2_2E0,V3a3_2E0,V4a4_2E0,V5a5_2E0,V6f_2E0] : s(A_27a,c_2Ebinary__ieee_2Eflags__CASE_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0a0_2E0),s(tyop_2Emin_2Ebool,V1a1_2E0),s(tyop_2Emin_2Ebool,V2a2_2E0),s(tyop_2Emin_2Ebool,V3a3_2E0),s(tyop_2Emin_2Ebool,V4a4_2E0),s(tyop_2Emin_2Ebool,V5a5_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V6f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V6f_2E0),s(tyop_2Emin_2Ebool,V0a0_2E0))),s(tyop_2Emin_2Ebool,V1a1_2E0))),s(tyop_2Emin_2Ebool,V2a2_2E0))),s(tyop_2Emin_2Ebool,V3a3_2E0))),s(tyop_2Emin_2Ebool,V4a4_2E0))),s(tyop_2Emin_2Ebool,V5a5_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__size__def,axiom,
    ! [V0a0_2E0,V1a1_2E0,V2a2_2E0,V3a3_2E0,V4a4_2E0,V5a5_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Eflags__size_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0a0_2E0),s(tyop_2Emin_2Ebool,V1a1_2E0),s(tyop_2Emin_2Ebool,V2a2_2E0),s(tyop_2Emin_2Ebool,V3a3_2E0),s(tyop_2Emin_2Ebool,V4a4_2E0),s(tyop_2Emin_2Ebool,V5a5_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V0a0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V1a1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V2a2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V3a3_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V4a4_2E0))),s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V5a5_2E0))))))))))))))) ).

fof(thm_2Ebinary__ieee_2Eflags__DivideByZero,axiom,
    ! [V0b_2E0,V1b0_2E0,V2b1_2E0,V3b2_2E0,V4b3_2E0,V5b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1b0_2E0),s(tyop_2Emin_2Ebool,V2b1_2E0),s(tyop_2Emin_2Ebool,V3b2_2E0),s(tyop_2Emin_2Ebool,V4b3_2E0),s(tyop_2Emin_2Ebool,V5b4_2E0))))) = s(tyop_2Emin_2Ebool,V0b_2E0) ).

fof(thm_2Ebinary__ieee_2Eflags__InvalidOp,axiom,
    ! [V0b_2E0,V1b0_2E0,V2b1_2E0,V3b2_2E0,V4b3_2E0,V5b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1b0_2E0),s(tyop_2Emin_2Ebool,V2b1_2E0),s(tyop_2Emin_2Ebool,V3b2_2E0),s(tyop_2Emin_2Ebool,V4b3_2E0),s(tyop_2Emin_2Ebool,V5b4_2E0))))) = s(tyop_2Emin_2Ebool,V1b0_2E0) ).

fof(thm_2Ebinary__ieee_2Eflags__Overflow,axiom,
    ! [V0b_2E0,V1b0_2E0,V2b1_2E0,V3b2_2E0,V4b3_2E0,V5b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1b0_2E0),s(tyop_2Emin_2Ebool,V2b1_2E0),s(tyop_2Emin_2Ebool,V3b2_2E0),s(tyop_2Emin_2Ebool,V4b3_2E0),s(tyop_2Emin_2Ebool,V5b4_2E0))))) = s(tyop_2Emin_2Ebool,V2b1_2E0) ).

fof(thm_2Ebinary__ieee_2Eflags__Precision,axiom,
    ! [V0b_2E0,V1b0_2E0,V2b1_2E0,V3b2_2E0,V4b3_2E0,V5b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1b0_2E0),s(tyop_2Emin_2Ebool,V2b1_2E0),s(tyop_2Emin_2Ebool,V3b2_2E0),s(tyop_2Emin_2Ebool,V4b3_2E0),s(tyop_2Emin_2Ebool,V5b4_2E0))))) = s(tyop_2Emin_2Ebool,V3b2_2E0) ).

fof(thm_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding,axiom,
    ! [V0b_2E0,V1b0_2E0,V2b1_2E0,V3b2_2E0,V4b3_2E0,V5b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1b0_2E0),s(tyop_2Emin_2Ebool,V2b1_2E0),s(tyop_2Emin_2Ebool,V3b2_2E0),s(tyop_2Emin_2Ebool,V4b3_2E0),s(tyop_2Emin_2Ebool,V5b4_2E0))))) = s(tyop_2Emin_2Ebool,V4b3_2E0) ).

fof(thm_2Ebinary__ieee_2Eflags__Underflow__AfterRounding,axiom,
    ! [V0b_2E0,V1b0_2E0,V2b1_2E0,V3b2_2E0,V4b3_2E0,V5b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1b0_2E0),s(tyop_2Emin_2Ebool,V2b1_2E0),s(tyop_2Emin_2Ebool,V3b2_2E0),s(tyop_2Emin_2Ebool,V4b3_2E0),s(tyop_2Emin_2Ebool,V5b4_2E0))))) = s(tyop_2Emin_2Ebool,V5b4_2E0) ).

fof(thm_2Ebinary__ieee_2Eflags__DivideByZero__fupd,axiom,
    ! [V0f_2E0,V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__InvalidOp__fupd,axiom,
    ! [V0f_2E0,V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0))),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__Overflow__fupd,axiom,
    ! [V0f_2E0,V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0))),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__Precision__fupd,axiom,
    ! [V0f_2E0,V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0))),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd,axiom,
    ! [V0f_2E0,V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0))),s(tyop_2Emin_2Ebool,V6b4_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd,axiom,
    ! [V0f_2E0,V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) ).

fof(thm_2Ebinary__ieee_2Eclear__flags__def,axiom,
    s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebool_2EARB_2E0))))))))))))) ).

fof(thm_2Ebinary__ieee_2Einvalidop__flags__def,axiom,
    s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0))) ).

fof(thm_2Ebinary__ieee_2Edividezero__flags__def,axiom,
    s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Edividezero__flags_2E0) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0))) ).

fof(thm_2Ebinary__ieee_2Erounding__TY__DEF,axiom,
    ! [F0_2E0] :
      ( ! [V1n_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_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_2EZERO_2E0)))))))))
     => ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Enum_2Enum),V0rep_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Erounding__BIJ,axiom,
    ( ! [V0a_2E0] : s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0))))) = s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0)
    & ! [V1r_2E0] :
        ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_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_2EZERO_2E0))))))))))
      <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,V1r_2E0))))) = s(tyop_2Enum_2Enum,V1r_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Erounding__size__def,axiom,
    ! [V0x_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).

fof(thm_2Ebinary__ieee_2Erounding__CASE,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0))))
        <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0x_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))))) )
     => ! [V0x_2E0,V1v0_2E0,V2v1_2E0,V3v2_2E0,V4v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0),s(A_27a,V1v0_2E0),s(A_27a,V2v1_2E0),s(A_27a,V3v2_2E0),s(A_27a,V4v3_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0x_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(A_27a,V1v0_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0x_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))))))),s(A_27a,V2v1_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0))),s(A_27a,V3v2_2E0),s(A_27a,V4v3_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Eis__closest__def,axiom,
    ! [A_27a,A_27b,V0s_2E0,V1x_2E0,V2a_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eis__closest_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2a_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0))))
        & ! [V3b_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V3b_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0))))
           => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V3b_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))) ) ) ) ).

fof(thm_2Ebinary__ieee_2Eclosest__such__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V1s_2E0,V2x_2E0,V0p_2E0,V3a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0p_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V3a_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eis__closest_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V3a_2E0))))
            & ! [V4b_2E0] :
                ( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eis__closest_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V4b_2E0))))
                  & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V4b_2E0)))) )
               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V3a_2E0)))) ) ) )
     => ! [V0p_2E0,V1s_2E0,V2x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Eclosest__such_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),V0p_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Eclosest__def,axiom,
    ! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Eclosest_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Eclosest__such_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) ).

fof(thm_2Ebinary__ieee_2Elargest__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_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_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_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))))) ).

fof(thm_2Ebinary__ieee_2Ethreshold__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_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_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_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))))))) ).

fof(thm_2Ebinary__ieee_2EULP__primitive__def,axiom,
    ! [A_27t,A_27w,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V3v_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F3_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [V3v_2E0,V4v1_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),F2_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_2E0))),s(tyop_2Ebool_2Eitself(A_27t),V4v1_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ecombin_2EI_2E1(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_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F3_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_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_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_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_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0)))))))))))
       => ( ! [V1ULP_2E0,V2a_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),V1ULP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),V2a_2E0))) = s(tyop_2Erealax_2Ereal,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),F2_2E0)))
         => ( ! [V0R_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),V0R_2E0)))
           => s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2EULP_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),F1_2E0))) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Eulp__def,axiom,
    ! [A_27t,A_27w] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Ebinary__ieee_2Eround__def,axiom,
    ! [A_27t,A_27w,F10_2E0,F0_2E0,F9_2E0,F8_2E0,F2_2E0,F7_2E0,F6_2E0,F3_2E0,F5_2E0,F4_2E0,F1_2E0] :
      ( ! [V3a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a_2E0))))
        <=> ~ p(s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__lsb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a_2E0)))))) )
     => ( ! [V1x_2E0,V2t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V2t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V2t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V2t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest__such_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__finite_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
       => ( ! [V7a_2E0,V1x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
            <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a_2E0))))
                & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))) ) )
         => ( ! [V1x_2E0,V7a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F8_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))
           => ( ! [V1x_2E0,V6t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F2_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V6t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V6t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V6t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F8_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
             => ( ! [V9a_2E0,V1x_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
                  <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a_2E0))))
                      & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0)))))) ) )
               => ( ! [V1x_2E0,V9a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))
                 => ( ! [V1x_2E0,V8t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F3_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V8t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V8t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V8t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
                   => ( ! [V5a_2E0,V1x_2E0] :
                          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
                        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a_2E0))))
                            & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))) ) )
                     => ( ! [V1x_2E0,V5a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F4_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))
                       => ( ! [V1x_2E0,V4t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F1_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V4t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V4t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V4t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F4_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
                         => ! [V0mode_2E0,V1x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F1_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F2_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F3_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))) ) ) ) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Eintegral__round__def,axiom,
    ! [A_27t,A_27w,F10_2E0,F0_2E0,F9_2E0,F8_2E0,F2_2E0,F7_2E0,F6_2E0,F3_2E0,F5_2E0,F4_2E0,F1_2E0] :
      ( ! [V3a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a_2E0))))
        <=> ? [V4n_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))
              & s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,V4n_2E0))) ) )
     => ( ! [V1x_2E0,V2t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V2t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V2t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V2t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest__such_2E3(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__integral_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
       => ( ! [V8a_2E0,V1x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
            <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a_2E0))))
                & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))) ) )
         => ( ! [V1x_2E0,V8a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F8_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F9_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))
           => ( ! [V1x_2E0,V7t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F2_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V7t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V7t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V7t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F8_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
             => ( ! [V10a_2E0,V1x_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
                  <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a_2E0))))
                      & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0)))))) ) )
               => ( ! [V1x_2E0,V10a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))
                 => ( ! [V1x_2E0,V9t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F3_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V9t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V9t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V9t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
                   => ( ! [V6a_2E0,V1x_2E0] :
                          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
                        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a_2E0))))
                            & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__ge_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))) ) )
                     => ( ! [V1x_2E0,V6a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F4_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))
                       => ( ! [V1x_2E0,V5t_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F1_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,V5t_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V5t_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__gt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,V5t_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eclosest_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F4_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,V1x_2E0)))))))
                         => ! [V0mode_2E0,V1x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eintegral__round_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F1_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F2_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F3_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))) ) ) ) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__TY__DEF,axiom,
    ! [A_27t,A_27w,F7_2E0,F6_2E0,F5_2E0,F4_2E0,F3_2E0,F2_2E0,F1_2E0,F0_2E0] :
      ( ! [V32n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F7_2E0),s(tyop_2Enum_2Enum,V32n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2EBOTTOM_2E0)
     => ( ! [V27n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F6_2E0),s(tyop_2Enum_2Enum,V27n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2EBOTTOM_2E0)
       => ( ! [V22n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F5_2E0),s(tyop_2Enum_2Enum,V22n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2EBOTTOM_2E0)
         => ( ! [V18n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F4_2E0),s(tyop_2Enum_2Enum,V18n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2EBOTTOM_2E0)
           => ( ! [V14n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F3_2E0),s(tyop_2Enum_2Enum,V14n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2EBOTTOM_2E0)
             => ( ! [V10n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F2_2E0),s(tyop_2Enum_2Enum,V10n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2EBOTTOM_2E0)
               => ( ! [V6n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F1_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2EBOTTOM_2E0)
                 => ( ! [V1a0_27_2E0] :
                        ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V1a0_27_2E0))))
                      <=> ! [V2_27fp__op_27_2E0] :
                            ( ! [V3a0_27_2E0] :
                                ( ( ? [V4a0_2E0,V5a1_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,V4a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F1_2E0)))
                                  | ? [V7a0_2E0,V8a1_2E0,V9a2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,V7a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F2_2E0)))
                                  | ? [V11a0_2E0,V12a1_2E0,V13a2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,V11a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F3_2E0)))
                                  | ? [V15a0_2E0,V16a1_2E0,V17a2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,V15a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V16a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F4_2E0)))
                                  | ? [V19a0_2E0,V20a1_2E0,V21a2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,V19a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F5_2E0)))
                                  | ? [V23a0_2E0,V24a1_2E0,V25a2_2E0,V26a3_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,V23a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V24a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26a3_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F6_2E0)))
                                  | ? [V28a0_2E0,V29a1_2E0,V30a2_2E0,V31a3_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Erounding,V28a0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V30a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a3_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F7_2E0))) )
                               => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),tyop_2Emin_2Ebool),V2_27fp__op_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V3a0_27_2E0)))) )
                           => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),tyop_2Emin_2Ebool),V2_27fp__op_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),V1a0_27_2E0)))) ) )
                   => ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Erounding,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),V0rep_2E0)))) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__case__def,axiom,
    ! [A_27a,A_27t,A_27w] :
      ( ! [V0a0_2E0,V1a1_2E0,V2f_2E0,V3f1_2E0,V4f2_2E0,V5f3_2E0,V6f4_2E0,V7f5_2E0,V8f6_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1a1_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V3f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V4f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V5f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V6f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V7f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V8f6_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V2f_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1a1_2E0)))
      & ! [V9a0_2E0,V10a1_2E0,V11a2_2E0,V12f_2E0,V13f1_2E0,V14f2_2E0,V15f3_2E0,V16f4_2E0,V17f5_2E0,V18f6_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11a2_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V12f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V13f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V14f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V15f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V16f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V17f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V18f6_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V13f1_2E0),s(tyop_2Ebinary__ieee_2Erounding,V9a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11a2_2E0)))
      & ! [V19a0_2E0,V20a1_2E0,V21a2_2E0,V22f_2E0,V23f1_2E0,V24f2_2E0,V25f3_2E0,V26f4_2E0,V27f5_2E0,V28f6_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V19a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V22f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V23f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V24f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V25f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V26f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V27f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V28f6_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V24f2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V19a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_2E0)))
      & ! [V29a0_2E0,V30a1_2E0,V31a2_2E0,V32f_2E0,V33f1_2E0,V34f2_2E0,V35f3_2E0,V36f4_2E0,V37f5_2E0,V38f6_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V29a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V30a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a2_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V32f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V33f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V34f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V35f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V36f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V37f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V38f6_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V35f3_2E0),s(tyop_2Ebinary__ieee_2Erounding,V29a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V30a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a2_2E0)))
      & ! [V39a0_2E0,V40a1_2E0,V41a2_2E0,V42f_2E0,V43f1_2E0,V44f2_2E0,V45f3_2E0,V46f4_2E0,V47f5_2E0,V48f6_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V39a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V40a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V41a2_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V42f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V43f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V44f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V45f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V46f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V47f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V48f6_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V46f4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V39a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V40a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V41a2_2E0)))
      & ! [V49a0_2E0,V50a1_2E0,V51a2_2E0,V52a3_2E0,V53f_2E0,V54f1_2E0,V55f2_2E0,V56f3_2E0,V57f4_2E0,V58f5_2E0,V59f6_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V49a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V50a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V51a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V52a3_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V53f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V54f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V55f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V56f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V57f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V58f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V59f6_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V58f5_2E0),s(tyop_2Ebinary__ieee_2Erounding,V49a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V50a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V51a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V52a3_2E0)))
      & ! [V60a0_2E0,V61a1_2E0,V62a2_2E0,V63a3_2E0,V64f_2E0,V65f1_2E0,V66f2_2E0,V67f3_2E0,V68f4_2E0,V69f5_2E0,V70f6_2E0] : s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V60a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V61a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V62a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V63a3_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V64f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V65f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V66f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V67f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V68f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V69f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V70f6_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V70f6_2E0),s(tyop_2Ebinary__ieee_2Erounding,V60a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V61a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V62a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V63a3_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__size__def,axiom,
    ! [A_27t,A_27w] :
      ( ! [V0f_2E0,V1f1_2E0,V2a0_2E0,V3a1_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V1f1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V2a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a1_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V2a0_2E0))),s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V1f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a1_2E0)))))))
      & ! [V4f_2E0,V5f1_2E0,V6a0_2E0,V7a1_2E0,V8a2_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V4f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V5f1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V6a0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V4f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V5f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a1_2E0))),s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V4f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V5f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a2_2E0)))))))))
      & ! [V9f_2E0,V10f1_2E0,V11a0_2E0,V12a1_2E0,V13a2_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V9f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V10f1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V11a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13a2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V11a0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V9f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V10f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a1_2E0))),s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V9f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V10f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13a2_2E0)))))))))
      & ! [V14f_2E0,V15f1_2E0,V16a0_2E0,V17a1_2E0,V18a2_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V14f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V15f1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18a2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V14f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V15f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0))),s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V14f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V15f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18a2_2E0)))))))))
      & ! [V19f_2E0,V20f1_2E0,V21a0_2E0,V22a1_2E0,V23a2_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V19f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V20f1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V21a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V21a0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V19f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V20f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22a1_2E0))),s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V19f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V20f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a2_2E0)))))))))
      & ! [V24f_2E0,V25f1_2E0,V26a0_2E0,V27a1_2E0,V28a2_2E0,V29a3_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V24f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V25f1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V26a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V27a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a3_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V26a0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V24f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V25f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V27a1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V24f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V25f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a2_2E0))),s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V24f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V25f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a3_2E0)))))))))))
      & ! [V30f_2E0,V31f1_2E0,V32a0_2E0,V33a1_2E0,V34a2_2E0,V35a3_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efp__op__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V30f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V31f1_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V32a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V34a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a3_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding__size_2E1(s(tyop_2Ebinary__ieee_2Erounding,V32a0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V30f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V31f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V30f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V31f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V34a2_2E0))),s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__size_2E3(s(tyop_2Emin_2Efun(A_27t,tyop_2Enum_2Enum),V30f_2E0),s(tyop_2Emin_2Efun(A_27w,tyop_2Enum_2Enum),V31f1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a3_2E0))))))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__some__qnan__def,axiom,
    ! [A_27t,A_27w,F1_2E0,F0_2E0] :
      ( ! [V2qnan_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2qnan_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2qnan_2E0))))
            & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__signalling_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2qnan_2E0)))) ) )
     => ( ! [V0fp__op_2E0,V1f_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0fp__op_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V1f_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V1f_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0fp__op_2E0)))))
       => ! [V0fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0fp__op_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0fp__op_2E0))))),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0fp__op_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1toneg_2E0,V3x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1toneg_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0)))
     => ! [V0mode_2E0,V1toneg_2E0,V2r_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__with__flags__def,axiom,
    ! [A_27t,A_27w,F2_2E0,F3_2E0,F5_2E0,F4_2E0,F1_2E0,F0_2E0] :
      ( ! [V3x_2E0,V2r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))))
        <=> s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))) != s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))) )
     => ( ! [V3x_2E0,V4a_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Erealax_2Ereal,V4a_2E0))))
          <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))))
              | p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_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_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Erealax_2Ereal,V4a_2E0)))) ) )
       => ( ! [V5inexact_2E0,V0mode_2E0,V1to__neg_2E0,V2r_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)))),F5_2E0),s(tyop_2Emin_2Ebool,V5inexact_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Emin_2Ebool,V1to__neg_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))))
            <=> ( p(s(tyop_2Emin_2Ebool,V5inexact_2E0))
                & p(s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__ls_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1to__neg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Esum_2Esum(A_27w,tyop_2Eone_2Eone)),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0)))))))) ) )
         => ( ! [V5inexact_2E0,V4a_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Emin_2Ebool,V5inexact_2E0))),s(tyop_2Erealax_2Ereal,V4a_2E0))))
              <=> ( p(s(tyop_2Emin_2Ebool,V5inexact_2E0))
                  & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V4a_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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0)))))))))) ) )
           => ( ! [V3x_2E0,V4a_2E0,V0mode_2E0,V1to__neg_2E0,V2r_2E0,V5inexact_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Erealax_2Ereal,V4a_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Emin_2Ebool,V1to__neg_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Emin_2Ebool,V5inexact_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Erealax_2Ereal,V4a_2E0))))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Emin_2Ebool,V5inexact_2E0))),s(tyop_2Erealax_2Ereal,V4a_2E0))))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)))),F5_2E0),s(tyop_2Emin_2Ebool,V5inexact_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Emin_2Ebool,V1to__neg_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V5inexact_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0))))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0)))
             => ( ! [V0mode_2E0,V1to__neg_2E0,V2r_2E0,V3x_2E0,V4a_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Emin_2Ebool,V1to__neg_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Erealax_2Ereal,V4a_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Erealax_2Ereal,V4a_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Emin_2Ebool,V1to__neg_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3x_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0)))))
               => ! [V0mode_2E0,V1to__neg_2E0,V2r_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1to__neg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Emin_2Ebool,V1to__neg_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1to__neg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))))) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Echeck__for__signalling__def,axiom,
    ! [A_27a,A_27b,V0l_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V0l_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__signalling_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V0l_2E0))))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0))) ).

fof(thm_2Ebinary__ieee_2Ereal__to__float__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0m_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0))))
        <=> s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
     => ! [V0m_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Ereal__to__float_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__round_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Ereal__to__float__with__flags__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0m_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0))))
        <=> s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
     => ! [V0m_2E0] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Ereal__to__float__with__flags_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),c_2Ebinary__ieee_2Efloat__round__with__flags_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__to__integral__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V0mode_2E0,V2r_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eintegral__round_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => ! [V0mode_2E0,V1x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round__to__integral_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__to__int__def,axiom,
    ! [A_27t,A_27w,F4_2E0,F3_2E0,F1_2E0,F2_2E0,F0_2E0] :
      ( ! [V4df_2E0,V3f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Erealax_2Ereal,V4df_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V4df_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_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,V4df_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_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)))))))))
              & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E1(s(tyop_2Einteger_2Eint,V3f_2E0)))))))) ) ) )
     => ( ! [V3f_2E0,V2r_2E0,V4df_2E0] : s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint))),F3_2E0),s(tyop_2Einteger_2Eint,V3f_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Erealax_2Ereal,V4df_2E0))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Erealax_2Ereal,V4df_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))))
       => ( ! [V2r_2E0,V3f_2E0] : s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),F1_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint))),F3_2E0),s(tyop_2Einteger_2Eint,V3f_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V2r_2E0),s(tyop_2Erealax_2Ereal,c_2Eintreal_2Ereal__of__int_2E1(s(tyop_2Einteger_2Eint,V3f_2E0)))))))))
         => ( ! [V1x_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
              <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
           => ( ! [V0mode_2E0,V1x_2E0,V2r_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ESOME_2E1(s(tyop_2Einteger_2Eint,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),F1_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))))))))
             => ! [V0mode_2E0,V1x_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__to__int_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ENONE_2E0))) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sqrt__def,axiom,
    ! [A_27t,A_27w,F1_2E0,F0_2E0] :
      ( ! [V0mode_2E0,V2r_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),F1_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Erealax_2Ereal,c_2Etransc_2Esqrt_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))))
     => ( ! [V1x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
          <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
       => ! [V0mode_2E0,V1x_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),F1_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__def,axiom,
    ! [A_27t,A_27w,F7_2E0,F5_2E0,F6_2E0,F4_2E0,F1_2E0,F2_2E0,F3_2E0,F0_2E0] :
      ( ! [V0mode_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))
        <=> s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
     => ( ! [V5r1_2E0,V6r2_2E0,V1x_2E0,V2y_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F5_2E0),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
          <=> ( s(tyop_2Erealax_2Ereal,V5r1_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Erealax_2Ereal,V6r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) ) )
       => ( ! [V1x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
         => ( ! [V0mode_2E0,V5r1_2E0,V1x_2E0,V2y_2E0,V6r2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F5_2E0),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,V5r1_2E0),s(tyop_2Erealax_2Ereal,V6r2_2E0)))))
           => ( ! [V4v1_2E0,V0mode_2E0,V1x_2E0,V2y_2E0,V5r1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V5r1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
             => ( ! [V1x_2E0,V7v7_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Erealax_2Ereal,V7v7_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0)))
               => ( ! [V1x_2E0,V2y_2E0] :
                      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                    <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
                 => ( ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3v_2E0,V4v1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
                   => ! [V0mode_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__def,axiom,
    ! [A_27t,A_27w,F7_2E0,F5_2E0,F6_2E0,F4_2E0,F1_2E0,F2_2E0,F3_2E0,F0_2E0] :
      ( ! [V0mode_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))
        <=> s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
     => ( ! [V5r1_2E0,V6r2_2E0,V1x_2E0,V2y_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F5_2E0),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
          <=> ( s(tyop_2Erealax_2Ereal,V5r1_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Erealax_2Ereal,V6r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) ) )
       => ( ! [V1x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
         => ( ! [V0mode_2E0,V5r1_2E0,V1x_2E0,V2y_2E0,V6r2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F5_2E0),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V5r1_2E0),s(tyop_2Erealax_2Ereal,V6r2_2E0)))))
           => ( ! [V4v1_2E0,V0mode_2E0,V1x_2E0,V2y_2E0,V5r1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V5r1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
             => ( ! [V1x_2E0,V7v7_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Erealax_2Ereal,V7v7_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0)))
               => ( ! [V1x_2E0,V2y_2E0] :
                      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                    <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
                 => ( ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3v_2E0,V4v1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
                   => ! [V0mode_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__def,axiom,
    ! [A_27t,A_27w,F8_2E0,F9_2E0,F2_2E0,F7_2E0,F4_2E0,F5_2E0,F6_2E0,F1_2E0,F3_2E0,F0_2E0] :
      ( ! [V7r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F8_2E0),s(tyop_2Erealax_2Ereal,V7r_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V7r_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [V1x_2E0,V2y_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F9_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
          <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
       => ( ! [V0mode_2E0,V1x_2E0,V2y_2E0,V7r_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V7r_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F8_2E0),s(tyop_2Erealax_2Ereal,V7r_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F9_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))))
         => ( ! [V1x_2E0,V2y_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
              <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
           => ( ! [V0mode_2E0,V1x_2E0,V2y_2E0,V5r_27_2E0,V6r2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V5r_27_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V5r_27_2E0),s(tyop_2Erealax_2Ereal,V6r2_2E0)))))
             => ( ! [V5r_27_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F5_2E0),s(tyop_2Erealax_2Ereal,V5r_27_2E0))))
                  <=> s(tyop_2Erealax_2Ereal,V5r_27_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
               => ( ! [V1x_2E0,V2y_2E0] :
                      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                    <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
                 => ( ! [V4v1_2E0,V0mode_2E0,V1x_2E0,V2y_2E0,V5r_27_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V5r_27_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V5r_27_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F5_2E0),s(tyop_2Erealax_2Ereal,V5r_27_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
                   => ( ! [V1x_2E0,V2y_2E0] :
                          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
                     => ( ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3v_2E0,V4v1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),F2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
                       => ! [V0mode_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))) ) ) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__def,axiom,
    ! [A_27t,A_27w,F6_2E0,F8_2E0,F7_2E0,F4_2E0,F5_2E0,F1_2E0,F3_2E0,F2_2E0,F0_2E0] :
      ( ! [V6r2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F6_2E0),s(tyop_2Erealax_2Ereal,V6r2_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V6r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [F7_2E0,V1x_2E0,V2y_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F8_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F7_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
          <=> ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) )
       => ( ! [V1x_2E0,V2y_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
         => ( ! [V5r1_2E0,V0mode_2E0,V1x_2E0,V2y_2E0,V6r2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V6r2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F6_2E0),s(tyop_2Erealax_2Ereal,V6r2_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F6_2E0),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Edividezero__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F8_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F7_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,V5r1_2E0),s(tyop_2Erealax_2Ereal,V6r2_2E0)))))))
           => ( ! [V1x_2E0,V2y_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
             => ( ! [V4v1_2E0,V0mode_2E0,V1x_2E0,V2y_2E0,V5r1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V5r1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F4_2E0),s(tyop_2Erealax_2Ereal,V5r1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
               => ( ! [V1x_2E0,V2y_2E0] :
                      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                    <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
                 => ( ! [V1x_2E0,V2y_2E0,V7v7_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,V7v7_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))
                   => ( ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3v_2E0,V4v1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V3v_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))))))
                     => ! [V0mode_2E0,V1x_2E0,V2y_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))) ) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__add__def,axiom,
    ! [A_27t,A_27w,F2_2E0,F10_2E0,F8_2E0,F9_2E0,F7_2E0,F3_2E0,F4_2E0,F6_2E0,F5_2E0,F1_2E0,F0_2E0] :
      ( ! [V1x_2E0,V2y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
            | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) ) )
     => ( ! [V0mode_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))
          <=> s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
       => ( ! [V6r1_2E0,V7r2_2E0,V4signP_2E0,V3z_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F8_2E0),s(tyop_2Erealax_2Ereal,V6r1_2E0))),s(tyop_2Erealax_2Ereal,V7r2_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
            <=> ( s(tyop_2Erealax_2Ereal,V6r1_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
                & s(tyop_2Erealax_2Ereal,V7r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
                & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) ) )
         => ( ! [V4signP_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F9_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
              <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
           => ( ! [V0mode_2E0,V4signP_2E0,V3z_2E0,V6r1_2E0,V7r2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Erealax_2Ereal,V6r1_2E0))),s(tyop_2Erealax_2Ereal,V7r2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F8_2E0),s(tyop_2Erealax_2Ereal,V6r1_2E0))),s(tyop_2Erealax_2Ereal,V7r2_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F9_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,V6r1_2E0),s(tyop_2Erealax_2Ereal,V7r2_2E0)))))
             => ( ! [V1x_2E0,V2y_2E0,V3z_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                  <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
                      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0)))) ) )
               => ( ! [V1x_2E0,V2y_2E0,V3z_2E0,V5infP_2E0,V4signP_2E0] :
                      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))))),F4_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
                    <=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
                          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) )
                        | ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
                          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) )
                        | ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                          & p(s(tyop_2Emin_2Ebool,V5infP_2E0))
                          & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) ) ) )
                 => ( ! [V3z_2E0,V5infP_2E0,V4signP_2E0] :
                        ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
                      <=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
                          | ( p(s(tyop_2Emin_2Ebool,V5infP_2E0))
                            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) ) ) )
                   => ( ! [V3z_2E0,V5infP_2E0,V4signP_2E0] :
                          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
                        <=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
                            | ( p(s(tyop_2Emin_2Ebool,V5infP_2E0))
                              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) )
                     => ( ! [V1x_2E0,V2y_2E0,V3z_2E0,V0mode_2E0,V4signP_2E0,V5infP_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))))),F4_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0)))))))))))))
                       => ( ! [V1x_2E0,V2y_2E0,V3z_2E0,V0mode_2E0,V4signP_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))
                         => ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3z_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul__add_2E4(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__xor_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))) ) ) ) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__sub__def,axiom,
    ! [A_27t,A_27w,F2_2E0,F10_2E0,F8_2E0,F9_2E0,F7_2E0,F3_2E0,F4_2E0,F5_2E0,F6_2E0,F1_2E0,F0_2E0] :
      ( ! [V1x_2E0,V2y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
        <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
            | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) ) )
     => ( ! [V0mode_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))
          <=> s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
       => ( ! [V6r1_2E0,V7r2_2E0,V4signP_2E0,V3z_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F8_2E0),s(tyop_2Erealax_2Ereal,V6r1_2E0))),s(tyop_2Erealax_2Ereal,V7r2_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
            <=> ( s(tyop_2Erealax_2Ereal,V6r1_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
                & s(tyop_2Erealax_2Ereal,V7r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
                & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) ) )
         => ( ! [V4signP_2E0] :
                ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F9_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
              <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
           => ( ! [V0mode_2E0,V4signP_2E0,V3z_2E0,V6r1_2E0,V7r2_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Erealax_2Ereal,V6r1_2E0))),s(tyop_2Erealax_2Ereal,V7r2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)))),F8_2E0),s(tyop_2Erealax_2Ereal,V6r1_2E0))),s(tyop_2Erealax_2Ereal,V7r2_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F9_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F10_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V6r1_2E0),s(tyop_2Erealax_2Ereal,V7r2_2E0)))))
             => ( ! [V1x_2E0,V2y_2E0,V3z_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                  <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
                      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
                      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0)))) ) )
               => ( ! [V1x_2E0,V2y_2E0,V3z_2E0,V5infP_2E0,V4signP_2E0] :
                      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))))),F4_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
                    <=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
                          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) )
                        | ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
                          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) )
                        | ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                          & p(s(tyop_2Emin_2Ebool,V5infP_2E0))
                          & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) ) ) )
                 => ( ! [V3z_2E0,V5infP_2E0,V4signP_2E0] :
                        ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
                      <=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
                          | ( p(s(tyop_2Emin_2Ebool,V5infP_2E0))
                            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) )
                   => ( ! [V3z_2E0,V5infP_2E0,V4signP_2E0] :
                          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))))
                        <=> ( ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))
                              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
                            | ( p(s(tyop_2Emin_2Ebool,V5infP_2E0))
                              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) ) ) )
                     => ( ! [V1x_2E0,V2y_2E0,V3z_2E0,V0mode_2E0,V4signP_2E0,V5infP_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Elist_2ENIL_2E0))))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))))),F4_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool))),F6_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Emin_2Ebool,V5infP_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F7_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0)))))))))))))
                       => ( ! [V1x_2E0,V2y_2E0,V3z_2E0,V0mode_2E0,V4signP_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4signP_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))))
                         => ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3z_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul__sub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))))),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3z_2E0))),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__xor_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))) ) ) ) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__TY__DEF,axiom,
    ! [F0_2E0] :
      ( ! [V1n_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_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_2EZERO_2E0)))))))))
     => ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Enum_2Enum),V0rep_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__BIJ,axiom,
    ( ! [V0a_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0)
    & ! [V1r_2E0] :
        ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_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_2EZERO_2E0))))))))))
      <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,V1r_2E0))))) = s(tyop_2Enum_2Enum,V1r_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__size__def,axiom,
    ! [V0x_2E0] : s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare__size_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__CASE,axiom,
    ! [A_27a,F0_2E0] :
      ( ! [V0x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0))))
        <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_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))))) )
     => ! [V0x_2E0,V1v0_2E0,V2v1_2E0,V3v2_2E0,V4v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0),s(A_27a,V1v0_2E0),s(A_27a,V2v1_2E0),s(A_27a,V3v2_2E0),s(A_27a,V4v3_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_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(A_27a,V1v0_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_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))))))),s(A_27a,V2v1_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0))),s(A_27a,V3v2_2E0),s(A_27a,V4v3_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__def,axiom,
    ! [A_27t,A_27w,F8_2E0,F6_2E0,F7_2E0,F1_2E0,F4_2E0,F5_2E0,F2_2E0,F3_2E0,F0_2E0] :
      ( ! [V4r1_2E0,V5r2_2E0] :
          ( p(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)),F8_2E0),s(tyop_2Erealax_2Ereal,V4r1_2E0))),s(tyop_2Erealax_2Ereal,V5r2_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V4r1_2E0) = s(tyop_2Erealax_2Ereal,V5r2_2E0) )
     => ( ! [V4r1_2E0,V5r2_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare)),F6_2E0),s(tyop_2Erealax_2Ereal,V4r1_2E0))),s(tyop_2Erealax_2Ereal,V5r2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V4r1_2E0),s(tyop_2Erealax_2Ereal,V5r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebool_2ECOND_2E3(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)),F8_2E0),s(tyop_2Erealax_2Ereal,V4r1_2E0))),s(tyop_2Erealax_2Ereal,V5r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)))))
       => ( ! [V1y_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
         => ( ! [V3v1_2E0,V1y_2E0,V4r1_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V3v1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Erealax_2Ereal,V4r1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V3v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare)),F6_2E0),s(tyop_2Erealax_2Ereal,V4r1_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F7_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)))
           => ( ! [V0x_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
                <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
             => ( ! [V0x_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
                  <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
               => ( ! [V0x_2E0,V6v7_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Erealax_2Ereal,V6v7_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F5_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)))
                 => ( ! [V0x_2E0,V1y_2E0] :
                        ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))))
                      <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) )
                   => ( ! [V1y_2E0,V0x_2E0,V2v_2E0,V3v1_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)))),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V2v_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,V3v1_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V2v_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare))),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V3v1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V3v1_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__compare)),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F4_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0))))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)))
                     => ! [V0x_2E0,V1y_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__compare_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__value),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Ebinary__ieee_2Efloat__compare)))),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))) ) ) ) ) ) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__less__than__def,axiom,
    ! [A_27t,A_27w,V0x_2E0,V1y_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__less__than_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))))
    <=> s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__compare_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__less__equal__def,axiom,
    ! [A_27t,A_27w,V0x_2E0,V1y_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__less__equal_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__compare_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__greater__than__def,axiom,
    ! [A_27t,A_27w,V0x_2E0,V1y_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__greater__than_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))))
    <=> s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__compare_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__greater__equal__def,axiom,
    ! [A_27t,A_27w,V0x_2E0,V1y_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__greater__equal_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__compare_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__equal__def,axiom,
    ! [A_27t,A_27w,V0x_2E0,V1y_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__equal_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))))
    <=> s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Efloat__compare_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0) ) ).

fof(thm_2Ebinary__ieee_2Eexponent__boundary__def,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eexponent__boundary_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0)))
        & s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__accessors,axiom,
    ! [A_27t,A_27w] :
      ( ! [V0c_2E0,V1c0_2E0,V2c1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2c1_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c_2E0)
      & ! [V3c_2E0,V4c0_2E0,V5c1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V4c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V5c1_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V4c0_2E0)
      & ! [V6c_2E0,V7c0_2E0,V8c1_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V6c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V7c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V8c1_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V8c1_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__fn__updates,axiom,
    ! [A_27t,A_27u,A_27w,A_27x] :
      ( ! [V0f_2E0,V1c_2E0,V2c0_2E0,V3c1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0)))
      & ! [V4f_2E0,V5c_2E0,V6c0_2E0,V7c1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V4f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V5c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V6c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V7c1_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V5c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V4f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V6c0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V7c1_2E0)))
      & ! [V8f_2E0,V9c_2E0,V10c0_2E0,V11c1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V8f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V9c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V10c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V11c1_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V9c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V10c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V8f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V11c1_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__accfupds,axiom,
    ! [A_27t,A_27u,A_27w,A_27x] :
      ( ! [V0f0_2E0,V1f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V0f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1f_2E0)))
      & ! [V2f0_2E0,V3f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V2f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3f_2E0)))
      & ! [V4f0_2E0,V5f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V4f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f_2E0)))
      & ! [V6f0_2E0,V7f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V6f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7f_2E0)))
      & ! [V8f0_2E0,V9f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V8f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9f_2E0)))
      & ! [V10f0_2E0,V11f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V10f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11f_2E0)))
      & ! [V12f0_2E0,V13f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V12f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V12f0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13f_2E0)))))
      & ! [V14f0_2E0,V15f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V14f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V14f0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15f_2E0)))))
      & ! [V16f0_2E0,V17f_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V16f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17f_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V16f0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17f_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__fupdfupds,axiom,
    ! [A_27t,A_27u,A_27v,A_27w,A_27x,A_27y] :
      ( ! [V0g_2E0,V1f0_2E0,V2f_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V1f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2f_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V1f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2f_2E0)))
      & ! [V3g_2E0,V4f0_2E0,V5f_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),V4f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V3g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),V4f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V3g_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f_2E0)))
      & ! [V6g_2E0,V7f0_2E0,V8f_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),V7f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V6g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8f_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),V7f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V6g_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8f_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__fupdfupds__comp,axiom,
    ! [A_27a,A_27t,A_27u,A_27v,A_27w,A_27x,A_27y] :
      ( ! [V0g_2E0,V1f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V1f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V1f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0)))))
      & ! [V2h_2E0,V3g_2E0,V4f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V4f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V4f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V3g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V2h_2E0)))
      & ! [V5g_2E0,V6f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),V6f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V5g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),V6f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V5g_2E0)))))
      & ! [V7h_2E0,V8g_2E0,V9f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),V9f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V8g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V7h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27y)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27y)),V9f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V8g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V7h_2E0)))
      & ! [V10g_2E0,V11f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),V11f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V10g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),V11f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V10g_2E0)))))
      & ! [V12h_2E0,V13g_2E0,V14f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),V14f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V13g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V12h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27v,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27v)),V14f0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V13g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V12h_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__fupdcanon,axiom,
    ! [A_27t,A_27u,A_27w,A_27x] :
      ( ! [V0g_2E0,V1f0_2E0,V2f_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V1f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2f_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V1f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2f_2E0)))))
      & ! [V3g_2E0,V4f0_2E0,V5f_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V4f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V3g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V3g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V4f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f_2E0)))))
      & ! [V6g_2E0,V7f0_2E0,V8f_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V7f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V6g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8f_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V6g_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V7f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8f_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__fupdcanon__comp,axiom,
    ! [A_27a,A_27t,A_27u,A_27w,A_27x] :
      ( ! [V0g_2E0,V1f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V1f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V0g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V1f0_2E0)))))
      & ! [V2h_2E0,V3g_2E0,V4f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V4f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V4f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V2h_2E0)))))
      & ! [V5g_2E0,V6f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V6f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V5g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V5g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V6f0_2E0)))))
      & ! [V7h_2E0,V8g_2E0,V9f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V9f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V8g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V7h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),V8g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V9f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V7h_2E0)))))
      & ! [V10g_2E0,V11f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V11f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V10g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V10g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V11f0_2E0)))))
      & ! [V12h_2E0,V13g_2E0,V14f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V14f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V13g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V12h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x)),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),V13g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w)),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),V14f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),V12h_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__component__equality,axiom,
    ! [A_27t,A_27w,V0f1_2E0,V1f2_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0f1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1f2_2E0)
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0f1_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1f2_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0f1_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1f2_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0f1_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1f2_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__updates__eq__literal,axiom,
    ! [A_27t,A_27u,A_27w,A_27x,V0f_2E0,V1c1_2E0,V2c0_2E0,V3c_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V2c0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V3c_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0f_2E0))))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V2c0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V3c_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2Efloat__literal__nchotomy,axiom,
    ! [A_27t,A_27u,A_27w,A_27x,V0f_2E0] :
    ? [V1c1_2E0,V2c0_2E0,V3c_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),V0f_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V2c0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V3c_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2EFORALL__float,axiom,
    ! [A_27t,A_27u,A_27w,A_27x,V0P_2E0] :
      ( ! [V1f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),V1f_2E0))))
    <=> ! [V2c1_2E0,V3c0_2E0,V4c_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V2c1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V3c0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V4c_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0)))))))))) ) ).

fof(thm_2Ebinary__ieee_2EEXISTS__float,axiom,
    ! [A_27t,A_27u,A_27w,A_27x,V0P_2E0] :
      ( ? [V1f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),V1f_2E0))))
    <=> ? [V2c1_2E0,V3c0_2E0,V4c_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V2c1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V3c0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V4c_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0)))))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__literal__11,axiom,
    ! [A_27t,A_27u,A_27w,A_27x,V0c11_2E0,V1c01_2E0,V2c1_2E0,V3c12_2E0,V4c02_2E0,V5c2_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c11_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V1c01_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V2c1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3c12_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27x),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V4c02_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27u,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V5c2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0)))))))
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0c11_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3c12_2E0)
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V1c01_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27x),V4c02_2E0)
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V2c1_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27u),V5c2_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Edatatype__float,axiom,
    ! [A_27t,A_27w,V0record_2E0,V1float_2E0,V2Significand_2E0,V3Sign_2E0,V4Exponent_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Emin_2Ebool)))),V0record_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1float_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3Sign_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V4Exponent_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2Significand_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Efloat__11,axiom,
    ! [A_27t,A_27w,V0a0_2E0,V1a1_2E0,V2a2_2E0,V3a0_27_2E0,V4a1_27_2E0,V5a2_27_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0a0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1a1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2a2_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3a0_27_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V4a1_27_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V5a2_27_2E0)))
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0a0_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3a0_27_2E0)
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1a1_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V4a1_27_2E0)
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2a2_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V5a2_27_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__nchotomy,axiom,
    ! [A_27t,A_27w,V0ff_2E0] :
    ? [V1c_2E0,V2c0_2E0,V3c1_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__Axiom,axiom,
    ! [A_27a,A_27t,A_27w,V0f_2E0] :
    ? [V1fn_2E0] :
    ! [V2a0_2E0,V3a1_2E0,V4a2_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),V1fn_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V2a0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3a1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V4a2_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V0f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V2a0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3a1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V4a2_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__induction,axiom,
    ! [A_27t,A_27w,V0P_2E0] :
      ( ! [V1c_2E0,V2c0_2E0,V3c1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V1c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V3c1_2E0))))))
     => ! [V4f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V4f_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__case__cong,axiom,
    ! [A_27a,A_27t,A_27w,V0f_27_2E0,V1M_2E0,V2M_27_2E0,V3f_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1M_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2M_27_2E0)
        & ! [V4a0_2E0,V5a1_2E0,V6a2_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4a0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V5a1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V6a2_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V3f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4a0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V5a1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V6a2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V0f_27_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V4a0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V5a1_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V6a2_2E0))) ) )
     => s(A_27a,c_2Ebinary__ieee_2Efloat__CASE_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1M_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V3f_2E0))) = s(A_27a,c_2Ebinary__ieee_2Efloat__CASE_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2M_27_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V0f_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__case__eq,axiom,
    ! [A_27a,A_27t,A_27w,V0x_2E0,V1v_2E0,V2f_2E0] :
      ( s(A_27a,c_2Ebinary__ieee_2Efloat__CASE_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V2f_2E0))) = s(A_27a,V1v_2E0)
    <=> ? [V3c_2E0,V4c0_2E0,V5c1_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Erecordtype_2Efloat_2E3(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3c_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V4c0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V5c1_2E0)))
          & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),A_27a))),V2f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3c_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V4c0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V5c1_2E0))) = s(A_27a,V1v_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Edatatype__float__value,axiom,
    ! [V0float__value_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__value),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Ebool))),V0float__value_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Ebinary__ieee_2Efloat__value),c_2Ebinary__ieee_2EFloat_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0))),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Efloat__value__11,axiom,
    ! [V0a_2E0,V1a_27_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V0a_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V1a_27_2E0)))
    <=> s(tyop_2Erealax_2Ereal,V0a_2E0) = s(tyop_2Erealax_2Ereal,V1a_27_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__distinct,axiom,
    ( ! [V0a_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V0a_2E0))) != s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0)
    & ! [V1a_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V1a_2E0))) != s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0) != s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__nchotomy,axiom,
    ! [V0ff_2E0] :
      ( ? [V1r_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V1r_2E0)))
      | s(tyop_2Ebinary__ieee_2Efloat__value,V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0)
      | s(tyop_2Ebinary__ieee_2Efloat__value,V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__Axiom,axiom,
    ! [A_27a,V0f0_2E0,V1f1_2E0,V2f2_2E0] :
    ? [V3fn_2E0] :
      ( ! [V4a_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,A_27a),V3fn_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V4a_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V0f0_2E0),s(tyop_2Erealax_2Ereal,V4a_2E0)))
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,A_27a),V3fn_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0))) = s(A_27a,V1f1_2E0)
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,A_27a),V3fn_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0))) = s(A_27a,V2f2_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__induction,axiom,
    ! [V0P_2E0] :
      ( ( ! [V1r_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V1r_2E0))))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)))) )
     => ! [V2f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,V2f_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__case__cong,axiom,
    ! [A_27a,V0v1_27_2E0,V1v_27_2E0,V2f_27_2E0,V3M_2E0,V4M_27_2E0,V5f_2E0,V6v_2E0,V7v1_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,V3M_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,V4M_27_2E0)
        & ! [V8a_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efloat__value,V4M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V8a_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V5f_2E0),s(tyop_2Erealax_2Ereal,V8a_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V2f_27_2E0),s(tyop_2Erealax_2Ereal,V8a_2E0))) )
        & ( s(tyop_2Ebinary__ieee_2Efloat__value,V4M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0)
         => s(A_27a,V6v_2E0) = s(A_27a,V1v_27_2E0) )
        & ( s(tyop_2Ebinary__ieee_2Efloat__value,V4M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
         => s(A_27a,V7v1_2E0) = s(A_27a,V0v1_27_2E0) ) )
     => s(A_27a,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V3M_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V5f_2E0),s(A_27a,V6v_2E0),s(A_27a,V7v1_2E0))) = s(A_27a,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V4M_27_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V2f_27_2E0),s(A_27a,V1v_27_2E0),s(A_27a,V0v1_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__value__case__eq,axiom,
    ! [A_27a,V0x_2E0,V1v1_2E0,V2v_27_2E0,V3v_2E0,V4f_2E0] :
      ( s(A_27a,c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V4f_2E0),s(A_27a,V3v_2E0),s(A_27a,V1v1_2E0))) = s(A_27a,V2v_27_2E0)
    <=> ( ? [V5r_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efloat__value,V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V5r_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,A_27a),V4f_2E0),s(tyop_2Erealax_2Ereal,V5r_2E0))) = s(A_27a,V2v_27_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Efloat__value,V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0)
          & s(A_27a,V3v_2E0) = s(A_27a,V2v_27_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Efloat__value,V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
          & s(A_27a,V1v1_2E0) = s(A_27a,V2v_27_2E0) ) ) ) ).

fof(thm_2Ebinary__ieee_2Eflags__accessors,axiom,
    ( ! [V0b_2E0,V1b0_2E0,V2b1_2E0,V3b2_2E0,V4b3_2E0,V5b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1b0_2E0),s(tyop_2Emin_2Ebool,V2b1_2E0),s(tyop_2Emin_2Ebool,V3b2_2E0),s(tyop_2Emin_2Ebool,V4b3_2E0),s(tyop_2Emin_2Ebool,V5b4_2E0))))) = s(tyop_2Emin_2Ebool,V0b_2E0)
    & ! [V6b_2E0,V7b0_2E0,V8b1_2E0,V9b2_2E0,V10b3_2E0,V11b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V6b_2E0),s(tyop_2Emin_2Ebool,V7b0_2E0),s(tyop_2Emin_2Ebool,V8b1_2E0),s(tyop_2Emin_2Ebool,V9b2_2E0),s(tyop_2Emin_2Ebool,V10b3_2E0),s(tyop_2Emin_2Ebool,V11b4_2E0))))) = s(tyop_2Emin_2Ebool,V7b0_2E0)
    & ! [V12b_2E0,V13b0_2E0,V14b1_2E0,V15b2_2E0,V16b3_2E0,V17b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V12b_2E0),s(tyop_2Emin_2Ebool,V13b0_2E0),s(tyop_2Emin_2Ebool,V14b1_2E0),s(tyop_2Emin_2Ebool,V15b2_2E0),s(tyop_2Emin_2Ebool,V16b3_2E0),s(tyop_2Emin_2Ebool,V17b4_2E0))))) = s(tyop_2Emin_2Ebool,V14b1_2E0)
    & ! [V18b_2E0,V19b0_2E0,V20b1_2E0,V21b2_2E0,V22b3_2E0,V23b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V18b_2E0),s(tyop_2Emin_2Ebool,V19b0_2E0),s(tyop_2Emin_2Ebool,V20b1_2E0),s(tyop_2Emin_2Ebool,V21b2_2E0),s(tyop_2Emin_2Ebool,V22b3_2E0),s(tyop_2Emin_2Ebool,V23b4_2E0))))) = s(tyop_2Emin_2Ebool,V21b2_2E0)
    & ! [V24b_2E0,V25b0_2E0,V26b1_2E0,V27b2_2E0,V28b3_2E0,V29b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V24b_2E0),s(tyop_2Emin_2Ebool,V25b0_2E0),s(tyop_2Emin_2Ebool,V26b1_2E0),s(tyop_2Emin_2Ebool,V27b2_2E0),s(tyop_2Emin_2Ebool,V28b3_2E0),s(tyop_2Emin_2Ebool,V29b4_2E0))))) = s(tyop_2Emin_2Ebool,V28b3_2E0)
    & ! [V30b_2E0,V31b0_2E0,V32b1_2E0,V33b2_2E0,V34b3_2E0,V35b4_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V30b_2E0),s(tyop_2Emin_2Ebool,V31b0_2E0),s(tyop_2Emin_2Ebool,V32b1_2E0),s(tyop_2Emin_2Ebool,V33b2_2E0),s(tyop_2Emin_2Ebool,V34b3_2E0),s(tyop_2Emin_2Ebool,V35b4_2E0))))) = s(tyop_2Emin_2Ebool,V35b4_2E0) ) ).

fof(thm_2Ebinary__ieee_2Eflags__fn__updates,axiom,
    ( ! [V0f_2E0,V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0)))
    & ! [V7f_2E0,V8b_2E0,V9b0_2E0,V10b1_2E0,V11b2_2E0,V12b3_2E0,V13b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V8b_2E0),s(tyop_2Emin_2Ebool,V9b0_2E0),s(tyop_2Emin_2Ebool,V10b1_2E0),s(tyop_2Emin_2Ebool,V11b2_2E0),s(tyop_2Emin_2Ebool,V12b3_2E0),s(tyop_2Emin_2Ebool,V13b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V8b_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f_2E0),s(tyop_2Emin_2Ebool,V9b0_2E0))),s(tyop_2Emin_2Ebool,V10b1_2E0),s(tyop_2Emin_2Ebool,V11b2_2E0),s(tyop_2Emin_2Ebool,V12b3_2E0),s(tyop_2Emin_2Ebool,V13b4_2E0)))
    & ! [V14f_2E0,V15b_2E0,V16b0_2E0,V17b1_2E0,V18b2_2E0,V19b3_2E0,V20b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V14f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V15b_2E0),s(tyop_2Emin_2Ebool,V16b0_2E0),s(tyop_2Emin_2Ebool,V17b1_2E0),s(tyop_2Emin_2Ebool,V18b2_2E0),s(tyop_2Emin_2Ebool,V19b3_2E0),s(tyop_2Emin_2Ebool,V20b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V15b_2E0),s(tyop_2Emin_2Ebool,V16b0_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V14f_2E0),s(tyop_2Emin_2Ebool,V17b1_2E0))),s(tyop_2Emin_2Ebool,V18b2_2E0),s(tyop_2Emin_2Ebool,V19b3_2E0),s(tyop_2Emin_2Ebool,V20b4_2E0)))
    & ! [V21f_2E0,V22b_2E0,V23b0_2E0,V24b1_2E0,V25b2_2E0,V26b3_2E0,V27b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V22b_2E0),s(tyop_2Emin_2Ebool,V23b0_2E0),s(tyop_2Emin_2Ebool,V24b1_2E0),s(tyop_2Emin_2Ebool,V25b2_2E0),s(tyop_2Emin_2Ebool,V26b3_2E0),s(tyop_2Emin_2Ebool,V27b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V22b_2E0),s(tyop_2Emin_2Ebool,V23b0_2E0),s(tyop_2Emin_2Ebool,V24b1_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21f_2E0),s(tyop_2Emin_2Ebool,V25b2_2E0))),s(tyop_2Emin_2Ebool,V26b3_2E0),s(tyop_2Emin_2Ebool,V27b4_2E0)))
    & ! [V28f_2E0,V29b_2E0,V30b0_2E0,V31b1_2E0,V32b2_2E0,V33b3_2E0,V34b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V29b_2E0),s(tyop_2Emin_2Ebool,V30b0_2E0),s(tyop_2Emin_2Ebool,V31b1_2E0),s(tyop_2Emin_2Ebool,V32b2_2E0),s(tyop_2Emin_2Ebool,V33b3_2E0),s(tyop_2Emin_2Ebool,V34b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V29b_2E0),s(tyop_2Emin_2Ebool,V30b0_2E0),s(tyop_2Emin_2Ebool,V31b1_2E0),s(tyop_2Emin_2Ebool,V32b2_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28f_2E0),s(tyop_2Emin_2Ebool,V33b3_2E0))),s(tyop_2Emin_2Ebool,V34b4_2E0)))
    & ! [V35f_2E0,V36b_2E0,V37b0_2E0,V38b1_2E0,V39b2_2E0,V40b3_2E0,V41b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V35f_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V36b_2E0),s(tyop_2Emin_2Ebool,V37b0_2E0),s(tyop_2Emin_2Ebool,V38b1_2E0),s(tyop_2Emin_2Ebool,V39b2_2E0),s(tyop_2Emin_2Ebool,V40b3_2E0),s(tyop_2Emin_2Ebool,V41b4_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V36b_2E0),s(tyop_2Emin_2Ebool,V37b0_2E0),s(tyop_2Emin_2Ebool,V38b1_2E0),s(tyop_2Emin_2Ebool,V39b2_2E0),s(tyop_2Emin_2Ebool,V40b3_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V35f_2E0),s(tyop_2Emin_2Ebool,V41b4_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__accfupds,axiom,
    ( ! [V0f0_2E0,V1f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V1f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V1f_2E0)))
    & ! [V2f0_2E0,V3f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V2f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V3f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V3f_2E0)))
    & ! [V4f0_2E0,V5f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0)))
    & ! [V6f0_2E0,V7f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V7f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V7f_2E0)))
    & ! [V8f0_2E0,V9f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V8f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V9f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V9f_2E0)))
    & ! [V10f0_2E0,V11f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0)))
    & ! [V12f0_2E0,V13f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V12f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V13f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V13f_2E0)))
    & ! [V14f0_2E0,V15f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V14f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V15f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V15f_2E0)))
    & ! [V16f0_2E0,V17f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0)))
    & ! [V18f0_2E0,V19f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V18f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V19f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V19f_2E0)))
    & ! [V20f0_2E0,V21f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V20f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V21f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V21f_2E0)))
    & ! [V22f0_2E0,V23f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V22f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V23f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V23f_2E0)))
    & ! [V24f0_2E0,V25f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V24f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V25f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V25f_2E0)))
    & ! [V26f0_2E0,V27f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V26f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V27f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V27f_2E0)))
    & ! [V28f0_2E0,V29f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V29f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V29f_2E0)))
    & ! [V30f0_2E0,V31f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V30f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V31f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V31f_2E0)))
    & ! [V32f0_2E0,V33f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V32f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V33f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V33f_2E0)))
    & ! [V34f0_2E0,V35f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V34f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V35f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V35f_2E0)))
    & ! [V36f0_2E0,V37f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V36f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V37f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V37f_2E0)))
    & ! [V38f0_2E0,V39f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V38f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V39f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V39f_2E0)))
    & ! [V40f0_2E0,V41f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V40f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V41f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V41f_2E0)))
    & ! [V42f0_2E0,V43f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V42f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V43f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V43f_2E0)))
    & ! [V44f0_2E0,V45f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V44f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V45f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V45f_2E0)))
    & ! [V46f0_2E0,V47f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V46f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V47f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V47f_2E0)))
    & ! [V48f0_2E0,V49f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V48f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V49f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V49f_2E0)))
    & ! [V50f0_2E0,V51f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V50f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V51f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V51f_2E0)))
    & ! [V52f0_2E0,V53f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V52f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V53f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V53f_2E0)))
    & ! [V54f0_2E0,V55f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V54f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V55f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V55f_2E0)))
    & ! [V56f0_2E0,V57f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V56f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V57f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V57f_2E0)))
    & ! [V58f0_2E0,V59f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V58f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V59f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V59f_2E0)))
    & ! [V60f0_2E0,V61f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V60f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V61f_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V60f0_2E0),s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V61f_2E0)))))
    & ! [V62f0_2E0,V63f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V62f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V63f_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V62f0_2E0),s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V63f_2E0)))))
    & ! [V64f0_2E0,V65f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V64f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V65f_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V64f0_2E0),s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V65f_2E0)))))
    & ! [V66f0_2E0,V67f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V66f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V67f_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V66f0_2E0),s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V67f_2E0)))))
    & ! [V68f0_2E0,V69f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V68f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V69f_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V68f0_2E0),s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V69f_2E0)))))
    & ! [V70f0_2E0,V71f_2E0] : s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V70f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V71f_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V70f0_2E0),s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V71f_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__fupdfupds,axiom,
    ( ! [V0g_2E0,V1f0_2E0,V2f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V2f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V2f_2E0)))
    & ! [V3g_2E0,V4f0_2E0,V5f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0)))
    & ! [V6g_2E0,V7f0_2E0,V8f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V8f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V8f_2E0)))
    & ! [V9g_2E0,V10f0_2E0,V11f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0)))
    & ! [V12g_2E0,V13f0_2E0,V14f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V12g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V14f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V12g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V14f_2E0)))
    & ! [V15g_2E0,V16f0_2E0,V17f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__fupdfupds__comp,axiom,
    ! [A_27a] :
      ( ! [V0g_2E0,V1f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0)))))
      & ! [V2h_2E0,V3g_2E0,V4f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V2h_2E0)))
      & ! [V5g_2E0,V6f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V5g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V5g_2E0)))))
      & ! [V7h_2E0,V8g_2E0,V9f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V8g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V7h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V8g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V7h_2E0)))
      & ! [V10g_2E0,V11f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V11f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V11f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10g_2E0)))))
      & ! [V12h_2E0,V13g_2E0,V14f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V14f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V12h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V14f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V12h_2E0)))
      & ! [V15g_2E0,V16f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0)))))
      & ! [V17h_2E0,V18g_2E0,V19f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V19f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V18g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V17h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V19f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V18g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V17h_2E0)))
      & ! [V20g_2E0,V21f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V20g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V20g_2E0)))))
      & ! [V22h_2E0,V23g_2E0,V24f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V24f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V23g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V22h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V24f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V23g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V22h_2E0)))
      & ! [V25g_2E0,V26f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V26f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V25g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V26f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V25g_2E0)))))
      & ! [V27h_2E0,V28g_2E0,V29f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V29f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V27h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V29f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28g_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V27h_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__fupdcanon,axiom,
    ( ! [V0g_2E0,V1f0_2E0,V2f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V2f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V2f_2E0)))))
    & ! [V3g_2E0,V4f0_2E0,V5f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0)))))
    & ! [V6g_2E0,V7f0_2E0,V8f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V8f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V8f_2E0)))))
    & ! [V9g_2E0,V10f0_2E0,V11f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0)))))
    & ! [V12g_2E0,V13f0_2E0,V14f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V12g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V14f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V12g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V14f_2E0)))))
    & ! [V15g_2E0,V16f0_2E0,V17f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0)))))
    & ! [V18g_2E0,V19f0_2E0,V20f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V19f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V18g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V20f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V18g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V19f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V20f_2E0)))))
    & ! [V21g_2E0,V22f0_2E0,V23f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V22f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V23f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V22f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V23f_2E0)))))
    & ! [V24g_2E0,V25f0_2E0,V26f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V25f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V24g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V26f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V24g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V25f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V26f_2E0)))))
    & ! [V27g_2E0,V28f0_2E0,V29f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V27g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V29f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V27g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V29f_2E0)))))
    & ! [V30g_2E0,V31f0_2E0,V32f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V31f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V30g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V32f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V30g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V31f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V32f_2E0)))))
    & ! [V33g_2E0,V34f0_2E0,V35f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V34f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V33g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V35f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V33g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V34f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V35f_2E0)))))
    & ! [V36g_2E0,V37f0_2E0,V38f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V37f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V36g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V38f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V36g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V37f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V38f_2E0)))))
    & ! [V39g_2E0,V40f0_2E0,V41f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V40f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V39g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V41f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V39g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V40f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V41f_2E0)))))
    & ! [V42g_2E0,V43f0_2E0,V44f_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V43f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V42g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V44f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V42g_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V43f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,V44f_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__fupdcanon__comp,axiom,
    ! [A_27a] :
      ( ! [V0g_2E0,V1f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0)))))
      & ! [V2h_2E0,V3g_2E0,V4f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V2h_2E0)))))
      & ! [V5g_2E0,V6f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V5g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V5g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6f0_2E0)))))
      & ! [V7h_2E0,V8g_2E0,V9f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V8g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V7h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V8g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V7h_2E0)))))
      & ! [V10g_2E0,V11f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V11f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V11f0_2E0)))))
      & ! [V12h_2E0,V13g_2E0,V14f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V14f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V12h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V14f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V12h_2E0)))))
      & ! [V15g_2E0,V16f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0)))))
      & ! [V17h_2E0,V18g_2E0,V19f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V19f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V18g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V17h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V18g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V19f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V17h_2E0)))))
      & ! [V20g_2E0,V21f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V20g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V20g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V21f0_2E0)))))
      & ! [V22h_2E0,V23g_2E0,V24f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V24f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V23g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V22h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V23g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V24f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V22h_2E0)))))
      & ! [V25g_2E0,V26f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V26f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V25g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V25g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V26f0_2E0)))))
      & ! [V27h_2E0,V28g_2E0,V29f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V29f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V27h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V28g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V29f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V27h_2E0)))))
      & ! [V30g_2E0,V31f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V31f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V30g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V30g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V31f0_2E0)))))
      & ! [V32h_2E0,V33g_2E0,V34f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V34f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V33g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V32h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V33g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V34f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V32h_2E0)))))
      & ! [V35g_2E0,V36f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V36f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V35g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V35g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V36f0_2E0)))))
      & ! [V37h_2E0,V38g_2E0,V39f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V39f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V38g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V37h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V38g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V39f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V37h_2E0)))))
      & ! [V40g_2E0,V41f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V41f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V40g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V40g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V41f0_2E0)))))
      & ! [V42h_2E0,V43g_2E0,V44f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V44f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V43g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V42h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V43g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V44f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V42h_2E0)))))
      & ! [V45g_2E0,V46f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V46f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V45g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V45g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V46f0_2E0)))))
      & ! [V47h_2E0,V48g_2E0,V49f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V49f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V48g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V47h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V48g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V49f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V47h_2E0)))))
      & ! [V50g_2E0,V51f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V51f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V50g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V50g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V51f0_2E0)))))
      & ! [V52h_2E0,V53g_2E0,V54f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V54f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V53g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V52h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V53g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V54f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V52h_2E0)))))
      & ! [V55g_2E0,V56f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V56f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V55g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V55g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V56f0_2E0)))))
      & ! [V57h_2E0,V58g_2E0,V59f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V59f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V58g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V57h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V58g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V59f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V57h_2E0)))))
      & ! [V60g_2E0,V61f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V61f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V60g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V60g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V61f0_2E0)))))
      & ! [V62h_2E0,V63g_2E0,V64f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V64f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V63g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V62h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V63g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V64f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V62h_2E0)))))
      & ! [V65g_2E0,V66f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V66f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V65g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V65g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V66f0_2E0)))))
      & ! [V67h_2E0,V68g_2E0,V69f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V69f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V68g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V67h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V68g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V69f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V67h_2E0)))))
      & ! [V70g_2E0,V71f0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V71f0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V70g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V70g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V71f0_2E0)))))
      & ! [V72h_2E0,V73g_2E0,V74f0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V74f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V73g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V72h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V73g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V74f0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ebinary__ieee_2Eflags),V72h_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__component__equality,axiom,
    ! [V0f1_2E0,V1f2_2E0] :
      ( s(tyop_2Ebinary__ieee_2Eflags,V0f1_2E0) = s(tyop_2Ebinary__ieee_2Eflags,V1f2_2E0)
    <=> ( s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V0f1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__DivideByZero_2E1(s(tyop_2Ebinary__ieee_2Eflags,V1f2_2E0)))
        & s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V0f1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__InvalidOp_2E1(s(tyop_2Ebinary__ieee_2Eflags,V1f2_2E0)))
        & s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V0f1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Overflow_2E1(s(tyop_2Ebinary__ieee_2Eflags,V1f2_2E0)))
        & s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V0f1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Precision_2E1(s(tyop_2Ebinary__ieee_2Eflags,V1f2_2E0)))
        & s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V0f1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V1f2_2E0)))
        & s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V0f1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding_2E1(s(tyop_2Ebinary__ieee_2Eflags,V1f2_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Eflags__updates__eq__literal,axiom,
    ! [V0f_2E0,V1b4_2E0,V2b3_2E0,V3b2_2E0,V4b1_2E0,V5b0_2E0,V6b_2E0] : s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V1b4_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V2b3_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V3b2_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V4b1_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V5b0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V6b_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V0f_2E0))))))))))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V1b4_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V2b3_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V3b2_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V4b1_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V5b0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V6b_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebool_2EARB_2E0))))))))))))) ).

fof(thm_2Ebinary__ieee_2Eflags__literal__nchotomy,axiom,
    ! [V0f_2E0] :
    ? [V1b4_2E0,V2b3_2E0,V3b2_2E0,V4b1_2E0,V5b0_2E0,V6b_2E0] : s(tyop_2Ebinary__ieee_2Eflags,V0f_2E0) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V1b4_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V2b3_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V3b2_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V4b1_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V5b0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V6b_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebool_2EARB_2E0))))))))))))) ).

fof(thm_2Ebinary__ieee_2EFORALL__flags,axiom,
    ! [V0P_2E0] :
      ( ! [V1f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Eflags,V1f_2E0))))
    <=> ! [V2b4_2E0,V3b3_2E0,V4b2_2E0,V5b1_2E0,V6b0_2E0,V7b_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V2b4_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V3b3_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V4b2_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V5b1_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V6b0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V7b_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebool_2EARB_2E0)))))))))))))))) ) ).

fof(thm_2Ebinary__ieee_2EEXISTS__flags,axiom,
    ! [V0P_2E0] :
      ( ? [V1f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Eflags,V1f_2E0))))
    <=> ? [V2b4_2E0,V3b3_2E0,V4b2_2E0,V5b1_2E0,V6b0_2E0,V7b_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V2b4_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V3b3_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V4b2_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V5b1_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V6b0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V7b_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebool_2EARB_2E0)))))))))))))))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__literal__11,axiom,
    ! [V0b41_2E0,V1b31_2E0,V2b21_2E0,V3b11_2E0,V4b01_2E0,V5b1_2E0,V6b42_2E0,V7b32_2E0,V8b22_2E0,V9b12_2E0,V10b02_2E0,V11b2_2E0] :
      ( s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V0b41_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V1b31_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V2b21_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V3b11_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V4b01_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V5b1_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebool_2EARB_2E0))))))))))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V6b42_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V7b32_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V8b22_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V9b12_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V10b02_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V11b2_2E0))),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebool_2EARB_2E0)))))))))))))
    <=> ( s(tyop_2Emin_2Ebool,V0b41_2E0) = s(tyop_2Emin_2Ebool,V6b42_2E0)
        & s(tyop_2Emin_2Ebool,V1b31_2E0) = s(tyop_2Emin_2Ebool,V7b32_2E0)
        & s(tyop_2Emin_2Ebool,V2b21_2E0) = s(tyop_2Emin_2Ebool,V8b22_2E0)
        & s(tyop_2Emin_2Ebool,V3b11_2E0) = s(tyop_2Emin_2Ebool,V9b12_2E0)
        & s(tyop_2Emin_2Ebool,V4b01_2E0) = s(tyop_2Emin_2Ebool,V10b02_2E0)
        & s(tyop_2Emin_2Ebool,V5b1_2E0) = s(tyop_2Emin_2Ebool,V11b2_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Edatatype__flags,axiom,
    ! [V0record_2E0,V1flags_2E0,V2Underflow__BeforeRounding_2E0,V3Underflow__AfterRounding_2E0,V4Precision_2E0,V5Overflow_2E0,V6InvalidOp_2E0,V7DivideByZero_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun(tyop_2Emin_2Ebool,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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,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_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))))))),V0record_2E0),s(tyop_2Ebinary__ieee_2Eflags,V1flags_2E0))),s(tyop_2Emin_2Ebool,V7DivideByZero_2E0))),s(tyop_2Emin_2Ebool,V6InvalidOp_2E0))),s(tyop_2Emin_2Ebool,V5Overflow_2E0))),s(tyop_2Emin_2Ebool,V4Precision_2E0))),s(tyop_2Emin_2Ebool,V2Underflow__BeforeRounding_2E0))),s(tyop_2Emin_2Ebool,V3Underflow__AfterRounding_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Eflags__11,axiom,
    ! [V0a0_2E0,V1a1_2E0,V2a2_2E0,V3a3_2E0,V4a4_2E0,V5a5_2E0,V6a0_27_2E0,V7a1_27_2E0,V8a2_27_2E0,V9a3_27_2E0,V10a4_27_2E0,V11a5_27_2E0] :
      ( s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V0a0_2E0),s(tyop_2Emin_2Ebool,V1a1_2E0),s(tyop_2Emin_2Ebool,V2a2_2E0),s(tyop_2Emin_2Ebool,V3a3_2E0),s(tyop_2Emin_2Ebool,V4a4_2E0),s(tyop_2Emin_2Ebool,V5a5_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V6a0_27_2E0),s(tyop_2Emin_2Ebool,V7a1_27_2E0),s(tyop_2Emin_2Ebool,V8a2_27_2E0),s(tyop_2Emin_2Ebool,V9a3_27_2E0),s(tyop_2Emin_2Ebool,V10a4_27_2E0),s(tyop_2Emin_2Ebool,V11a5_27_2E0)))
    <=> ( s(tyop_2Emin_2Ebool,V0a0_2E0) = s(tyop_2Emin_2Ebool,V6a0_27_2E0)
        & s(tyop_2Emin_2Ebool,V1a1_2E0) = s(tyop_2Emin_2Ebool,V7a1_27_2E0)
        & s(tyop_2Emin_2Ebool,V2a2_2E0) = s(tyop_2Emin_2Ebool,V8a2_27_2E0)
        & s(tyop_2Emin_2Ebool,V3a3_2E0) = s(tyop_2Emin_2Ebool,V9a3_27_2E0)
        & s(tyop_2Emin_2Ebool,V4a4_2E0) = s(tyop_2Emin_2Ebool,V10a4_27_2E0)
        & s(tyop_2Emin_2Ebool,V5a5_2E0) = s(tyop_2Emin_2Ebool,V11a5_27_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Eflags__nchotomy,axiom,
    ! [V0ff_2E0] :
    ? [V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : s(tyop_2Ebinary__ieee_2Eflags,V0ff_2E0) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__Axiom,axiom,
    ! [A_27a,V0f_2E0] :
    ? [V1fn_2E0] :
    ! [V2a0_2E0,V3a1_2E0,V4a2_2E0,V5a3_2E0,V6a4_2E0,V7a5_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,A_27a),V1fn_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V2a0_2E0),s(tyop_2Emin_2Ebool,V3a1_2E0),s(tyop_2Emin_2Ebool,V4a2_2E0),s(tyop_2Emin_2Ebool,V5a3_2E0),s(tyop_2Emin_2Ebool,V6a4_2E0),s(tyop_2Emin_2Ebool,V7a5_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V0f_2E0),s(tyop_2Emin_2Ebool,V2a0_2E0))),s(tyop_2Emin_2Ebool,V3a1_2E0))),s(tyop_2Emin_2Ebool,V4a2_2E0))),s(tyop_2Emin_2Ebool,V5a3_2E0))),s(tyop_2Emin_2Ebool,V6a4_2E0))),s(tyop_2Emin_2Ebool,V7a5_2E0))) ).

fof(thm_2Ebinary__ieee_2Eflags__induction,axiom,
    ! [V0P_2E0] :
      ( ! [V1b_2E0,V2b0_2E0,V3b1_2E0,V4b2_2E0,V5b3_2E0,V6b4_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Emin_2Ebool,V2b0_2E0),s(tyop_2Emin_2Ebool,V3b1_2E0),s(tyop_2Emin_2Ebool,V4b2_2E0),s(tyop_2Emin_2Ebool,V5b3_2E0),s(tyop_2Emin_2Ebool,V6b4_2E0))))))
     => ! [V7f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Eflags,V7f_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__case__cong,axiom,
    ! [A_27a,V0f_27_2E0,V1M_2E0,V2M_27_2E0,V3f_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Eflags,V1M_2E0) = s(tyop_2Ebinary__ieee_2Eflags,V2M_27_2E0)
        & ! [V4a0_2E0,V5a1_2E0,V6a2_2E0,V7a3_2E0,V8a4_2E0,V9a5_2E0] :
            ( s(tyop_2Ebinary__ieee_2Eflags,V2M_27_2E0) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V4a0_2E0),s(tyop_2Emin_2Ebool,V5a1_2E0),s(tyop_2Emin_2Ebool,V6a2_2E0),s(tyop_2Emin_2Ebool,V7a3_2E0),s(tyop_2Emin_2Ebool,V8a4_2E0),s(tyop_2Emin_2Ebool,V9a5_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V3f_2E0),s(tyop_2Emin_2Ebool,V4a0_2E0))),s(tyop_2Emin_2Ebool,V5a1_2E0))),s(tyop_2Emin_2Ebool,V6a2_2E0))),s(tyop_2Emin_2Ebool,V7a3_2E0))),s(tyop_2Emin_2Ebool,V8a4_2E0))),s(tyop_2Emin_2Ebool,V9a5_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V0f_27_2E0),s(tyop_2Emin_2Ebool,V4a0_2E0))),s(tyop_2Emin_2Ebool,V5a1_2E0))),s(tyop_2Emin_2Ebool,V6a2_2E0))),s(tyop_2Emin_2Ebool,V7a3_2E0))),s(tyop_2Emin_2Ebool,V8a4_2E0))),s(tyop_2Emin_2Ebool,V9a5_2E0))) ) )
     => s(A_27a,c_2Ebinary__ieee_2Eflags__CASE_2E2(s(tyop_2Ebinary__ieee_2Eflags,V1M_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V3f_2E0))) = s(A_27a,c_2Ebinary__ieee_2Eflags__CASE_2E2(s(tyop_2Ebinary__ieee_2Eflags,V2M_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V0f_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eflags__case__eq,axiom,
    ! [A_27a,V0x_2E0,V1v_2E0,V2f_2E0] :
      ( s(A_27a,c_2Ebinary__ieee_2Eflags__CASE_2E2(s(tyop_2Ebinary__ieee_2Eflags,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V2f_2E0))) = s(A_27a,V1v_2E0)
    <=> ? [V3b_2E0,V4b0_2E0,V5b1_2E0,V6b2_2E0,V7b3_2E0,V8b4_2E0] :
          ( s(tyop_2Ebinary__ieee_2Eflags,V0x_2E0) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Erecordtype_2Eflags_2E6(s(tyop_2Emin_2Ebool,V3b_2E0),s(tyop_2Emin_2Ebool,V4b0_2E0),s(tyop_2Emin_2Ebool,V5b1_2E0),s(tyop_2Emin_2Ebool,V6b2_2E0),s(tyop_2Emin_2Ebool,V7b3_2E0),s(tyop_2Emin_2Ebool,V8b4_2E0)))
          & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a)))))),V2f_2E0),s(tyop_2Emin_2Ebool,V3b_2E0))),s(tyop_2Emin_2Ebool,V4b0_2E0))),s(tyop_2Emin_2Ebool,V5b1_2E0))),s(tyop_2Emin_2Ebool,V6b2_2E0))),s(tyop_2Emin_2Ebool,V7b3_2E0))),s(tyop_2Emin_2Ebool,V8b4_2E0))) = s(A_27a,V1v_2E0) ) ) ).

fof(thm_2Ebinary__ieee_2Enum2rounding__rounding2num,axiom,
    ! [V0a_2E0] : s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0))))) = s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) ).

fof(thm_2Ebinary__ieee_2Erounding2num__num2rounding,axiom,
    ! [V0r_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_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_2EZERO_2E0))))))))))
    <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,V0r_2E0))))) = s(tyop_2Enum_2Enum,V0r_2E0) ) ).

fof(thm_2Ebinary__ieee_2Enum2rounding__11,axiom,
    ! [V0r_2E0,V1r_27_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_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_2EZERO_2E0))))))))))
     => ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_27_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_2EZERO_2E0))))))))))
       => ( s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,V0r_2E0))) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,V1r_27_2E0)))
        <=> s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,V1r_27_2E0) ) ) ) ).

fof(thm_2Ebinary__ieee_2Erounding2num__11,axiom,
    ! [V0a_2E0,V1a_27_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V1a_27_2E0)))
    <=> s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V1a_27_2E0) ) ).

fof(thm_2Ebinary__ieee_2Enum2rounding__ONTO,axiom,
    ! [V0a_2E0] :
    ? [V1r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,V1r_2E0)))
      & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_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_2EZERO_2E0)))))))))) ) ).

fof(thm_2Ebinary__ieee_2Erounding2num__ONTO,axiom,
    ! [V0r_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_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_2EZERO_2E0))))))))))
    <=> ? [V1a_2E0] : s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V1a_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Enum2rounding__thm,axiom,
    ( s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_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_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_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_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2Enum2rounding_2E1(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_2EZERO_2E0))))))))) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0) ) ).

fof(thm_2Ebinary__ieee_2Erounding2num__thm,axiom,
    ( s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
    & s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_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_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_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)))))
    & s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_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_2EZERO_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Erounding__EQ__rounding,axiom,
    ! [V0a_2E0,V1a_27_2E0] :
      ( s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V1a_27_2E0)
    <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Erounding2num_2E1(s(tyop_2Ebinary__ieee_2Erounding,V1a_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Erounding__case__def,axiom,
    ! [A_27a] :
      ( ! [V0v0_2E0,V1v1_2E0,V2v2_2E0,V3v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(A_27a,V0v0_2E0),s(A_27a,V1v1_2E0),s(A_27a,V2v2_2E0),s(A_27a,V3v3_2E0))) = s(A_27a,V0v0_2E0)
      & ! [V4v0_2E0,V5v1_2E0,V6v2_2E0,V7v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0),s(A_27a,V4v0_2E0),s(A_27a,V5v1_2E0),s(A_27a,V6v2_2E0),s(A_27a,V7v3_2E0))) = s(A_27a,V5v1_2E0)
      & ! [V8v0_2E0,V9v1_2E0,V10v2_2E0,V11v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0),s(A_27a,V8v0_2E0),s(A_27a,V9v1_2E0),s(A_27a,V10v2_2E0),s(A_27a,V11v3_2E0))) = s(A_27a,V10v2_2E0)
      & ! [V12v0_2E0,V13v1_2E0,V14v2_2E0,V15v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(A_27a,V12v0_2E0),s(A_27a,V13v1_2E0),s(A_27a,V14v2_2E0),s(A_27a,V15v3_2E0))) = s(A_27a,V15v3_2E0) ) ).

fof(thm_2Ebinary__ieee_2Edatatype__rounding,axiom,
    ! [V0rounding_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool)))),V0rounding_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0))),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0))),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0))),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Erounding__distinct,axiom,
    ( s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0) != s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0) != s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0) != s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0) != s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0) != s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0)
    & s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) != s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0) ) ).

fof(thm_2Ebinary__ieee_2Erounding__nchotomy,axiom,
    ! [V0a_2E0] :
      ( s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0)
      | s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0)
      | s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0)
      | s(tyop_2Ebinary__ieee_2Erounding,V0a_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0) ) ).

fof(thm_2Ebinary__ieee_2Erounding__Axiom,axiom,
    ! [A_27a,V0x0_2E0,V1x1_2E0,V2x2_2E0,V3x3_2E0] :
    ? [V4f_2E0] :
      ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0))) = s(A_27a,V0x0_2E0)
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0))) = s(A_27a,V1x1_2E0)
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0))) = s(A_27a,V2x2_2E0)
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0))) = s(A_27a,V3x3_2E0) ) ).

fof(thm_2Ebinary__ieee_2Erounding__induction,axiom,
    ! [V0P_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0)))) )
     => ! [V1a_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Erounding,V1a_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Erounding__case__cong,axiom,
    ! [A_27a,V0v3_27_2E0,V1v2_27_2E0,V2v1_27_2E0,V3v0_27_2E0,V4M_2E0,V5M_27_2E0,V6v0_2E0,V7v1_2E0,V8v2_2E0,V9v3_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Erounding,V4M_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V5M_27_2E0)
        & ( s(tyop_2Ebinary__ieee_2Erounding,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0)
         => s(A_27a,V6v0_2E0) = s(A_27a,V3v0_27_2E0) )
        & ( s(tyop_2Ebinary__ieee_2Erounding,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0)
         => s(A_27a,V7v1_2E0) = s(A_27a,V2v1_27_2E0) )
        & ( s(tyop_2Ebinary__ieee_2Erounding,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0)
         => s(A_27a,V8v2_2E0) = s(A_27a,V1v2_27_2E0) )
        & ( s(tyop_2Ebinary__ieee_2Erounding,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0)
         => s(A_27a,V9v3_2E0) = s(A_27a,V0v3_27_2E0) ) )
     => s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V4M_2E0),s(A_27a,V6v0_2E0),s(A_27a,V7v1_2E0),s(A_27a,V8v2_2E0),s(A_27a,V9v3_2E0))) = s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V5M_27_2E0),s(A_27a,V3v0_27_2E0),s(A_27a,V2v1_27_2E0),s(A_27a,V1v2_27_2E0),s(A_27a,V0v3_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Erounding__case__eq,axiom,
    ! [A_27a,V0x_2E0,V1v3_2E0,V2v2_2E0,V3v1_2E0,V4v0_2E0,V5v_2E0] :
      ( s(A_27a,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0),s(A_27a,V4v0_2E0),s(A_27a,V3v1_2E0),s(A_27a,V2v2_2E0),s(A_27a,V1v3_2E0))) = s(A_27a,V5v_2E0)
    <=> ( ( s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0)
          & s(A_27a,V4v0_2E0) = s(A_27a,V5v_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0)
          & s(A_27a,V3v1_2E0) = s(A_27a,V5v_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0)
          & s(A_27a,V2v2_2E0) = s(A_27a,V5v_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Erounding,V0x_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0)
          & s(A_27a,V1v3_2E0) = s(A_27a,V5v_2E0) ) ) ) ).

fof(thm_2Ebinary__ieee_2EULP__ind,axiom,
    ! [A_27t,A_27w,V0P_2E0] :
      ( ! [V1e_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1e_2E0),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))
     => ! [V2v_2E0,V3v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V2v_2E0),s(tyop_2Ebool_2Eitself(A_27t),V3v1_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2EULP__def,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V0e_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V0e_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V0e_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ! [V0e_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V0e_2E0),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_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_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V0e_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_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V0e_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_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))) ) ).

fof(thm_2Ebinary__ieee_2Edatatype__fp__op,axiom,
    ! [A_27t,A_27w,V0fp__op_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),tyop_2Emin_2Ebool))))))),V0fp__op_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))),c_2Ebinary__ieee_2EFP__Sqrt_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Add_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Sub_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Mul_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w)))),c_2Ebinary__ieee_2EFP__Div_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),c_2Ebinary__ieee_2EFP__MulAdd_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w))))),c_2Ebinary__ieee_2EFP__MulSub_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Efp__op__11,axiom,
    ! [A_27t,A_27w] :
      ( ! [V0a0_2E0,V1a1_2E0,V2a0_27_2E0,V3a1_27_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1a1_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V2a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a1_27_2E0)))
        <=> ( s(tyop_2Ebinary__ieee_2Erounding,V0a0_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V2a0_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1a1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V3a1_27_2E0) ) )
      & ! [V4a0_2E0,V5a1_2E0,V6a2_2E0,V7a0_27_2E0,V8a1_27_2E0,V9a2_27_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V4a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V7a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a2_27_2E0)))
        <=> ( s(tyop_2Ebinary__ieee_2Erounding,V4a0_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V7a0_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8a1_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a2_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a2_27_2E0) ) )
      & ! [V10a0_2E0,V11a1_2E0,V12a2_2E0,V13a0_27_2E0,V14a1_27_2E0,V15a2_27_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V10a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V13a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V14a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15a2_27_2E0)))
        <=> ( s(tyop_2Ebinary__ieee_2Erounding,V10a0_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V13a0_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11a1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V14a1_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a2_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15a2_27_2E0) ) )
      & ! [V16a0_2E0,V17a1_2E0,V18a2_2E0,V19a0_27_2E0,V20a1_27_2E0,V21a2_27_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18a2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V19a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_27_2E0)))
        <=> ( s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V19a0_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a1_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18a2_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_27_2E0) ) )
      & ! [V22a0_2E0,V23a1_2E0,V24a2_2E0,V25a0_27_2E0,V26a1_27_2E0,V27a2_27_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V22a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V24a2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V25a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V27a2_27_2E0)))
        <=> ( s(tyop_2Ebinary__ieee_2Erounding,V22a0_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V25a0_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26a1_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V24a2_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V27a2_27_2E0) ) )
      & ! [V28a0_2E0,V29a1_2E0,V30a2_2E0,V31a3_2E0,V32a0_27_2E0,V33a1_27_2E0,V34a2_27_2E0,V35a3_27_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V28a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V30a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a3_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V32a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V34a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a3_27_2E0)))
        <=> ( s(tyop_2Ebinary__ieee_2Erounding,V28a0_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V32a0_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a1_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V30a2_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V34a2_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a3_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a3_27_2E0) ) )
      & ! [V36a0_2E0,V37a1_2E0,V38a2_2E0,V39a3_2E0,V40a0_27_2E0,V41a1_27_2E0,V42a2_27_2E0,V43a3_27_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V36a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V37a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V38a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V39a3_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V40a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V41a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V42a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V43a3_27_2E0)))
        <=> ( s(tyop_2Ebinary__ieee_2Erounding,V36a0_2E0) = s(tyop_2Ebinary__ieee_2Erounding,V40a0_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V37a1_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V41a1_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V38a2_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V42a2_27_2E0)
            & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V39a3_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V43a3_27_2E0) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__distinct,axiom,
    ! [A_27t,A_27w] :
      ( ! [V0a2_2E0,V1a1_27_2E0,V2a1_2E0,V3a0_27_2E0,V4a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V4a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2a1_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a2_2E0)))
      & ! [V5a2_2E0,V6a1_27_2E0,V7a1_2E0,V8a0_27_2E0,V9a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V9a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7a1_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V8a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V6a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5a2_2E0)))
      & ! [V10a2_2E0,V11a1_27_2E0,V12a1_2E0,V13a0_27_2E0,V14a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V14a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a1_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V13a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10a2_2E0)))
      & ! [V15a2_2E0,V16a1_27_2E0,V17a1_2E0,V18a0_27_2E0,V19a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V19a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V18a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V16a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15a2_2E0)))
      & ! [V20a3_2E0,V21a2_2E0,V22a1_27_2E0,V23a1_2E0,V24a0_27_2E0,V25a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V25a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a1_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V24a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a3_2E0)))
      & ! [V26a3_2E0,V27a2_2E0,V28a1_27_2E0,V29a1_2E0,V30a0_27_2E0,V31a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V31a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a1_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V30a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V27a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26a3_2E0)))
      & ! [V32a2_27_2E0,V33a2_2E0,V34a1_27_2E0,V35a1_2E0,V36a0_27_2E0,V37a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V37a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V36a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V34a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V32a2_27_2E0)))
      & ! [V38a2_27_2E0,V39a2_2E0,V40a1_27_2E0,V41a1_2E0,V42a0_27_2E0,V43a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V43a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V41a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V39a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V42a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V40a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V38a2_27_2E0)))
      & ! [V44a2_27_2E0,V45a2_2E0,V46a1_27_2E0,V47a1_2E0,V48a0_27_2E0,V49a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V49a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V47a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V45a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V48a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V46a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V44a2_27_2E0)))
      & ! [V50a3_2E0,V51a2_27_2E0,V52a2_2E0,V53a1_27_2E0,V54a1_2E0,V55a0_27_2E0,V56a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V56a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V54a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V52a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V55a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V53a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V51a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V50a3_2E0)))
      & ! [V57a3_2E0,V58a2_27_2E0,V59a2_2E0,V60a1_27_2E0,V61a1_2E0,V62a0_27_2E0,V63a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V63a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V61a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V59a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V62a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V60a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V58a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V57a3_2E0)))
      & ! [V64a2_27_2E0,V65a2_2E0,V66a1_27_2E0,V67a1_2E0,V68a0_27_2E0,V69a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V69a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V67a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V65a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V68a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V66a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V64a2_27_2E0)))
      & ! [V70a2_27_2E0,V71a2_2E0,V72a1_27_2E0,V73a1_2E0,V74a0_27_2E0,V75a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V75a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V73a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V71a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V74a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V72a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V70a2_27_2E0)))
      & ! [V76a3_2E0,V77a2_27_2E0,V78a2_2E0,V79a1_27_2E0,V80a1_2E0,V81a0_27_2E0,V82a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V82a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V80a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V78a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V81a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V79a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V77a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V76a3_2E0)))
      & ! [V83a3_2E0,V84a2_27_2E0,V85a2_2E0,V86a1_27_2E0,V87a1_2E0,V88a0_27_2E0,V89a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V89a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V87a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V85a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V88a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V86a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V84a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V83a3_2E0)))
      & ! [V90a2_27_2E0,V91a2_2E0,V92a1_27_2E0,V93a1_2E0,V94a0_27_2E0,V95a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V95a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V93a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V91a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V94a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V92a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V90a2_27_2E0)))
      & ! [V96a3_2E0,V97a2_27_2E0,V98a2_2E0,V99a1_27_2E0,V100a1_2E0,V101a0_27_2E0,V102a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V102a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V100a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V98a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V101a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V99a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V97a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V96a3_2E0)))
      & ! [V103a3_2E0,V104a2_27_2E0,V105a2_2E0,V106a1_27_2E0,V107a1_2E0,V108a0_27_2E0,V109a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V109a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V107a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V105a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V108a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V106a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V104a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V103a3_2E0)))
      & ! [V110a3_2E0,V111a2_27_2E0,V112a2_2E0,V113a1_27_2E0,V114a1_2E0,V115a0_27_2E0,V116a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V116a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V114a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V112a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V115a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V113a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V111a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V110a3_2E0)))
      & ! [V117a3_2E0,V118a2_27_2E0,V119a2_2E0,V120a1_27_2E0,V121a1_2E0,V122a0_27_2E0,V123a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V123a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V121a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V119a2_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V122a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V120a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V118a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V117a3_2E0)))
      & ! [V124a3_27_2E0,V125a3_2E0,V126a2_27_2E0,V127a2_2E0,V128a1_27_2E0,V129a1_2E0,V130a0_27_2E0,V131a0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V131a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V129a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V127a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V125a3_2E0))) != s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V130a0_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V128a1_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V126a2_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V124a3_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__nchotomy,axiom,
    ! [A_27t,A_27w,V0ff_2E0] :
      ( ? [V1r_2E0,V2f_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V1r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2f_2E0)))
      | ? [V3r_2E0,V4f_2E0,V5f0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V4f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f0_2E0)))
      | ? [V6r_2E0,V7f_2E0,V8f0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8f0_2E0)))
      | ? [V9r_2E0,V10f_2E0,V11f0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11f0_2E0)))
      | ? [V12r_2E0,V13f_2E0,V14f0_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V12r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V14f0_2E0)))
      | ? [V15r_2E0,V16f_2E0,V17f0_2E0,V18f1_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V15r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V16f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18f1_2E0)))
      | ? [V19r_2E0,V20f_2E0,V21f0_2E0,V22f1_2E0] : s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0ff_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V19r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22f1_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__Axiom,axiom,
    ! [A_27a,A_27t,A_27w,V0f0_2E0,V1f1_2E0,V2f2_2E0,V3f3_2E0,V4f4_2E0,V5f5_2E0,V6f6_2E0] :
    ? [V7fn_2E0] :
      ( ! [V8a0_2E0,V9a1_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a),V7fn_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V8a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a1_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V0f0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V8a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V9a1_2E0)))
      & ! [V10a0_2E0,V11a1_2E0,V12a2_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a),V7fn_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V10a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a2_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V1f1_2E0),s(tyop_2Ebinary__ieee_2Erounding,V10a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12a2_2E0)))
      & ! [V13a0_2E0,V14a1_2E0,V15a2_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a),V7fn_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V13a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V14a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15a2_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V2f2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V13a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V14a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15a2_2E0)))
      & ! [V16a0_2E0,V17a1_2E0,V18a2_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a),V7fn_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18a2_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V3f3_2E0),s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18a2_2E0)))
      & ! [V19a0_2E0,V20a1_2E0,V21a2_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a),V7fn_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V19a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V4f4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V19a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21a2_2E0)))
      & ! [V22a0_2E0,V23a1_2E0,V24a2_2E0,V25a3_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a),V7fn_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V22a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V24a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25a3_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V5f5_2E0),s(tyop_2Ebinary__ieee_2Erounding,V22a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V24a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25a3_2E0)))
      & ! [V26a0_2E0,V27a1_2E0,V28a2_2E0,V29a3_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),A_27a),V7fn_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V26a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V27a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a3_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V6f6_2E0),s(tyop_2Ebinary__ieee_2Erounding,V26a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V27a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a3_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__induction,axiom,
    ! [A_27t,A_27w,V0P_2E0] :
      ( ( ! [V1r_2E0,V2f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V1r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2f_2E0))))))
        & ! [V3r_2E0,V4f_2E0,V5f0_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V4f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V5f0_2E0))))))
        & ! [V6r_2E0,V7f_2E0,V8f0_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V7f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V8f0_2E0))))))
        & ! [V9r_2E0,V10f_2E0,V11f0_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V11f0_2E0))))))
        & ! [V12r_2E0,V13f_2E0,V14f0_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V12r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V14f0_2E0))))))
        & ! [V15r_2E0,V16f_2E0,V17f0_2E0,V18f1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V15r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V16f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18f1_2E0))))))
        & ! [V19r_2E0,V20f_2E0,V21f0_2E0,V22f1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V19r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20f_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22f1_2E0)))))) )
     => ! [V23f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V23f_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__case__cong,axiom,
    ! [A_27a,A_27t,A_27w,V0f6_27_2E0,V1f5_27_2E0,V2f4_27_2E0,V3f3_27_2E0,V4f2_27_2E0,V5f1_27_2E0,V6f_27_2E0,V7M_2E0,V8M_27_2E0,V9f_2E0,V10f1_2E0,V11f2_2E0,V12f3_2E0,V13f4_2E0,V14f5_2E0,V15f6_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V7M_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0)
        & ! [V16a0_2E0,V17a1_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V9f_2E0),s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V6f_27_2E0),s(tyop_2Ebinary__ieee_2Erounding,V16a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V17a1_2E0))) )
        & ! [V18a0_2E0,V19a1_2E0,V20a2_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V18a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V19a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a2_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V10f1_2E0),s(tyop_2Ebinary__ieee_2Erounding,V18a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V19a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V5f1_27_2E0),s(tyop_2Ebinary__ieee_2Erounding,V18a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V19a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V20a2_2E0))) )
        & ! [V21a0_2E0,V22a1_2E0,V23a2_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V21a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a2_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V11f2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V21a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V4f2_27_2E0),s(tyop_2Ebinary__ieee_2Erounding,V21a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V23a2_2E0))) )
        & ! [V24a0_2E0,V25a1_2E0,V26a2_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V24a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26a2_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V12f3_2E0),s(tyop_2Ebinary__ieee_2Erounding,V24a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26a2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V3f3_27_2E0),s(tyop_2Ebinary__ieee_2Erounding,V24a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26a2_2E0))) )
        & ! [V27a0_2E0,V28a1_2E0,V29a2_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V27a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a2_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V13f4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V27a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V2f4_27_2E0),s(tyop_2Ebinary__ieee_2Erounding,V27a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29a2_2E0))) )
        & ! [V30a0_2E0,V31a1_2E0,V32a2_2E0,V33a3_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V30a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V32a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a3_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V14f5_2E0),s(tyop_2Ebinary__ieee_2Erounding,V30a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V32a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V1f5_27_2E0),s(tyop_2Ebinary__ieee_2Erounding,V30a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V31a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V32a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V33a3_2E0))) )
        & ! [V34a0_2E0,V35a1_2E0,V36a2_2E0,V37a3_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V34a0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V36a2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V37a3_2E0)))
           => s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V15f6_2E0),s(tyop_2Ebinary__ieee_2Erounding,V34a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V36a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V37a3_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V0f6_27_2E0),s(tyop_2Ebinary__ieee_2Erounding,V34a0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V35a1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V36a2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V37a3_2E0))) ) )
     => s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V7M_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V9f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V10f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V11f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V12f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V13f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V14f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V15f6_2E0))) = s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V8M_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V6f_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V5f1_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V4f2_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V3f3_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V2f4_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V1f5_27_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V0f6_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efp__op__case__eq,axiom,
    ! [A_27a,A_27t,A_27w,V0x_2E0,V1v_2E0,V2f6_2E0,V3f5_2E0,V4f4_2E0,V5f3_2E0,V6f2_2E0,V7f1_2E0,V8f_2E0] :
      ( s(A_27a,c_2Ebinary__ieee_2Efp__op__CASE_2E8(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V8f_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V7f1_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V6f2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V5f3_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V4f4_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V3f5_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V2f6_2E0))) = s(A_27a,V1v_2E0)
    <=> ( ? [V9r_2E0,V10f_27_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sqrt_2E2(s(tyop_2Ebinary__ieee_2Erounding,V9r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10f_27_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),V8f_2E0),s(tyop_2Ebinary__ieee_2Erounding,V9r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V10f_27_2E0))) = s(A_27a,V1v_2E0) )
        | ? [V11r_2E0,V12f_27_2E0,V13f0_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V11r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12f_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13f0_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V7f1_2E0),s(tyop_2Ebinary__ieee_2Erounding,V11r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V12f_27_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V13f0_2E0))) = s(A_27a,V1v_2E0) )
        | ? [V14r_2E0,V15f_27_2E0,V16f0_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V14r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15f_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V16f0_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V6f2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V14r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V15f_27_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V16f0_2E0))) = s(A_27a,V1v_2E0) )
        | ? [V17r_2E0,V18f_27_2E0,V19f0_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V17r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18f_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V19f0_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V5f3_2E0),s(tyop_2Ebinary__ieee_2Erounding,V17r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V18f_27_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V19f0_2E0))) = s(A_27a,V1v_2E0) )
        | ? [V20r_2E0,V21f_27_2E0,V22f0_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V20r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21f_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22f0_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),V4f4_2E0),s(tyop_2Ebinary__ieee_2Erounding,V20r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V21f_27_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V22f0_2E0))) = s(A_27a,V1v_2E0) )
        | ? [V23r_2E0,V24f_27_2E0,V25f0_2E0,V26f1_27_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulAdd_2E4(s(tyop_2Ebinary__ieee_2Erounding,V23r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V24f_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26f1_27_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V3f5_2E0),s(tyop_2Ebinary__ieee_2Erounding,V23r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V24f_27_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V25f0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V26f1_27_2E0))) = s(A_27a,V1v_2E0) )
        | ? [V27r_2E0,V28f_27_2E0,V29f0_2E0,V30f1_27_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__MulSub_2E4(s(tyop_2Ebinary__ieee_2Erounding,V27r_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28f_27_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29f0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V30f1_27_2E0)))
            & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),A_27a)))),V2f6_2E0),s(tyop_2Ebinary__ieee_2Erounding,V27r_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V28f_27_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V29f0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V30f1_27_2E0))) = s(A_27a,V1v_2E0) ) ) ) ).

fof(thm_2Ebinary__ieee_2Enum2float__compare__float__compare2num,axiom,
    ! [V0a_2E0] : s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) ).

fof(thm_2Ebinary__ieee_2Efloat__compare2num__num2float__compare,axiom,
    ! [V0r_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_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_2EZERO_2E0))))))))))
    <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,V0r_2E0))))) = s(tyop_2Enum_2Enum,V0r_2E0) ) ).

fof(thm_2Ebinary__ieee_2Enum2float__compare__11,axiom,
    ! [V0r_2E0,V1r_27_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_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_2EZERO_2E0))))))))))
     => ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_27_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_2EZERO_2E0))))))))))
       => ( s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,V0r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,V1r_27_2E0)))
        <=> s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,V1r_27_2E0) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare2num__11,axiom,
    ! [V0a_2E0,V1a_27_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V1a_27_2E0)))
    <=> s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,V1a_27_2E0) ) ).

fof(thm_2Ebinary__ieee_2Enum2float__compare__ONTO,axiom,
    ! [V0a_2E0] :
    ? [V1r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,V1r_2E0)))
      & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_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_2EZERO_2E0)))))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare2num__ONTO,axiom,
    ! [V0r_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_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_2EZERO_2E0))))))))))
    <=> ? [V1a_2E0] : s(tyop_2Enum_2Enum,V0r_2E0) = s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V1a_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Enum2float__compare__thm,axiom,
    ( s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_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_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_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_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2Enum2float__compare_2E1(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_2EZERO_2E0))))))))) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare2num__thm,axiom,
    ( s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
    & s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_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_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_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)))))
    & s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_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_2EZERO_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__EQ__float__compare,axiom,
    ! [V0a_2E0,V1a_27_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,V1a_27_2E0)
    <=> s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebinary__ieee_2Efloat__compare2num_2E1(s(tyop_2Ebinary__ieee_2Efloat__compare,V1a_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__case__def,axiom,
    ! [A_27a] :
      ( ! [V0v0_2E0,V1v1_2E0,V2v2_2E0,V3v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0),s(A_27a,V0v0_2E0),s(A_27a,V1v1_2E0),s(A_27a,V2v2_2E0),s(A_27a,V3v3_2E0))) = s(A_27a,V0v0_2E0)
      & ! [V4v0_2E0,V5v1_2E0,V6v2_2E0,V7v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0),s(A_27a,V4v0_2E0),s(A_27a,V5v1_2E0),s(A_27a,V6v2_2E0),s(A_27a,V7v3_2E0))) = s(A_27a,V5v1_2E0)
      & ! [V8v0_2E0,V9v1_2E0,V10v2_2E0,V11v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0),s(A_27a,V8v0_2E0),s(A_27a,V9v1_2E0),s(A_27a,V10v2_2E0),s(A_27a,V11v3_2E0))) = s(A_27a,V10v2_2E0)
      & ! [V12v0_2E0,V13v1_2E0,V14v2_2E0,V15v3_2E0] : s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0),s(A_27a,V12v0_2E0),s(A_27a,V13v1_2E0),s(A_27a,V14v2_2E0),s(A_27a,V15v3_2E0))) = s(A_27a,V15v3_2E0) ) ).

fof(thm_2Ebinary__ieee_2Edatatype__float__compare,axiom,
    ! [V0float__compare_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool)))),V0float__compare_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0))),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__distinct,axiom,
    ( s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0) != s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0) != s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0) != s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0) != s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0) != s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)
    & s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0) != s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__nchotomy,axiom,
    ! [V0a_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0)
      | s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0)
      | s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)
      | s(tyop_2Ebinary__ieee_2Efloat__compare,V0a_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__Axiom,axiom,
    ! [A_27a,V0x0_2E0,V1x1_2E0,V2x2_2E0,V3x3_2E0] :
    ? [V4f_2E0] :
      ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0))) = s(A_27a,V0x0_2E0)
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0))) = s(A_27a,V1x1_2E0)
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0))) = s(A_27a,V2x2_2E0)
      & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,A_27a),V4f_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0))) = s(A_27a,V3x3_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__induction,axiom,
    ! [V0P_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0))))
        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)))) )
     => ! [V1a_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__compare,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebinary__ieee_2Efloat__compare,V1a_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__case__cong,axiom,
    ! [A_27a,V0v3_27_2E0,V1v2_27_2E0,V2v1_27_2E0,V3v0_27_2E0,V4M_2E0,V5M_27_2E0,V6v0_2E0,V7v1_2E0,V8v2_2E0,V9v3_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__compare,V4M_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,V5M_27_2E0)
        & ( s(tyop_2Ebinary__ieee_2Efloat__compare,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0)
         => s(A_27a,V6v0_2E0) = s(A_27a,V3v0_27_2E0) )
        & ( s(tyop_2Ebinary__ieee_2Efloat__compare,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0)
         => s(A_27a,V7v1_2E0) = s(A_27a,V2v1_27_2E0) )
        & ( s(tyop_2Ebinary__ieee_2Efloat__compare,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)
         => s(A_27a,V8v2_2E0) = s(A_27a,V1v2_27_2E0) )
        & ( s(tyop_2Ebinary__ieee_2Efloat__compare,V5M_27_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)
         => s(A_27a,V9v3_2E0) = s(A_27a,V0v3_27_2E0) ) )
     => s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,V4M_2E0),s(A_27a,V6v0_2E0),s(A_27a,V7v1_2E0),s(A_27a,V8v2_2E0),s(A_27a,V9v3_2E0))) = s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,V5M_27_2E0),s(A_27a,V3v0_27_2E0),s(A_27a,V2v1_27_2E0),s(A_27a,V1v2_27_2E0),s(A_27a,V0v3_27_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__compare__case__eq,axiom,
    ! [A_27a,V0x_2E0,V1v3_2E0,V2v2_2E0,V3v1_2E0,V4v0_2E0,V5v_2E0] :
      ( s(A_27a,c_2Ebinary__ieee_2Efloat__compare__CASE_2E5(s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0),s(A_27a,V4v0_2E0),s(A_27a,V3v1_2E0),s(A_27a,V2v2_2E0),s(A_27a,V1v3_2E0))) = s(A_27a,V5v_2E0)
    <=> ( ( s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2ELT_2E0)
          & s(A_27a,V4v0_2E0) = s(A_27a,V5v_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EEQ_2E0)
          & s(A_27a,V3v1_2E0) = s(A_27a,V5v_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EGT_2E0)
          & s(A_27a,V2v2_2E0) = s(A_27a,V5v_2E0) )
        | ( s(tyop_2Ebinary__ieee_2Efloat__compare,V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat__compare,c_2Ebinary__ieee_2EUN_2E0)
          & s(A_27a,V1v3_2E0) = s(A_27a,V5v_2E0) ) ) ) ).

fof(thm_2Ebinary__ieee_2Ezero__lt__twopow,axiom,
    ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_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,V0n_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Ezero__le__twopow,axiom,
    ! [V0n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_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,V0n_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Ezero__neq__twopow,axiom,
    ! [V0n_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,V0n_2E0))) != s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).

fof(thm_2Ebinary__ieee_2Ezero__le__pos__div__twopow,axiom,
    ! [V0m_2E0,V1n_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,V0m_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,V1n_2E0)))))))) ).

fof(thm_2Ebinary__ieee_2Ediv__eq0,axiom,
    ! [V0a_2E0,V1b_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,V1b_2E0))))
     => ( s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,V0a_2E0),s(tyop_2Erealax_2Ereal,V1b_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      <=> s(tyop_2Erealax_2Ereal,V0a_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Eexp__ge2,axiom,
    ! [V0b_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_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_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,V0b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(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,V0b_2E0))) ).

fof(thm_2Ebinary__ieee_2Eexp__gt2,axiom,
    ! [V0b_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_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_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,V0b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(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,V0b_2E0))) ).

fof(thm_2Ebinary__ieee_2Ele2,axiom,
    ! [V0n_2E0,V1m_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_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,V0n_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_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,V1m_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_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_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V0n_2E0),s(tyop_2Erealax_2Ereal,V1m_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__components,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27e,A_27f,A_27g,A_27h,A_27i,A_27j,A_27t,A_27w] :
      ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0)
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0)
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2Eword__T_2E0)
      & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2Eword__T_2E0)
      & ! [V0fp__op_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Eword__T_2E0)
      & ! [V1fp__op_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V1fp__op_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & ! [V2x_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),V2x_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__1comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27e,A_27f),V2x_2E0)))))
      & ! [V3x_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),V3x_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27g,A_27h),V3x_2E0)))
      & ! [V4x_2E0] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),V4x_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27i,A_27j),V4x_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__distinct,axiom,
    ! [A_27a,A_27b,A_27t,A_27w] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V0fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V0fp__op_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V1fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V1fp__op_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V2fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V2fp__op_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V3fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V3fp__op_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V4fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V4fp__op_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V5fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V5fp__op_2E0)))
      & ! [V6fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V6fp__op_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V7fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),V7fp__op_2E0)))
      & ! [V8x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V8x_2E0))) != s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V8x_2E0) ) ).

fof(thm_2Ebinary__ieee_2Efloat__values,axiom,
    ! [A_27a,A_27b,A_27t,A_27w] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0)
      & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EInfinity_2E0)
      & ! [V0fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
      & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))
      & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))
      & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0)))))))))))
      & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_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_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_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))))) ) ).

fof(thm_2Ebinary__ieee_2Ezero__to__real,axiom,
    ! [A_27t,A_27w] :
      ( s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
      & s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Esign__not__zero,axiom,
    ! [V0s_2E0] : 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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0))))) != s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ).

fof(thm_2Ebinary__ieee_2Efloat__sets,axiom,
    ! [A_27t,A_27w] :
      ( s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__zero_2E0) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))
      & s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__infinite_2E0) = s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Einfinity__properties,axiom,
    ! [A_27t,A_27w] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2Ezero__properties,axiom,
    ! [A_27t,A_27w] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2Esome__nan__properties,axiom,
    ! [A_27a,A_27b,V0fp__op_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__signalling_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V0fp__op_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2Emin__properties,axiom,
    ! [A_27t,A_27w] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      <=> ( s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_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))))) ) )
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__integral_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      <=> ( s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_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))))) ) )
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2Etop__properties,axiom,
    ! [A_27t,A_27w] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      <=> s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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))))) )
      & ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      <=> s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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))))) )
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2Ebottom__properties,axiom,
    ! [A_27t,A_27w] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      & ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      <=> s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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))))) )
      & ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
      <=> s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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))))) )
      & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__zero,axiom,
    ! [A_27a,A_27b,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__finite,axiom,
    ! [A_27a,A_27b,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
        | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
        | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__cases__finite,axiom,
    ! [A_27a,A_27b,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__distinct__finite,axiom,
    ! [A_27a,A_27b,V0x_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__cases,axiom,
    ! [A_27a,A_27b,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__distinct,axiom,
    ! [A_27a,A_27b,V0x_2E0] :
      ( ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) )
      & ~ ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0)))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__infinities,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
    <=> ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
        | s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__infinities__distinct,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ~ ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
        & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
    ! [A_27a,A_27b,V0x_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))) ).

fof(thm_2Ebinary__ieee_2Efloat__negate__negate,axiom,
    ! [A_27a,A_27b,V0x_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0) ).

fof(thm_2Ebinary__ieee_2Eulp,axiom,
    ! [A_27t,A_27w] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ).

fof(thm_2Ebinary__ieee_2Eneg__ulp,axiom,
    ! [A_27t,A_27w] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))) ).

fof(thm_2Ebinary__ieee_2EULP__le__mono,axiom,
    ! [A_27a,A_27t,V0e1_2E0,V1e2_2E0] :
      ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1e2_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
     => s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0e1_2E0),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1e2_2E0),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__ls_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V0e1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1e2_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eulp__lt__ULP,axiom,
    ! [A_27t,A_27w,V0e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V0e_2E0),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0)))))))) ).

fof(thm_2Ebinary__ieee_2Eulp__lt__largest,axiom,
    ! [A_27t,A_27w] : p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Eulp__lt__threshold,axiom,
    ! [A_27t,A_27w] : p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Eabs__float__value,axiom,
    ( ! [V0b_2E0,V1c_2E0,V2d_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0b_2E0))))),s(tyop_2Erealax_2Ereal,V1c_2E0))),s(tyop_2Erealax_2Ereal,V2d_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V1c_2E0),s(tyop_2Erealax_2Ereal,V2d_2E0)))))
    & ! [V3b_2E0,V4c_2E0] : s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3b_2E0))))),s(tyop_2Erealax_2Ereal,V4c_2E0))))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V4c_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eless__than__ulp,axiom,
    ! [A_27t,A_27w,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_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
    <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__is__zero__to__real,axiom,
    ! [A_27a,A_27b,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))))
    <=> s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V0x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__to__real__eq,axiom,
    ! [A_27t,A_27w,V0x_2E0,V1y_2E0] :
      ( s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0)))
    <=> ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0)
        | ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0)))) ) ) ) ).

fof(thm_2Ebinary__ieee_2Ediff__float__ULP,axiom,
    ! [A_27t,A_27w,V0x_2E0,V1y_2E0] :
      ( ( s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))) != s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0)))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eexponent__boundary_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1y_2E0)))))))))) ) ).

fof(thm_2Ebinary__ieee_2Ediff__lt__ulp__eq0,axiom,
    ! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2x_2E0] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eexponent__boundary_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),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_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_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,V2x_2E0),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2x_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2x_2E0))))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))) )
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0) ) ).

fof(thm_2Ebinary__ieee_2Ediff__lt__ulp__even,axiom,
    ! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2x_2E0] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eexponent__boundary_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))) )
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0) ) ).

fof(thm_2Ebinary__ieee_2Ediff__lt__ulp__even4,axiom,
    ! [A_27t,A_27w,V0a_2E0,V1b_2E0,V2x_2E0] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Eexponent__boundary_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))) )
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardZero,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0,V2r_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_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,V2r_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTiesToEven,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0,V2r_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
        & ( ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_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))))))) )
         => p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0)))))) )
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V2r_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & ( s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V2r_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0)))))
         => ~ p(s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__lsb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0)))))) )
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,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_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTiesToEven0,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0,V2r_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ebinary__ieee_2Efloat__Significand_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
        & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_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)))))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V1x_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V2r_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2EULP_2E1(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),c_2Epair_2E_2C_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ebinary__ieee_2Efloat__Exponent_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0))),s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))
        & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,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_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) )
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0y_2E0) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardZero__is__zero,axiom,
    ! [A_27t,A_27w,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_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
     => ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
        | s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTiesToEven__is__zero,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
     => ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
        | s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardZero__is__minus__zero,axiom,
    ! [A_27t,A_27w,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_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardZero__is__plus__zero,axiom,
    ! [A_27t,A_27w,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_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTiesToEven__is__minus__zero,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTiesToEven__is__plus__zero,axiom,
    ! [A_27t,A_27w,V0x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Eabs_2E1(s(tyop_2Erealax_2Ereal,V0x_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Erealax_2Ereal,V0x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Elargest__is__positive,axiom,
    ! [A_27t,A_27w] : p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Ethreshold__is__positive,axiom,
    ! [A_27t,A_27w] : p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Eround__roundTiesToEven__plus__infinity,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTiesToEven__minus__infinity,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ereal_2Ereal__lte_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardZero__top,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardZero__bottom,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardPositive__plus__infinity,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardPositive__bottom,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardNegative__top,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,V1x_2E0))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Eround__roundTowardNegative__minus__infinity,axiom,
    ! [A_27t,A_27w,V0y_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V1x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0),s(tyop_2Erealax_2Ereal,V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__roundTowardZero__top,axiom,
    ! [A_27t,A_27w,V0b_2E0,V1y_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__roundTowardZero__bottom,axiom,
    ! [A_27t,A_27w,V0b_2E0,V1y_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardZero_2E0),s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__roundTowardPositive__plus__infinity,axiom,
    ! [A_27t,A_27w,V0b_2E0,V1y_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0),s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__roundTowardPositive__bottom,axiom,
    ! [A_27t,A_27w,V0b_2E0,V1y_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardPositive_2E0),s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__roundTowardNegative__top,axiom,
    ! [A_27t,A_27w,V0b_2E0,V1y_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,V2x_2E0))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0),s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__roundTowardNegative__minus__infinity,axiom,
    ! [A_27t,A_27w,V0b_2E0,V1y_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V2x_2E0),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0),s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Erealax_2Ereal,V2x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__minus__zero,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2Efloat__minus__infinity,axiom,
    ! [A_27t,A_27w] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2Eword__T_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))) ).

fof(thm_2Ebinary__ieee_2Efloat__round__non__zero,axiom,
    ! [A_27a,A_27b,V0mode_2E0,V1toneg_2E0,V2r_2E0,V3s_2E0,V4e_2E0,V5f_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V4e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V5f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebool_2EARB_2E0)))))))
        & ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V4e_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
          | s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V5f_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) )
     => s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V4e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V5f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebool_2EARB_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__plus__infinity,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1toneg_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__minus__infinity,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1toneg_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__top,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1toneg_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__bottom,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1toneg_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Eround_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
     => s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,V1toneg_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__bottom_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__to__real,axiom,
    ! [A_27t,A_27w,F2_2E0,F0_2E0,F1_2E0] :
      ( ! [V0s_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
     => ( ! [V0s_2E0,V3r_2E0] : s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0))),s(tyop_2Erealax_2Ereal,V3r_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,V3r_2E0))),s(tyop_2Erealax_2Ereal,V3r_2E0)))
       => ( ! [V1e_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1e_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1e_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
         => ! [V0s_2E0,V1e_2E0,V2f_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2EARB_2E0))))))))) = s(tyop_2Erealax_2Ereal,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),F0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1e_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(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_2Ereal__of__num_2E1(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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2f_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(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_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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V1e_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27t),V2f_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))))))))) ) ) ) ).

fof(thm_2Ebinary__ieee_2Elargest,axiom,
    ! [A_27t,A_27w] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(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_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Ereal__sub_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_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_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))))))))) ).

fof(thm_2Ebinary__ieee_2Ethreshold,axiom,
    ! [A_27t,A_27w] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(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_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_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_2Ereal__sub_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_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_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_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_2Ewords_2Edimword_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0))))))))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(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_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))))))))) ).

fof(thm_2Ebinary__ieee_2Elargest__is__top,axiom,
    ! [A_27t,A_27w] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(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_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))))))
     => s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__top_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Elargest__lt__threshold,axiom,
    ! [A_27t,A_27w] : p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Elargest_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))) ).

fof(thm_2Ebinary__ieee_2Efloat__tests,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27e,A_27f,A_27g,A_27h,A_27i,A_27j,A_27k,A_27l,A_27m,A_27n] :
      ( ! [V0s_2E0,V1e_2E0,V2f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__nan_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V0s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V2f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27b,A_27a),c_2Ebool_2EARB_2E0))))))))))
        <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1e_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),V2f_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) )
      & ! [V3s_2E0,V4e_2E0,V5f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__signalling_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V3s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),V4e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),V5f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27d,A_27c),c_2Ebool_2EARB_2E0))))))))))
        <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),V4e_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2En2w_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)))))))))
            & ~ p(s(tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),V5f_2E0))))
            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),V5f_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) )
      & ! [V6s_2E0,V7e_2E0,V8f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__infinite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V6s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),V7e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),V8f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27f,A_27e),c_2Ebool_2EARB_2E0))))))))))
        <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),V7e_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27e),c_2Ewords_2En2w_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_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),V8f_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27f),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) )
      & ! [V9s_2E0,V10e_2E0,V11f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__normal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V9s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),V10e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27h),V11f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27h,A_27g),c_2Ebool_2EARB_2E0))))))))))
        <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),V10e_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),V10e_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27g),c_2Ewords_2En2w_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))))))))) ) )
      & ! [V12s_2E0,V13e_2E0,V14f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__subnormal_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V12s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),V13e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),V14f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27j,A_27i),c_2Ebool_2EARB_2E0))))))))))
        <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),V13e_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27i),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),V14f_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27j),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) )
      & ! [V15s_2E0,V16e_2E0,V17f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__zero_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V15s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),V16e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),V17f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27l,A_27k),c_2Ebool_2EARB_2E0))))))))))
        <=> ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),V16e_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27k),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
            & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),V17f_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27l),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) ) )
      & ! [V18s_2E0,V19e_2E0,V20f_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),c_2Ebinary__ieee_2Efloat__Sign__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),V18s_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),c_2Ebinary__ieee_2Efloat__Exponent__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),V19e_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),c_2Ebinary__ieee_2Efloat__Significand__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n)),c_2Ecombin_2EK_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27n),V20f_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27n,A_27m),c_2Ebool_2EARB_2E0))))))))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),V19e_2E0) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27m),c_2Ewords_2En2w_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))))))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__infinity__negate__abs,axiom,
    ! [A_27t,A_27w] :
      ( s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__abs_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__abs_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__round__to__integral__compute,axiom,
    ! [A_27a,A_27b,A_27t,A_27w] :
      ( ! [V0m_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round__to__integral_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0m_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V1m_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__round__to__integral_2E2(s(tyop_2Ebinary__ieee_2Erounding,V1m_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))
      & ! [V2m_2E0,V3fp__op_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__round__to__integral_2E2(s(tyop_2Ebinary__ieee_2Erounding,V2m_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V3fp__op_2E0))))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V3fp__op_2E0))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__compute,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27t,A_27w] :
      ( ! [V0mode_2E0,V1x_2E0,V2fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0)))))))
      & ! [V3mode_2E0,V4x_2E0,V5fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0)))))))))
      & ! [V6mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))
      & ! [V7mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V7mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V7mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))))
      & ! [V8mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V8mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))
      & ! [V9mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__nan,axiom,
    ! [A_27a,A_27b,V0mode_2E0,V1x_2E0,V2y_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
        | s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0) )
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__finite,axiom,
    ! [A_27a,A_27b,F2_2E0,F0_2E0,F1_2E0] :
      ( ! [V0mode_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))
        <=> s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
     => ( ! [V3r1_2E0,V4r2_2E0,V1x_2E0,V2y_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Erealax_2Ereal,V3r1_2E0))),s(tyop_2Erealax_2Ereal,V4r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))))
          <=> ( s(tyop_2Erealax_2Ereal,V3r1_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Erealax_2Ereal,V4r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) ) )
       => ( ! [V1x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
         => ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3r1_2E0,V4r2_2E0] :
              ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V3r1_2E0)))
                & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V4r2_2E0))) )
             => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Erealax_2Ereal,V3r1_2E0))),s(tyop_2Erealax_2Ereal,V4r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,V3r1_2E0),s(tyop_2Erealax_2Ereal,V4r2_2E0))))) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__finite__plus__infinity,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__plus__infinity__finite,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__finite__minus__infinity,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__add__minus__infinity__finite,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__add_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__compute,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27t,A_27w] :
      ( ! [V0mode_2E0,V1x_2E0,V2fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0)))))))
      & ! [V3mode_2E0,V4x_2E0,V5fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0)))))))))
      & ! [V6mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))))
      & ! [V7mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V7mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))
      & ! [V8mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V8mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V8mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))))
      & ! [V9mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__nan,axiom,
    ! [A_27a,A_27b,V0mode_2E0,V1x_2E0,V2y_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
        | s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0) )
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__finite,axiom,
    ! [A_27a,A_27b,F2_2E0,F0_2E0,F1_2E0] :
      ( ! [V0mode_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))
        <=> s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0) = s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTowardNegative_2E0) )
     => ( ! [V3r1_2E0,V4r2_2E0,V1x_2E0,V2y_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Erealax_2Ereal,V3r1_2E0))),s(tyop_2Erealax_2Ereal,V4r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))))
          <=> ( s(tyop_2Erealax_2Ereal,V3r1_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Erealax_2Ereal,V4r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
              & s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) ) )
       => ( ! [V1x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_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))))))) )
         => ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3r1_2E0,V4r2_2E0] :
              ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V3r1_2E0)))
                & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V4r2_2E0))) )
             => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Erealax_2Ereal,V3r1_2E0))),s(tyop_2Erealax_2Ereal,V4r2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V3r1_2E0),s(tyop_2Erealax_2Ereal,V4r2_2E0))))) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__finite__plus__infinity,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__plus__infinity__finite,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__finite__minus__infinity,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__sub__minus__infinity__finite,axiom,
    ! [A_27t,A_27w,V0mode_2E0,V1x_2E0,V2r_2E0] :
      ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__sub_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__compute,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27t,A_27w] :
      ( ! [V0mode_2E0,V1x_2E0,V2fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0)))))))
      & ! [V3mode_2E0,V4x_2E0,V5fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0)))))))))
      & ! [V6mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))
      & ! [V7mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V7mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))
      & ! [V8mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V8mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))
      & ! [V9mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__nan,axiom,
    ! [A_27a,A_27b,V0mode_2E0,V1x_2E0,V2y_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
        | s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0) )
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__finite,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V1x_2E0,V2y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) )
     => ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3r1_2E0,V4r2_2E0] :
          ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V3r1_2E0)))
            & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V4r2_2E0))) )
         => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))),s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,V3r1_2E0),s(tyop_2Erealax_2Ereal,V4r2_2E0))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__finite__plus__infinity,axiom,
    ! [A_27t,A_27w,F0_2E0,F1_2E0] :
      ( ! [V2r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V2r_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [V1x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
          <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
       => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
           => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__plus__infinity__finite,axiom,
    ! [A_27t,A_27w,F0_2E0,F1_2E0] :
      ( ! [V2r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V2r_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [V1x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
          <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
       => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
           => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__finite__minus__infinity,axiom,
    ! [A_27t,A_27w,F0_2E0,F1_2E0] :
      ( ! [V2r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V2r_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [V1x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
          <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
       => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
           => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__mul__minus__infinity__finite,axiom,
    ! [A_27t,A_27w,F0_2E0,F1_2E0] :
      ( ! [V2r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V2r_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [V1x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
          <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
       => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
            ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
           => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__compute,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27t,A_27w] :
      ( ! [V0mode_2E0,V1x_2E0,V2fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),V2fp__op_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0)))))))
      & ! [V3mode_2E0,V4x_2E0,V5fp__op_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d)),c_2Elist_2ENIL_2E0))))),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V3mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),V4x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27c,A_27d),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27c,A_27d),V5fp__op_2E0)))))))))
      & ! [V6mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V6mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))))
      & ! [V7mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V7mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V7mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))))
      & ! [V8mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V8mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V8mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0)))))))))
      & ! [V9mode_2E0] : s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V9mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__nan,axiom,
    ! [A_27a,A_27b,V0mode_2E0,V1x_2E0,V2y_2E0] :
      ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)
        | s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0) )
     => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))))))) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__finite,axiom,
    ! [A_27t,A_27w,F0_2E0,F2_2E0,F1_2E0] :
      ( ! [V4r2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V4r2_2E0))))
        <=> s(tyop_2Erealax_2Ereal,V4r2_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ( ! [F1_2E0,V1x_2E0,V2y_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
          <=> ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0)))) )
       => ( ! [V1x_2E0,V2y_2E0] :
              ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))
            <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) )
         => ! [V0mode_2E0,V1x_2E0,V2y_2E0,V3r1_2E0,V4r2_2E0] :
              ( ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V3r1_2E0)))
                & s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V4r2_2E0))) )
             => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V4r2_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Erealax_2Ereal,V3r1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Einvalidop__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27t,A_27w),c_2Ebinary__ieee_2EFP__Div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Edividezero__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__round__with__flags_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool)),F1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2y_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,V3r1_2E0),s(tyop_2Erealax_2Ereal,V4r2_2E0))))))) ) ) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__finite__plus__infinity,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
         => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__plus__infinity__finite,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
         => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__finite__minus__infinity,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
         => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__zero_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))) ) ) ).

fof(thm_2Ebinary__ieee_2Efloat__div__minus__infinity__finite,axiom,
    ! [A_27t,A_27w,F0_2E0] :
      ( ! [V1x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))))
        <=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) )
     => ! [V0mode_2E0,V1x_2E0,V2r_2E0] :
          ( s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2EFloat_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))
         => s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__div_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eclear__flags_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__minus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Ebinary__ieee_2Efloat__plus__infinity_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_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) ) ).

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