ITP001 Axioms: ITP136+5.ax
%------------------------------------------------------------------------------
% File : ITP136+5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : ieee+2.ax [Gau20]
% : HL4136+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 254 ( 110 unt; 0 def)
% Number of atoms : 762 ( 220 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 522 ( 14 ~; 18 |; 91 &)
% ( 45 <=>; 354 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 4 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 178 ( 178 usr; 142 con; 0-5 aty)
% Number of variables : 368 ( 358 !; 10 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(ne_ty_2Eieee_2Eccode,axiom,
ne(ty_2Eieee_2Eccode) ).
fof(ne_ty_2Eieee_2Efloat,axiom,
ne(ty_2Eieee_2Efloat) ).
fof(ne_ty_2Eieee_2Eroundmode,axiom,
ne(ty_2Eieee_2Eroundmode) ).
fof(mem_c_2Eieee_2EEq,axiom,
mem(c_2Eieee_2EEq,ty_2Eieee_2Eccode) ).
fof(mem_c_2Eieee_2EExponent,axiom,
mem(c_2Eieee_2EExponent,arr(ty_2Eieee_2Efloat,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2EFinite,axiom,
mem(c_2Eieee_2EFinite,arr(ty_2Eieee_2Efloat,bool)) ).
fof(mem_c_2Eieee_2EFloat,axiom,
mem(c_2Eieee_2EFloat,arr(ty_2Erealax_2Ereal,ty_2Eieee_2Efloat)) ).
fof(mem_c_2Eieee_2EFraction,axiom,
mem(c_2Eieee_2EFraction,arr(ty_2Eieee_2Efloat,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2EGt,axiom,
mem(c_2Eieee_2EGt,ty_2Eieee_2Eccode) ).
fof(mem_c_2Eieee_2EInfinity,axiom,
mem(c_2Eieee_2EInfinity,arr(ty_2Eieee_2Efloat,bool)) ).
fof(mem_c_2Eieee_2EIsdenormal,axiom,
mem(c_2Eieee_2EIsdenormal,arr(ty_2Eieee_2Efloat,bool)) ).
fof(mem_c_2Eieee_2EIsintegral,axiom,
mem(c_2Eieee_2EIsintegral,arr(ty_2Eieee_2Efloat,bool)) ).
fof(mem_c_2Eieee_2EIsnan,axiom,
mem(c_2Eieee_2EIsnan,arr(ty_2Eieee_2Efloat,bool)) ).
fof(mem_c_2Eieee_2EIsnormal,axiom,
mem(c_2Eieee_2EIsnormal,arr(ty_2Eieee_2Efloat,bool)) ).
fof(mem_c_2Eieee_2EIszero,axiom,
mem(c_2Eieee_2EIszero,arr(ty_2Eieee_2Efloat,bool)) ).
fof(mem_c_2Eieee_2ELt,axiom,
mem(c_2Eieee_2ELt,ty_2Eieee_2Eccode) ).
fof(mem_c_2Eieee_2EMinus__infinity,axiom,
mem(c_2Eieee_2EMinus__infinity,ty_2Eieee_2Efloat) ).
fof(mem_c_2Eieee_2EMinus__zero,axiom,
mem(c_2Eieee_2EMinus__zero,ty_2Eieee_2Efloat) ).
fof(mem_c_2Eieee_2EPlus__infinity,axiom,
mem(c_2Eieee_2EPlus__infinity,ty_2Eieee_2Efloat) ).
fof(mem_c_2Eieee_2EPlus__zero,axiom,
mem(c_2Eieee_2EPlus__zero,ty_2Eieee_2Efloat) ).
fof(mem_c_2Eieee_2EROUNDFLOAT,axiom,
mem(c_2Eieee_2EROUNDFLOAT,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat)) ).
fof(mem_c_2Eieee_2ESign,axiom,
mem(c_2Eieee_2ESign,arr(ty_2Eieee_2Efloat,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2ETo__nearest,axiom,
mem(c_2Eieee_2ETo__nearest,ty_2Eieee_2Eroundmode) ).
fof(mem_c_2Eieee_2ETo__ninfinity,axiom,
mem(c_2Eieee_2ETo__ninfinity,ty_2Eieee_2Eroundmode) ).
fof(mem_c_2Eieee_2ETo__pinfinity,axiom,
mem(c_2Eieee_2ETo__pinfinity,ty_2Eieee_2Eroundmode) ).
fof(mem_c_2Eieee_2EUlp,axiom,
mem(c_2Eieee_2EUlp,arr(ty_2Eieee_2Efloat,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Eieee_2EUn,axiom,
mem(c_2Eieee_2EUn,ty_2Eieee_2Eccode) ).
fof(mem_c_2Eieee_2EVal,axiom,
mem(c_2Eieee_2EVal,arr(ty_2Eieee_2Efloat,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Eieee_2Ebias,axiom,
mem(c_2Eieee_2Ebias,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Ebottomfloat,axiom,
mem(c_2Eieee_2Ebottomfloat,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Eccode2num,axiom,
mem(c_2Eieee_2Eccode2num,arr(ty_2Eieee_2Eccode,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Eccode__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eieee_2Eccode__CASE(A_27a),arr(ty_2Eieee_2Eccode,arr(A_27a,arr(A_27a,arr(A_27a,arr(A_27a,A_27a)))))) ) ).
fof(mem_c_2Eieee_2Eccode__size,axiom,
mem(c_2Eieee_2Eccode__size,arr(ty_2Eieee_2Eccode,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Eclosest,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eieee_2Eclosest(A_27a),arr(arr(A_27a,ty_2Erealax_2Ereal),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(ty_2Erealax_2Ereal,A_27a))))) ) ).
fof(mem_c_2Eieee_2Edefloat,axiom,
mem(c_2Eieee_2Edefloat,arr(ty_2Eieee_2Efloat,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Eemax,axiom,
mem(c_2Eieee_2Eemax,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Eencoding,axiom,
mem(c_2Eieee_2Eencoding,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum))) ).
fof(mem_c_2Eieee_2Eexponent,axiom,
mem(c_2Eieee_2Eexponent,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Eexpwidth,axiom,
mem(c_2Eieee_2Eexpwidth,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Efadd,axiom,
mem(c_2Eieee_2Efadd,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))))) ).
fof(mem_c_2Eieee_2Efcompare,axiom,
mem(c_2Eieee_2Efcompare,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Eieee_2Eccode)))) ).
fof(mem_c_2Eieee_2Efdiv,axiom,
mem(c_2Eieee_2Efdiv,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))))) ).
fof(mem_c_2Eieee_2Efeq,axiom,
mem(c_2Eieee_2Efeq,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool)))) ).
fof(mem_c_2Eieee_2Efge,axiom,
mem(c_2Eieee_2Efge,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool)))) ).
fof(mem_c_2Eieee_2Efgt,axiom,
mem(c_2Eieee_2Efgt,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool)))) ).
fof(mem_c_2Eieee_2Efintrnd,axiom,
mem(c_2Eieee_2Efintrnd,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))))) ).
fof(mem_c_2Eieee_2Efle,axiom,
mem(c_2Eieee_2Efle,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool)))) ).
fof(mem_c_2Eieee_2Efloat,axiom,
mem(c_2Eieee_2Efloat,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Eieee_2Efloat)) ).
fof(mem_c_2Eieee_2Efloat__To__zero,axiom,
mem(c_2Eieee_2Efloat__To__zero,ty_2Eieee_2Eroundmode) ).
fof(mem_c_2Eieee_2Efloat__abs,axiom,
mem(c_2Eieee_2Efloat__abs,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat)) ).
fof(mem_c_2Eieee_2Efloat__add,axiom,
mem(c_2Eieee_2Efloat__add,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat))) ).
fof(mem_c_2Eieee_2Efloat__div,axiom,
mem(c_2Eieee_2Efloat__div,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat))) ).
fof(mem_c_2Eieee_2Efloat__eq,axiom,
mem(c_2Eieee_2Efloat__eq,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,bool))) ).
fof(mem_c_2Eieee_2Efloat__format,axiom,
mem(c_2Eieee_2Efloat__format,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Efloat__ge,axiom,
mem(c_2Eieee_2Efloat__ge,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,bool))) ).
fof(mem_c_2Eieee_2Efloat__gt,axiom,
mem(c_2Eieee_2Efloat__gt,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,bool))) ).
fof(mem_c_2Eieee_2Efloat__le,axiom,
mem(c_2Eieee_2Efloat__le,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,bool))) ).
fof(mem_c_2Eieee_2Efloat__lt,axiom,
mem(c_2Eieee_2Efloat__lt,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,bool))) ).
fof(mem_c_2Eieee_2Efloat__mul,axiom,
mem(c_2Eieee_2Efloat__mul,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat))) ).
fof(mem_c_2Eieee_2Efloat__neg,axiom,
mem(c_2Eieee_2Efloat__neg,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat)) ).
fof(mem_c_2Eieee_2Efloat__rem,axiom,
mem(c_2Eieee_2Efloat__rem,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat))) ).
fof(mem_c_2Eieee_2Efloat__sqrt,axiom,
mem(c_2Eieee_2Efloat__sqrt,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat)) ).
fof(mem_c_2Eieee_2Efloat__sub,axiom,
mem(c_2Eieee_2Efloat__sub,arr(ty_2Eieee_2Efloat,arr(ty_2Eieee_2Efloat,ty_2Eieee_2Efloat))) ).
fof(mem_c_2Eieee_2Eflt,axiom,
mem(c_2Eieee_2Eflt,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool)))) ).
fof(mem_c_2Eieee_2Efmul,axiom,
mem(c_2Eieee_2Efmul,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))))) ).
fof(mem_c_2Eieee_2Efneg,axiom,
mem(c_2Eieee_2Efneg,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))))) ).
fof(mem_c_2Eieee_2Efraction,axiom,
mem(c_2Eieee_2Efraction,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Efracwidth,axiom,
mem(c_2Eieee_2Efracwidth,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Efrem,axiom,
mem(c_2Eieee_2Efrem,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))))) ).
fof(mem_c_2Eieee_2Efsqrt,axiom,
mem(c_2Eieee_2Efsqrt,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))))) ).
fof(mem_c_2Eieee_2Efsub,axiom,
mem(c_2Eieee_2Efsub,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))))) ).
fof(mem_c_2Eieee_2Eintround,axiom,
mem(c_2Eieee_2Eintround,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))))) ).
fof(mem_c_2Eieee_2Eis__closest,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eieee_2Eis__closest(A_27a),arr(arr(A_27a,ty_2Erealax_2Ereal),arr(arr(A_27a,bool),arr(ty_2Erealax_2Ereal,arr(A_27a,bool))))) ) ).
fof(mem_c_2Eieee_2Eis__denormal,axiom,
mem(c_2Eieee_2Eis__denormal,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Eis__double,axiom,
mem(c_2Eieee_2Eis__double,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ).
fof(mem_c_2Eieee_2Eis__double__extended,axiom,
mem(c_2Eieee_2Eis__double__extended,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ).
fof(mem_c_2Eieee_2Eis__finite,axiom,
mem(c_2Eieee_2Eis__finite,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Eis__infinity,axiom,
mem(c_2Eieee_2Eis__infinity,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Eis__integral,axiom,
mem(c_2Eieee_2Eis__integral,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Eis__nan,axiom,
mem(c_2Eieee_2Eis__nan,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Eis__normal,axiom,
mem(c_2Eieee_2Eis__normal,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Eis__single,axiom,
mem(c_2Eieee_2Eis__single,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ).
fof(mem_c_2Eieee_2Eis__single__extended,axiom,
mem(c_2Eieee_2Eis__single__extended,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ).
fof(mem_c_2Eieee_2Eis__valid,axiom,
mem(c_2Eieee_2Eis__valid,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Eis__zero,axiom,
mem(c_2Eieee_2Eis__zero,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))) ).
fof(mem_c_2Eieee_2Elargest,axiom,
mem(c_2Eieee_2Elargest,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Erealax_2Ereal)) ).
fof(mem_c_2Eieee_2Eminus,axiom,
mem(c_2Eieee_2Eminus,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))) ).
fof(mem_c_2Eieee_2Eminus__infinity,axiom,
mem(c_2Eieee_2Eminus__infinity,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Eminus__zero,axiom,
mem(c_2Eieee_2Eminus__zero,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Enum2ccode,axiom,
mem(c_2Eieee_2Enum2ccode,arr(ty_2Enum_2Enum,ty_2Eieee_2Eccode)) ).
fof(mem_c_2Eieee_2Enum2roundmode,axiom,
mem(c_2Eieee_2Enum2roundmode,arr(ty_2Enum_2Enum,ty_2Eieee_2Eroundmode)) ).
fof(mem_c_2Eieee_2Eplus__infinity,axiom,
mem(c_2Eieee_2Eplus__infinity,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Eplus__zero,axiom,
mem(c_2Eieee_2Eplus__zero,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Erem,axiom,
mem(c_2Eieee_2Erem,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ).
fof(mem_c_2Eieee_2Eround,axiom,
mem(c_2Eieee_2Eround,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Eieee_2Eroundmode,arr(ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))))) ).
fof(mem_c_2Eieee_2Eroundmode2num,axiom,
mem(c_2Eieee_2Eroundmode2num,arr(ty_2Eieee_2Eroundmode,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Eroundmode__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eieee_2Eroundmode__CASE(A_27a),arr(ty_2Eieee_2Eroundmode,arr(A_27a,arr(A_27a,arr(A_27a,arr(A_27a,A_27a)))))) ) ).
fof(mem_c_2Eieee_2Eroundmode__size,axiom,
mem(c_2Eieee_2Eroundmode__size,arr(ty_2Eieee_2Eroundmode,ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Esign,axiom,
mem(c_2Eieee_2Esign,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Esome__nan,axiom,
mem(c_2Eieee_2Esome__nan,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Ethreshold,axiom,
mem(c_2Eieee_2Ethreshold,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Erealax_2Ereal)) ).
fof(mem_c_2Eieee_2Etopfloat,axiom,
mem(c_2Eieee_2Etopfloat,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) ).
fof(mem_c_2Eieee_2Eulp,axiom,
mem(c_2Eieee_2Eulp,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))) ).
fof(mem_c_2Eieee_2Evalof,axiom,
mem(c_2Eieee_2Evalof,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))) ).
fof(mem_c_2Eieee_2Ewordlength,axiom,
mem(c_2Eieee_2Ewordlength,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ).
fof(mem_c_2Eieee_2Ezerosign,axiom,
mem(c_2Eieee_2Ezerosign,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Enum_2Enum,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))))) ).
fof(ax_thm_2Eieee_2Eexpwidth,axiom,
! [V0ew] :
( mem(V0ew,ty_2Enum_2Enum)
=> ! [V1fw] :
( mem(V1fw,ty_2Enum_2Enum)
=> ap(c_2Eieee_2Eexpwidth,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0ew),V1fw)) = V0ew ) ) ).
fof(ax_thm_2Eieee_2Efracwidth,axiom,
! [V0ew] :
( mem(V0ew,ty_2Enum_2Enum)
=> ! [V1fw] :
( mem(V1fw,ty_2Enum_2Enum)
=> ap(c_2Eieee_2Efracwidth,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0ew),V1fw)) = V1fw ) ) ).
fof(ax_thm_2Eieee_2Ewordlength,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Ewordlength,V0X) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Eieee_2Eexpwidth,V0X)),ap(c_2Eieee_2Efracwidth,V0X))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(ax_thm_2Eieee_2Eemax,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Eemax,V0X) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Eexpwidth,V0X))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(ax_thm_2Eieee_2Ebias,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Ebias,V0X) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Eexpwidth,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(ax_thm_2Eieee_2Eis__single,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(c_2Eieee_2Eis__single,V0X))
<=> ( ap(c_2Eieee_2Eexpwidth,V0X) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))
& ap(c_2Eieee_2Ewordlength,V0X) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__double,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(c_2Eieee_2Eis__double,V0X))
<=> ( ap(c_2Eieee_2Eexpwidth,V0X) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))
& ap(c_2Eieee_2Ewordlength,V0X) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__single__extended,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(c_2Eieee_2Eis__single__extended,V0X))
<=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Eieee_2Eexpwidth,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))
& p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Eieee_2Ewordlength,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__double__extended,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(c_2Eieee_2Eis__double__extended,V0X))
<=> ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Eieee_2Eexpwidth,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Eieee_2Ewordlength,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) ) ) ) ).
fof(ax_thm_2Eieee_2Esign,axiom,
! [V0s] :
( mem(V0s,ty_2Enum_2Enum)
=> ! [V1e] :
( mem(V1e,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,ty_2Enum_2Enum)
=> ap(c_2Eieee_2Esign,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1e),V2f))) = V0s ) ) ) ).
fof(ax_thm_2Eieee_2Eexponent,axiom,
! [V0s] :
( mem(V0s,ty_2Enum_2Enum)
=> ! [V1e] :
( mem(V1e,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,ty_2Enum_2Enum)
=> ap(c_2Eieee_2Eexponent,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1e),V2f))) = V1e ) ) ) ).
fof(ax_thm_2Eieee_2Efraction,axiom,
! [V0s] :
( mem(V0s,ty_2Enum_2Enum)
=> ! [V1e] :
( mem(V1e,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,ty_2Enum_2Enum)
=> ap(c_2Eieee_2Efraction,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1e),V2f))) = V2f ) ) ) ).
fof(ax_thm_2Eieee_2Eis__nan,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__nan,V0X),V1a))
<=> ( ap(c_2Eieee_2Eexponent,V1a) = ap(c_2Eieee_2Eemax,V0X)
& ap(c_2Eieee_2Efraction,V1a) != c_2Enum_2E0 ) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__infinity,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__infinity,V0X),V1a))
<=> ( ap(c_2Eieee_2Eexponent,V1a) = ap(c_2Eieee_2Eemax,V0X)
& ap(c_2Eieee_2Efraction,V1a) = c_2Enum_2E0 ) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__normal,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__normal,V0X),V1a))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Eieee_2Eexponent,V1a)))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Eexponent,V1a)),ap(c_2Eieee_2Eemax,V0X))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__denormal,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__denormal,V0X),V1a))
<=> ( ap(c_2Eieee_2Eexponent,V1a) = c_2Enum_2E0
& ap(c_2Eieee_2Efraction,V1a) != c_2Enum_2E0 ) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__zero,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__zero,V0X),V1a))
<=> ( ap(c_2Eieee_2Eexponent,V1a) = c_2Enum_2E0
& ap(c_2Eieee_2Efraction,V1a) = c_2Enum_2E0 ) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__valid,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1s] :
( mem(V1s,ty_2Enum_2Enum)
=> ! [V2e] :
( mem(V2e,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V1s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2e),V3f))))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1s),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2e),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Eexpwidth,V0X))))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3f),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Efracwidth,V0X)))) ) ) ) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__finite,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__finite,V0X),V1a))
<=> ( p(ap(ap(c_2Eieee_2Eis__valid,V0X),V1a))
& ( p(ap(ap(c_2Eieee_2Eis__normal,V0X),V1a))
| p(ap(ap(c_2Eieee_2Eis__denormal,V0X),V1a))
| p(ap(ap(c_2Eieee_2Eis__zero,V0X),V1a)) ) ) ) ) ) ).
fof(ax_thm_2Eieee_2Eplus__infinity,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Eplus__infinity,V0X) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Eieee_2Eemax,V0X)),c_2Enum_2E0)) ) ).
fof(ax_thm_2Eieee_2Eminus__infinity,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Eminus__infinity,V0X) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Eieee_2Eemax,V0X)),c_2Enum_2E0)) ) ).
fof(ax_thm_2Eieee_2Eplus__zero,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Eplus__zero,V0X) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)) ) ).
fof(ax_thm_2Eieee_2Eminus__zero,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Eminus__zero,V0X) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)) ) ).
fof(ax_thm_2Eieee_2Etopfloat,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Etopfloat,V0X) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Eemax,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Efracwidth,V0X))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(ax_thm_2Eieee_2Ebottomfloat,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Ebottomfloat,V0X) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Eemax,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Efracwidth,V0X))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ).
fof(ax_thm_2Eieee_2Eminus,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(c_2Eieee_2Eminus,V0X),V1a) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Esign,V1a))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Eieee_2Eexponent,V1a)),ap(c_2Eieee_2Efraction,V1a))) ) ) ).
fof(ax_thm_2Eieee_2Eencoding,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1s] :
( mem(V1s,ty_2Enum_2Enum)
=> ! [V2e] :
( mem(V2e,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,ty_2Enum_2Enum)
=> ap(ap(c_2Eieee_2Eencoding,V0X),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V1s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2e),V3f))) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1s),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Ewordlength,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Earithmetic_2E_2A,V2e),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Efracwidth,V0X))))),V3f) ) ) ) ) ).
fof(ax_thm_2Eieee_2Evalof,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1s] :
( mem(V1s,ty_2Enum_2Enum)
=> ! [V2e] :
( mem(V2e,ty_2Enum_2Enum)
=> ! [V3f] :
( mem(V3f,ty_2Enum_2Enum)
=> ap(ap(c_2Eieee_2Evalof,V0X),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V1s),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2e),V3f))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2e),c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1s)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,V3f)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Efracwidth,V0X))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V1s)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V2e)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X))))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,V3f)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Efracwidth,V0X)))))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Elargest,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Elargest,V0X) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Eemax,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X)))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Efracwidth,V0X))))) ) ).
fof(ax_thm_2Eieee_2Ethreshold,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Ethreshold,V0X) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Eemax,V0X)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X)))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,ap(c_2Eieee_2Efracwidth,V0X)))))) ) ).
fof(ax_thm_2Eieee_2Eulp,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(c_2Eieee_2Eulp,V0X),V1a) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Eieee_2Evalof,V0X),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Eieee_2Eexponent,V1a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Eieee_2Evalof,V0X),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Eieee_2Eexponent,V1a)),c_2Enum_2E0)))) ) ) ).
fof(ax_thm_2Eieee_2Eroundmode__TY__DEF,axiom,
? [V0rep] :
( mem(V0rep,arr(ty_2Eieee_2Eroundmode,ty_2Enum_2Enum))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Enum_2Enum,ty_2Eieee_2Eroundmode),f2948),V0rep)) ) ).
fof(ax_thm_2Eieee_2Eroundmode__BIJ,axiom,
( ! [V0a] :
( mem(V0a,ty_2Eieee_2Eroundmode)
=> ap(c_2Eieee_2Enum2roundmode,ap(c_2Eieee_2Eroundmode2num,V0a)) = V0a )
& ! [V1r] :
( mem(V1r,ty_2Enum_2Enum)
=> ( p(ap(f2949,V1r))
<=> ap(c_2Eieee_2Eroundmode2num,ap(c_2Eieee_2Enum2roundmode,V1r)) = V1r ) ) ) ).
fof(conj_thm_2Eieee_2Enum2roundmode__roundmode2num,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eroundmode)
=> ap(c_2Eieee_2Enum2roundmode,ap(c_2Eieee_2Eroundmode2num,V0a)) = V0a ) ).
fof(conj_thm_2Eieee_2Eroundmode2num__num2roundmode,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
<=> ap(c_2Eieee_2Eroundmode2num,ap(c_2Eieee_2Enum2roundmode,V0r)) = V0r ) ) ).
fof(conj_thm_2Eieee_2Enum2roundmode__11,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ! [V1r_27] :
( mem(V1r_27,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1r_27),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
=> ( ap(c_2Eieee_2Enum2roundmode,V0r) = ap(c_2Eieee_2Enum2roundmode,V1r_27)
<=> V0r = V1r_27 ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eroundmode2num__11,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eroundmode)
=> ! [V1a_27] :
( mem(V1a_27,ty_2Eieee_2Eroundmode)
=> ( ap(c_2Eieee_2Eroundmode2num,V0a) = ap(c_2Eieee_2Eroundmode2num,V1a_27)
<=> V0a = V1a_27 ) ) ) ).
fof(conj_thm_2Eieee_2Enum2roundmode__ONTO,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eroundmode)
=> ? [V1r] :
( mem(V1r,ty_2Enum_2Enum)
& V0a = ap(c_2Eieee_2Enum2roundmode,V1r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Eieee_2Eroundmode2num__ONTO,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
<=> ? [V1a] :
( mem(V1a,ty_2Eieee_2Eroundmode)
& V0r = ap(c_2Eieee_2Eroundmode2num,V1a) ) ) ) ).
fof(conj_thm_2Eieee_2Enum2roundmode__thm,axiom,
( ap(c_2Eieee_2Enum2roundmode,c_2Enum_2E0) = c_2Eieee_2ETo__nearest
& ap(c_2Eieee_2Enum2roundmode,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = c_2Eieee_2Efloat__To__zero
& ap(c_2Eieee_2Enum2roundmode,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Eieee_2ETo__pinfinity
& ap(c_2Eieee_2Enum2roundmode,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = c_2Eieee_2ETo__ninfinity ) ).
fof(conj_thm_2Eieee_2Eroundmode2num__thm,axiom,
( ap(c_2Eieee_2Eroundmode2num,c_2Eieee_2ETo__nearest) = c_2Enum_2E0
& ap(c_2Eieee_2Eroundmode2num,c_2Eieee_2Efloat__To__zero) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& ap(c_2Eieee_2Eroundmode2num,c_2Eieee_2ETo__pinfinity) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))
& ap(c_2Eieee_2Eroundmode2num,c_2Eieee_2ETo__ninfinity) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Eieee_2Eroundmode__EQ__roundmode,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eroundmode)
=> ! [V1a_27] :
( mem(V1a_27,ty_2Eieee_2Eroundmode)
=> ( V0a = V1a_27
<=> ap(c_2Eieee_2Eroundmode2num,V0a) = ap(c_2Eieee_2Eroundmode2num,V1a_27) ) ) ) ).
fof(ax_thm_2Eieee_2Eroundmode__size__def,axiom,
! [V0x] :
( mem(V0x,ty_2Eieee_2Eroundmode)
=> ap(c_2Eieee_2Eroundmode__size,V0x) = c_2Enum_2E0 ) ).
fof(ax_thm_2Eieee_2Eroundmode__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Eieee_2Eroundmode)
=> ! [V1v0] :
( mem(V1v0,A_27a)
=> ! [V2v1] :
( mem(V2v1,A_27a)
=> ! [V3v2] :
( mem(V3v2,A_27a)
=> ! [V4v3] :
( mem(V4v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),V0x),V1v0),V2v1),V3v2),V4v3) = ap(f2950(A_27a,V2v1,V3v2,V4v3,V1v0),ap(c_2Eieee_2Eroundmode2num,V0x)) ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eroundmode__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0v0] :
( mem(V0v0,A_27a)
=> ! [V1v1] :
( mem(V1v1,A_27a)
=> ! [V2v2] :
( mem(V2v2,A_27a)
=> ! [V3v3] :
( mem(V3v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),c_2Eieee_2ETo__nearest),V0v0),V1v1),V2v2),V3v3) = V0v0 ) ) ) )
& ! [V4v0] :
( mem(V4v0,A_27a)
=> ! [V5v1] :
( mem(V5v1,A_27a)
=> ! [V6v2] :
( mem(V6v2,A_27a)
=> ! [V7v3] :
( mem(V7v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),c_2Eieee_2Efloat__To__zero),V4v0),V5v1),V6v2),V7v3) = V5v1 ) ) ) )
& ! [V8v0] :
( mem(V8v0,A_27a)
=> ! [V9v1] :
( mem(V9v1,A_27a)
=> ! [V10v2] :
( mem(V10v2,A_27a)
=> ! [V11v3] :
( mem(V11v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),c_2Eieee_2ETo__pinfinity),V8v0),V9v1),V10v2),V11v3) = V10v2 ) ) ) )
& ! [V12v0] :
( mem(V12v0,A_27a)
=> ! [V13v1] :
( mem(V13v1,A_27a)
=> ! [V14v2] :
( mem(V14v2,A_27a)
=> ! [V15v3] :
( mem(V15v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),c_2Eieee_2ETo__ninfinity),V12v0),V13v1),V14v2),V15v3) = V15v3 ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Edatatype__roundmode,axiom,
! [V0roundmode] :
( mem(V0roundmode,arr(ty_2Eieee_2Eroundmode,arr(ty_2Eieee_2Eroundmode,arr(ty_2Eieee_2Eroundmode,arr(ty_2Eieee_2Eroundmode,bool)))))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(V0roundmode,c_2Eieee_2ETo__nearest),c_2Eieee_2Efloat__To__zero),c_2Eieee_2ETo__pinfinity),c_2Eieee_2ETo__ninfinity))) ) ).
fof(conj_thm_2Eieee_2Eroundmode__distinct,axiom,
( c_2Eieee_2ETo__nearest != c_2Eieee_2Efloat__To__zero
& c_2Eieee_2ETo__nearest != c_2Eieee_2ETo__pinfinity
& c_2Eieee_2ETo__nearest != c_2Eieee_2ETo__ninfinity
& c_2Eieee_2Efloat__To__zero != c_2Eieee_2ETo__pinfinity
& c_2Eieee_2Efloat__To__zero != c_2Eieee_2ETo__ninfinity
& c_2Eieee_2ETo__pinfinity != c_2Eieee_2ETo__ninfinity ) ).
fof(conj_thm_2Eieee_2Eroundmode__nchotomy,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eroundmode)
=> ( V0a = c_2Eieee_2ETo__nearest
| V0a = c_2Eieee_2Efloat__To__zero
| V0a = c_2Eieee_2ETo__pinfinity
| V0a = c_2Eieee_2ETo__ninfinity ) ) ).
fof(conj_thm_2Eieee_2Eroundmode__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x0] :
( mem(V0x0,A_27a)
=> ! [V1x1] :
( mem(V1x1,A_27a)
=> ! [V2x2] :
( mem(V2x2,A_27a)
=> ! [V3x3] :
( mem(V3x3,A_27a)
=> ? [V4f] :
( mem(V4f,arr(ty_2Eieee_2Eroundmode,A_27a))
& ap(V4f,c_2Eieee_2ETo__nearest) = V0x0
& ap(V4f,c_2Eieee_2Efloat__To__zero) = V1x1
& ap(V4f,c_2Eieee_2ETo__pinfinity) = V2x2
& ap(V4f,c_2Eieee_2ETo__ninfinity) = V3x3 ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eroundmode__induction,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Eieee_2Eroundmode,bool))
=> ( ( p(ap(V0P,c_2Eieee_2ETo__nearest))
& p(ap(V0P,c_2Eieee_2ETo__ninfinity))
& p(ap(V0P,c_2Eieee_2ETo__pinfinity))
& p(ap(V0P,c_2Eieee_2Efloat__To__zero)) )
=> ! [V1a] :
( mem(V1a,ty_2Eieee_2Eroundmode)
=> p(ap(V0P,V1a)) ) ) ) ).
fof(conj_thm_2Eieee_2Eroundmode__case__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v0_27] :
( mem(V0v0_27,A_27a)
=> ! [V1v1_27] :
( mem(V1v1_27,A_27a)
=> ! [V2v2_27] :
( mem(V2v2_27,A_27a)
=> ! [V3v3_27] :
( mem(V3v3_27,A_27a)
=> ! [V4M] :
( mem(V4M,ty_2Eieee_2Eroundmode)
=> ! [V5M_27] :
( mem(V5M_27,ty_2Eieee_2Eroundmode)
=> ! [V6v0] :
( mem(V6v0,A_27a)
=> ! [V7v1] :
( mem(V7v1,A_27a)
=> ! [V8v2] :
( mem(V8v2,A_27a)
=> ! [V9v3] :
( mem(V9v3,A_27a)
=> ( ( V4M = V5M_27
& ( V5M_27 = c_2Eieee_2ETo__nearest
=> V6v0 = V0v0_27 )
& ( V5M_27 = c_2Eieee_2Efloat__To__zero
=> V7v1 = V1v1_27 )
& ( V5M_27 = c_2Eieee_2ETo__pinfinity
=> V8v2 = V2v2_27 )
& ( V5M_27 = c_2Eieee_2ETo__ninfinity
=> V9v3 = V3v3_27 ) )
=> ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),V4M),V6v0),V7v1),V8v2),V9v3) = ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),V5M_27),V0v0_27),V1v1_27),V2v2_27),V3v3_27) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eroundmode__case__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Eieee_2Eroundmode)
=> ! [V1v0] :
( mem(V1v0,A_27a)
=> ! [V2v1] :
( mem(V2v1,A_27a)
=> ! [V3v2] :
( mem(V3v2,A_27a)
=> ! [V4v3] :
( mem(V4v3,A_27a)
=> ! [V5v] :
( mem(V5v,A_27a)
=> ( ap(ap(ap(ap(ap(c_2Eieee_2Eroundmode__CASE(A_27a),V0x),V1v0),V2v1),V3v2),V4v3) = V5v
<=> ( ( V0x = c_2Eieee_2ETo__nearest
& V1v0 = V5v )
| ( V0x = c_2Eieee_2Efloat__To__zero
& V2v1 = V5v )
| ( V0x = c_2Eieee_2ETo__pinfinity
& V3v2 = V5v )
| ( V0x = c_2Eieee_2ETo__ninfinity
& V4v3 = V5v ) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__closest,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,arr(A_27a,ty_2Erealax_2Ereal))
=> ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ! [V3a] :
( mem(V3a,A_27a)
=> ( p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(A_27a),V0v),V1s),V2x),V3a))
<=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3a),V1s))
& ! [V4b] :
( mem(V4b,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4b),V1s))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(V0v,V3a)),V2x))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(V0v,V4b)),V2x)))) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f3062,axiom,
! [A_27a,V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ! [V0v] :
( mem(V0v,arr(A_27a,ty_2Erealax_2Ereal))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ! [V1p] :
( mem(V1p,arr(A_27a,bool))
=> ! [V5b] : ap(f3062(A_27a,V3x,V0v,V2s,V1p),V5b) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(ap(ap(c_2Eieee_2Eis__closest(A_27a),V0v),V2s),V3x),V5b)),ap(V1p,V5b)) ) ) ) ) ).
fof(lameq_f3063,axiom,
! [A_27a,V1p] :
( mem(V1p,arr(A_27a,bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ! [V0v] :
( mem(V0v,arr(A_27a,ty_2Erealax_2Ereal))
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ! [V4a] : ap(f3063(A_27a,V1p,V2s,V0v,V3x),V4a) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(ap(ap(c_2Eieee_2Eis__closest(A_27a),V0v),V2s),V3x),V4a)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_3F(A_27a),f3062(A_27a,V3x,V0v,V2s,V1p))),ap(V1p,V4a))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Eclosest,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v] :
( mem(V0v,arr(A_27a,ty_2Erealax_2Ereal))
=> ! [V1p] :
( mem(V1p,arr(A_27a,bool))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ap(ap(ap(ap(c_2Eieee_2Eclosest(A_27a),V0v),V1p),V2s),V3x) = ap(c_2Emin_2E_40(A_27a),f3063(A_27a,V1p,V2s,V0v,V3x)) ) ) ) ) ) ).
fof(lameq_f3064,axiom,
! [V2a] : ap(f3064,V2a) = ap(c_2Earithmetic_2EEVEN,ap(c_2Eieee_2Efraction,V2a)) ).
fof(lameq_f3065,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V3a] : ap(f3065(V0X),V3a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V3a),ap(ap(c_2Eieee_2Eis__finite,V0X),V3a)) ) ).
fof(lameq_f3066,axiom,
! [V4X] :
( mem(V4X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V5x] :
( mem(V5x,ty_2Erealax_2Ereal)
=> ! [V7a] : ap(f3066(V4X,V5x),V7a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V7a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__finite,V4X),V7a)),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Eieee_2Evalof,V4X),V7a))),ap(c_2Ereal_2Eabs,V5x)))) ) ) ).
fof(lameq_f3067,axiom,
! [V8X] :
( mem(V8X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V9x] :
( mem(V9x,ty_2Erealax_2Ereal)
=> ! [V11a] : ap(f3067(V8X,V9x),V11a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V11a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__finite,V8X),V11a)),ap(ap(c_2Ereal_2Ereal__ge,ap(ap(c_2Eieee_2Evalof,V8X),V11a)),V9x))) ) ) ).
fof(lameq_f3068,axiom,
! [V12X] :
( mem(V12X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V13x] :
( mem(V13x,ty_2Erealax_2Ereal)
=> ! [V15a] : ap(f3068(V12X,V13x),V15a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V15a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__finite,V12X),V15a)),ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Eieee_2Evalof,V12X),V15a)),V13x))) ) ) ).
fof(ax_thm_2Eieee_2Eround__def,axiom,
( ! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eround,V0X),c_2Eieee_2ETo__nearest),V1x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__lte,V1x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Ethreshold,V0X)))),ap(c_2Eieee_2Eminus__infinity,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__ge,V1x),ap(c_2Eieee_2Ethreshold,V0X))),ap(c_2Eieee_2Eplus__infinity,V0X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V0X)),f3064),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3065(V0X))),V1x))) ) )
& ! [V4X] :
( mem(V4X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V5x] :
( mem(V5x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eround,V4X),c_2Eieee_2Efloat__To__zero),V5x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Erealax_2Ereal__lt,V5x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Elargest,V4X)))),ap(c_2Eieee_2Ebottomfloat,V4X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__gt,V5x),ap(c_2Eieee_2Elargest,V4X))),ap(c_2Eieee_2Etopfloat,V4X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V4X)),k(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Ebool_2ET)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3066(V4X,V5x))),V5x))) ) )
& ! [V8X] :
( mem(V8X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V9x] :
( mem(V9x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eround,V8X),c_2Eieee_2ETo__pinfinity),V9x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Erealax_2Ereal__lt,V9x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Elargest,V8X)))),ap(c_2Eieee_2Ebottomfloat,V8X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__gt,V9x),ap(c_2Eieee_2Elargest,V8X))),ap(c_2Eieee_2Eplus__infinity,V8X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V8X)),k(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Ebool_2ET)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3067(V8X,V9x))),V9x))) ) )
& ! [V12X] :
( mem(V12X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V13x] :
( mem(V13x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eround,V12X),c_2Eieee_2ETo__ninfinity),V13x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Erealax_2Ereal__lt,V13x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Elargest,V12X)))),ap(c_2Eieee_2Eminus__infinity,V12X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__gt,V13x),ap(c_2Eieee_2Elargest,V12X))),ap(c_2Eieee_2Etopfloat,V12X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V12X)),k(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Ebool_2ET)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3068(V12X,V13x))),V13x))) ) ) ) ).
fof(ax_thm_2Eieee_2Eis__integral,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__integral,V0X),V1a))
<=> ( p(ap(ap(c_2Eieee_2Eis__finite,V0X),V1a))
& ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& ap(c_2Ereal_2Eabs,ap(ap(c_2Eieee_2Evalof,V0X),V1a)) = ap(c_2Ereal_2Ereal__of__num,V2n) ) ) ) ) ) ).
fof(lameq_f3069,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V3n] : ap(f3069(V0X,V2a),V3n) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Earithmetic_2EEVEN,V3n)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Ereal_2Eabs,ap(ap(c_2Eieee_2Evalof,V0X),V2a))),ap(c_2Ereal_2Ereal__of__num,V3n))) ) ) ).
fof(lameq_f3070,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V2a] : ap(f3070(V0X),V2a) = ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f3069(V0X,V2a)) ) ).
fof(lameq_f3071,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V4a] : ap(f3071(V0X),V4a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V4a),ap(ap(c_2Eieee_2Eis__integral,V0X),V4a)) ) ).
fof(lameq_f3072,axiom,
! [V5X] :
( mem(V5X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V6x] :
( mem(V6x,ty_2Erealax_2Ereal)
=> ! [V8a] : ap(f3072(V5X,V6x),V8a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V8a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__integral,V5X),V8a)),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Eieee_2Evalof,V5X),V8a))),ap(c_2Ereal_2Eabs,V6x)))) ) ) ).
fof(lameq_f3073,axiom,
! [V9X] :
( mem(V9X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V10x] :
( mem(V10x,ty_2Erealax_2Ereal)
=> ! [V12a] : ap(f3073(V9X,V10x),V12a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V12a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__integral,V9X),V12a)),ap(ap(c_2Ereal_2Ereal__ge,ap(ap(c_2Eieee_2Evalof,V9X),V12a)),V10x))) ) ) ).
fof(lameq_f3074,axiom,
! [V13X] :
( mem(V13X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V14x] :
( mem(V14x,ty_2Erealax_2Ereal)
=> ! [V16a] : ap(f3074(V13X,V14x),V16a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V16a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__integral,V13X),V16a)),ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Eieee_2Evalof,V13X),V16a)),V14x))) ) ) ).
fof(ax_thm_2Eieee_2Eintround__def,axiom,
( ! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eintround,V0X),c_2Eieee_2ETo__nearest),V1x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__lte,V1x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Ethreshold,V0X)))),ap(c_2Eieee_2Eminus__infinity,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__ge,V1x),ap(c_2Eieee_2Ethreshold,V0X))),ap(c_2Eieee_2Eplus__infinity,V0X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V0X)),f3070(V0X)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3071(V0X))),V1x))) ) )
& ! [V5X] :
( mem(V5X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V6x] :
( mem(V6x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eintround,V5X),c_2Eieee_2Efloat__To__zero),V6x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Erealax_2Ereal__lt,V6x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Elargest,V5X)))),ap(c_2Eieee_2Ebottomfloat,V5X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__gt,V6x),ap(c_2Eieee_2Elargest,V5X))),ap(c_2Eieee_2Etopfloat,V5X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V5X)),k(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Ebool_2ET)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3072(V5X,V6x))),V6x))) ) )
& ! [V9X] :
( mem(V9X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V10x] :
( mem(V10x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eintround,V9X),c_2Eieee_2ETo__pinfinity),V10x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Erealax_2Ereal__lt,V10x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Elargest,V9X)))),ap(c_2Eieee_2Ebottomfloat,V9X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__gt,V10x),ap(c_2Eieee_2Elargest,V9X))),ap(c_2Eieee_2Eplus__infinity,V9X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V9X)),k(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Ebool_2ET)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3073(V9X,V10x))),V10x))) ) )
& ! [V13X] :
( mem(V13X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V14x] :
( mem(V14x,ty_2Erealax_2Ereal)
=> ap(ap(ap(c_2Eieee_2Eintround,V13X),c_2Eieee_2ETo__ninfinity),V14x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Erealax_2Ereal__lt,V14x),ap(c_2Erealax_2Ereal__neg,ap(c_2Eieee_2Elargest,V13X)))),ap(c_2Eieee_2Eminus__infinity,V13X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ereal_2Ereal__gt,V14x),ap(c_2Eieee_2Elargest,V13X))),ap(c_2Eieee_2Etopfloat,V13X)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Eieee_2Evalof,V13X)),k(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Ebool_2ET)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3074(V13X,V14x))),V14x))) ) ) ) ).
fof(lameq_f3075,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] : ap(f3075(V0X),V1a) = ap(ap(c_2Eieee_2Eis__nan,V0X),V1a) ) ).
fof(ax_thm_2Eieee_2Esome__nan,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Eieee_2Esome__nan,V0X) = ap(c_2Emin_2E_40(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3075(V0X)) ) ).
fof(ax_thm_2Eieee_2Ezerosign,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1s] :
( mem(V1s,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(c_2Eieee_2Ezerosign,V0X),V1s),V2a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__zero,V0X),V2a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1s),c_2Enum_2E0)),ap(c_2Eieee_2Eplus__zero,V0X)),ap(c_2Eieee_2Eminus__zero,V0X))),V2a) ) ) ) ).
fof(lameq_f3076,axiom,
! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V2n] : ap(f3076(V1y,V0x),V2n) = ap(ap(c_2Ereal_2Ereal__sub,V0x),ap(ap(c_2Erealax_2Ereal__mul,V2n),V1y)) ) ) ).
fof(lameq_f3077,axiom,
! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ! [V4n] : ap(f3077(V3x),V4n) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Earithmetic_2EEVEN,V4n)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Ereal_2Eabs,V3x)),ap(c_2Ereal_2Ereal__of__num,V4n))) ) ).
fof(lameq_f3078,axiom,
! [V3x] : ap(f3078,V3x) = ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f3077(V3x)) ).
fof(lameq_f3079,axiom,
! [V5x] :
( mem(V5x,ty_2Erealax_2Ereal)
=> ! [V6n] : ap(f3079(V5x),V6n) = ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Ereal_2Eabs,V5x)),ap(c_2Ereal_2Ereal__of__num,V6n)) ) ).
fof(lameq_f3080,axiom,
! [V5x] : ap(f3080,V5x) = ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,bool),V5x),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f3079(V5x))) ).
fof(ax_thm_2Eieee_2Erem,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1y] :
( mem(V1y,ty_2Erealax_2Ereal)
=> ap(ap(c_2Eieee_2Erem,V0x),V1y) = ap(ap(c_2Ebool_2ELET(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),f3076(V1y,V0x)),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Erealax_2Ereal),c_2Ecombin_2EI(ty_2Erealax_2Ereal)),f3078),ap(c_2Epred__set_2EGSPEC(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),f3080)),ap(ap(c_2Ereal_2E_2F,V0x),V1y))) ) ) ).
fof(ax_thm_2Eieee_2Efintrnd,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(c_2Eieee_2Efintrnd,V0X),V1m),V2a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__nan,V0X),V2a)),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),V2a),ap(ap(ap(c_2Eieee_2Ezerosign,V0X),ap(c_2Eieee_2Esign,V2a)),ap(ap(ap(c_2Eieee_2Eintround,V0X),V1m),ap(ap(c_2Eieee_2Evalof,V0X),V2a))))) ) ) ) ).
fof(ax_thm_2Eieee_2Efadd,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V3b] :
( mem(V3b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(ap(c_2Eieee_2Efadd,V0X),V1m),V2a),V3b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V2a)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V3b)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b)))))))),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),V2a),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b)),V3b),ap(ap(ap(c_2Eieee_2Ezerosign,V0X),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__zero,V0X),V2a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__zero,V0X),V3b)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b))))),ap(c_2Eieee_2Esign,V2a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Eieee_2Eroundmode),V1m),c_2Eieee_2ETo__ninfinity)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0))),ap(ap(ap(c_2Eieee_2Eround,V0X),V1m),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Eieee_2Evalof,V0X),V2a)),ap(ap(c_2Eieee_2Evalof,V0X),V3b))))))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efsub,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V3b] :
( mem(V3b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(ap(c_2Eieee_2Efsub,V0X),V1m),V2a),V3b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V2a)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V3b)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b))))))),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),V2a),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b)),ap(ap(c_2Eieee_2Eminus,V0X),V3b)),ap(ap(ap(c_2Eieee_2Ezerosign,V0X),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__zero,V0X),V2a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__zero,V0X),V3b)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b)))))),ap(c_2Eieee_2Esign,V2a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Eieee_2Eroundmode),V1m),c_2Eieee_2ETo__ninfinity)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0))),ap(ap(ap(c_2Eieee_2Eround,V0X),V1m),ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Eieee_2Evalof,V0X),V2a)),ap(ap(c_2Eieee_2Evalof,V0X),V3b))))))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efmul,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V3b] :
( mem(V3b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(ap(c_2Eieee_2Efmul,V0X),V1m),V2a),V3b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V2a)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V3b)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__zero,V0X),V2a)),ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Eieee_2Eis__zero,V0X),V3b)))))),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b))),ap(c_2Eieee_2Eplus__infinity,V0X)),ap(c_2Eieee_2Eminus__infinity,V0X))),ap(ap(ap(c_2Eieee_2Ezerosign,V0X),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b))),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(ap(c_2Eieee_2Eround,V0X),V1m),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Eieee_2Evalof,V0X),V2a)),ap(ap(c_2Eieee_2Evalof,V0X),V3b)))))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efdiv,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V3b] :
( mem(V3b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(ap(c_2Eieee_2Efdiv,V0X),V1m),V2a),V3b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V2a)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V3b)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__zero,V0X),V2a)),ap(ap(c_2Eieee_2Eis__zero,V0X),V3b))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b)))))),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Eieee_2Eis__zero,V0X),V3b))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b))),ap(c_2Eieee_2Eplus__infinity,V0X)),ap(c_2Eieee_2Eminus__infinity,V0X))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b))),ap(c_2Eieee_2Eplus__zero,V0X)),ap(c_2Eieee_2Eminus__zero,V0X))),ap(ap(ap(c_2Eieee_2Ezerosign,V0X),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Eieee_2Esign,V3b))),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(ap(c_2Eieee_2Eround,V0X),V1m),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Eieee_2Evalof,V0X),V2a)),ap(ap(c_2Eieee_2Evalof,V0X),V3b))))))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efsqrt,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(c_2Eieee_2Efsqrt,V0X),V1m),V2a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__nan,V0X),V2a)),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__zero,V0X),V2a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),c_2Enum_2E0)))),V2a),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Eieee_2Ezerosign,V0X),ap(c_2Eieee_2Esign,V2a)),ap(ap(ap(c_2Eieee_2Eround,V0X),V1m),ap(c_2Etransc_2Esqrt,ap(ap(c_2Eieee_2Evalof,V0X),V2a))))))) ) ) ) ).
fof(ax_thm_2Eieee_2Efrem,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V3b] :
( mem(V3b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(ap(c_2Eieee_2Efrem,V0X),V1m),V2a),V3b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V2a)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V3b)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2a)),ap(ap(c_2Eieee_2Eis__zero,V0X),V3b))))),ap(c_2Eieee_2Esome__nan,V0X)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(c_2Eieee_2Eis__infinity,V0X),V3b)),V2a),ap(ap(ap(c_2Eieee_2Ezerosign,V0X),ap(c_2Eieee_2Esign,V2a)),ap(ap(ap(c_2Eieee_2Eround,V0X),V1m),ap(ap(c_2Eieee_2Erem,ap(ap(c_2Eieee_2Evalof,V0X),V2a)),ap(ap(c_2Eieee_2Evalof,V0X),V3b)))))) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efneg,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1m] :
( mem(V1m,ty_2Eieee_2Eroundmode)
=> ! [V2a] :
( mem(V2a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(c_2Eieee_2Efneg,V0X),V1m),V2a) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Esign,V2a))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Eieee_2Eexponent,V2a)),ap(c_2Eieee_2Efraction,V2a))) ) ) ) ).
fof(ax_thm_2Eieee_2Eccode__TY__DEF,axiom,
? [V0rep] :
( mem(V0rep,arr(ty_2Eieee_2Eccode,ty_2Enum_2Enum))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Enum_2Enum,ty_2Eieee_2Eccode),f2948),V0rep)) ) ).
fof(ax_thm_2Eieee_2Eccode__BIJ,axiom,
( ! [V0a] :
( mem(V0a,ty_2Eieee_2Eccode)
=> ap(c_2Eieee_2Enum2ccode,ap(c_2Eieee_2Eccode2num,V0a)) = V0a )
& ! [V1r] :
( mem(V1r,ty_2Enum_2Enum)
=> ( p(ap(f2949,V1r))
<=> ap(c_2Eieee_2Eccode2num,ap(c_2Eieee_2Enum2ccode,V1r)) = V1r ) ) ) ).
fof(conj_thm_2Eieee_2Enum2ccode__ccode2num,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eccode)
=> ap(c_2Eieee_2Enum2ccode,ap(c_2Eieee_2Eccode2num,V0a)) = V0a ) ).
fof(conj_thm_2Eieee_2Eccode2num__num2ccode,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
<=> ap(c_2Eieee_2Eccode2num,ap(c_2Eieee_2Enum2ccode,V0r)) = V0r ) ) ).
fof(conj_thm_2Eieee_2Enum2ccode__11,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ! [V1r_27] :
( mem(V1r_27,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1r_27),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
=> ( ap(c_2Eieee_2Enum2ccode,V0r) = ap(c_2Eieee_2Enum2ccode,V1r_27)
<=> V0r = V1r_27 ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eccode2num__11,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eccode)
=> ! [V1a_27] :
( mem(V1a_27,ty_2Eieee_2Eccode)
=> ( ap(c_2Eieee_2Eccode2num,V0a) = ap(c_2Eieee_2Eccode2num,V1a_27)
<=> V0a = V1a_27 ) ) ) ).
fof(conj_thm_2Eieee_2Enum2ccode__ONTO,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eccode)
=> ? [V1r] :
( mem(V1r,ty_2Enum_2Enum)
& V0a = ap(c_2Eieee_2Enum2ccode,V1r)
& p(ap(ap(c_2Eprim__rec_2E_3C,V1r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ).
fof(conj_thm_2Eieee_2Eccode2num__ONTO,axiom,
! [V0r] :
( mem(V0r,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))
<=> ? [V1a] :
( mem(V1a,ty_2Eieee_2Eccode)
& V0r = ap(c_2Eieee_2Eccode2num,V1a) ) ) ) ).
fof(conj_thm_2Eieee_2Enum2ccode__thm,axiom,
( ap(c_2Eieee_2Enum2ccode,c_2Enum_2E0) = c_2Eieee_2EGt
& ap(c_2Eieee_2Enum2ccode,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = c_2Eieee_2ELt
& ap(c_2Eieee_2Enum2ccode,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Eieee_2EEq
& ap(c_2Eieee_2Enum2ccode,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = c_2Eieee_2EUn ) ).
fof(conj_thm_2Eieee_2Eccode2num__thm,axiom,
( ap(c_2Eieee_2Eccode2num,c_2Eieee_2EGt) = c_2Enum_2E0
& ap(c_2Eieee_2Eccode2num,c_2Eieee_2ELt) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))
& ap(c_2Eieee_2Eccode2num,c_2Eieee_2EEq) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))
& ap(c_2Eieee_2Eccode2num,c_2Eieee_2EUn) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ).
fof(conj_thm_2Eieee_2Eccode__EQ__ccode,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eccode)
=> ! [V1a_27] :
( mem(V1a_27,ty_2Eieee_2Eccode)
=> ( V0a = V1a_27
<=> ap(c_2Eieee_2Eccode2num,V0a) = ap(c_2Eieee_2Eccode2num,V1a_27) ) ) ) ).
fof(ax_thm_2Eieee_2Eccode__size__def,axiom,
! [V0x] :
( mem(V0x,ty_2Eieee_2Eccode)
=> ap(c_2Eieee_2Eccode__size,V0x) = c_2Enum_2E0 ) ).
fof(ax_thm_2Eieee_2Eccode__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Eieee_2Eccode)
=> ! [V1v0] :
( mem(V1v0,A_27a)
=> ! [V2v1] :
( mem(V2v1,A_27a)
=> ! [V3v2] :
( mem(V3v2,A_27a)
=> ! [V4v3] :
( mem(V4v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),V0x),V1v0),V2v1),V3v2),V4v3) = ap(f2950(A_27a,V2v1,V3v2,V4v3,V1v0),ap(c_2Eieee_2Eccode2num,V0x)) ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eccode__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0v0] :
( mem(V0v0,A_27a)
=> ! [V1v1] :
( mem(V1v1,A_27a)
=> ! [V2v2] :
( mem(V2v2,A_27a)
=> ! [V3v3] :
( mem(V3v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),c_2Eieee_2EGt),V0v0),V1v1),V2v2),V3v3) = V0v0 ) ) ) )
& ! [V4v0] :
( mem(V4v0,A_27a)
=> ! [V5v1] :
( mem(V5v1,A_27a)
=> ! [V6v2] :
( mem(V6v2,A_27a)
=> ! [V7v3] :
( mem(V7v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),c_2Eieee_2ELt),V4v0),V5v1),V6v2),V7v3) = V5v1 ) ) ) )
& ! [V8v0] :
( mem(V8v0,A_27a)
=> ! [V9v1] :
( mem(V9v1,A_27a)
=> ! [V10v2] :
( mem(V10v2,A_27a)
=> ! [V11v3] :
( mem(V11v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),c_2Eieee_2EEq),V8v0),V9v1),V10v2),V11v3) = V10v2 ) ) ) )
& ! [V12v0] :
( mem(V12v0,A_27a)
=> ! [V13v1] :
( mem(V13v1,A_27a)
=> ! [V14v2] :
( mem(V14v2,A_27a)
=> ! [V15v3] :
( mem(V15v3,A_27a)
=> ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),c_2Eieee_2EUn),V12v0),V13v1),V14v2),V15v3) = V15v3 ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Edatatype__ccode,axiom,
! [V0ccode] :
( mem(V0ccode,arr(ty_2Eieee_2Eccode,arr(ty_2Eieee_2Eccode,arr(ty_2Eieee_2Eccode,arr(ty_2Eieee_2Eccode,bool)))))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(ap(ap(V0ccode,c_2Eieee_2EGt),c_2Eieee_2ELt),c_2Eieee_2EEq),c_2Eieee_2EUn))) ) ).
fof(conj_thm_2Eieee_2Eccode__distinct,axiom,
( c_2Eieee_2EGt != c_2Eieee_2ELt
& c_2Eieee_2EGt != c_2Eieee_2EEq
& c_2Eieee_2EGt != c_2Eieee_2EUn
& c_2Eieee_2ELt != c_2Eieee_2EEq
& c_2Eieee_2ELt != c_2Eieee_2EUn
& c_2Eieee_2EEq != c_2Eieee_2EUn ) ).
fof(conj_thm_2Eieee_2Eccode__nchotomy,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Eccode)
=> ( V0a = c_2Eieee_2EGt
| V0a = c_2Eieee_2ELt
| V0a = c_2Eieee_2EEq
| V0a = c_2Eieee_2EUn ) ) ).
fof(conj_thm_2Eieee_2Eccode__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x0] :
( mem(V0x0,A_27a)
=> ! [V1x1] :
( mem(V1x1,A_27a)
=> ! [V2x2] :
( mem(V2x2,A_27a)
=> ! [V3x3] :
( mem(V3x3,A_27a)
=> ? [V4f] :
( mem(V4f,arr(ty_2Eieee_2Eccode,A_27a))
& ap(V4f,c_2Eieee_2EGt) = V0x0
& ap(V4f,c_2Eieee_2ELt) = V1x1
& ap(V4f,c_2Eieee_2EEq) = V2x2
& ap(V4f,c_2Eieee_2EUn) = V3x3 ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eccode__induction,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Eieee_2Eccode,bool))
=> ( ( p(ap(V0P,c_2Eieee_2EEq))
& p(ap(V0P,c_2Eieee_2EGt))
& p(ap(V0P,c_2Eieee_2ELt))
& p(ap(V0P,c_2Eieee_2EUn)) )
=> ! [V1a] :
( mem(V1a,ty_2Eieee_2Eccode)
=> p(ap(V0P,V1a)) ) ) ) ).
fof(conj_thm_2Eieee_2Eccode__case__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0v0_27] :
( mem(V0v0_27,A_27a)
=> ! [V1v1_27] :
( mem(V1v1_27,A_27a)
=> ! [V2v2_27] :
( mem(V2v2_27,A_27a)
=> ! [V3v3_27] :
( mem(V3v3_27,A_27a)
=> ! [V4M] :
( mem(V4M,ty_2Eieee_2Eccode)
=> ! [V5M_27] :
( mem(V5M_27,ty_2Eieee_2Eccode)
=> ! [V6v0] :
( mem(V6v0,A_27a)
=> ! [V7v1] :
( mem(V7v1,A_27a)
=> ! [V8v2] :
( mem(V8v2,A_27a)
=> ! [V9v3] :
( mem(V9v3,A_27a)
=> ( ( V4M = V5M_27
& ( V5M_27 = c_2Eieee_2EGt
=> V6v0 = V0v0_27 )
& ( V5M_27 = c_2Eieee_2ELt
=> V7v1 = V1v1_27 )
& ( V5M_27 = c_2Eieee_2EEq
=> V8v2 = V2v2_27 )
& ( V5M_27 = c_2Eieee_2EUn
=> V9v3 = V3v3_27 ) )
=> ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),V4M),V6v0),V7v1),V8v2),V9v3) = ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),V5M_27),V0v0_27),V1v1_27),V2v2_27),V3v3_27) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Eieee_2Eccode__case__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Eieee_2Eccode)
=> ! [V1v0] :
( mem(V1v0,A_27a)
=> ! [V2v1] :
( mem(V2v1,A_27a)
=> ! [V3v2] :
( mem(V3v2,A_27a)
=> ! [V4v3] :
( mem(V4v3,A_27a)
=> ! [V5v] :
( mem(V5v,A_27a)
=> ( ap(ap(ap(ap(ap(c_2Eieee_2Eccode__CASE(A_27a),V0x),V1v0),V2v1),V3v2),V4v3) = V5v
<=> ( ( V0x = c_2Eieee_2EGt
& V1v0 = V5v )
| ( V0x = c_2Eieee_2ELt
& V2v1 = V5v )
| ( V0x = c_2Eieee_2EEq
& V3v2 = V5v )
| ( V0x = c_2Eieee_2EUn
& V4v3 = V5v ) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efcompare,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V2b] :
( mem(V2b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eieee_2Eis__nan,V0X),V1a)),ap(ap(c_2Eieee_2Eis__nan,V0X),V2b))),c_2Eieee_2EUn),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V1a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V1a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2b)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2b)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2Eieee_2EEq),c_2Eieee_2ELt)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V1a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V1a)),c_2Enum_2E0))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2b)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2b)),c_2Enum_2E0))),c_2Eieee_2EEq),c_2Eieee_2EGt)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2b)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2b)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),c_2Eieee_2EGt),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eieee_2Eis__infinity,V0X),V2b)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Esign,V2b)),c_2Enum_2E0))),c_2Eieee_2ELt),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Eieee_2Evalof,V0X),V1a)),ap(ap(c_2Eieee_2Evalof,V0X),V2b))),c_2Eieee_2ELt),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Eccode),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(ap(c_2Eieee_2Evalof,V0X),V1a)),ap(ap(c_2Eieee_2Evalof,V0X),V2b))),c_2Eieee_2EEq),c_2Eieee_2EGt))))))) ) ) ) ).
fof(ax_thm_2Eieee_2Eflt,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V2b] :
( mem(V2b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(ap(c_2Eieee_2Eflt,V0X),V1a),V2b))
<=> ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = c_2Eieee_2ELt ) ) ) ) ).
fof(ax_thm_2Eieee_2Efle,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V2b] :
( mem(V2b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(ap(c_2Eieee_2Efle,V0X),V1a),V2b))
<=> ( ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = c_2Eieee_2ELt
| ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = c_2Eieee_2EEq ) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efgt,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V2b] :
( mem(V2b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(ap(c_2Eieee_2Efgt,V0X),V1a),V2b))
<=> ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = c_2Eieee_2EGt ) ) ) ) ).
fof(ax_thm_2Eieee_2Efge,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V2b] :
( mem(V2b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(ap(c_2Eieee_2Efge,V0X),V1a),V2b))
<=> ( ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = c_2Eieee_2EGt
| ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = c_2Eieee_2EEq ) ) ) ) ) ).
fof(ax_thm_2Eieee_2Efeq,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ! [V2b] :
( mem(V2b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(ap(c_2Eieee_2Efeq,V0X),V1a),V2b))
<=> ap(ap(ap(c_2Eieee_2Efcompare,V0X),V1a),V2b) = c_2Eieee_2EEq ) ) ) ) ).
fof(ax_thm_2Eieee_2Efloat__format,axiom,
c_2Eieee_2Efloat__format = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) ).
fof(ax_thm_2Eieee_2Efloat__TY__DEF,axiom,
? [V0rep] :
( mem(V0rep,arr(ty_2Eieee_2Efloat,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Eieee_2Efloat),ap(c_2Eieee_2Eis__valid,c_2Eieee_2Efloat__format)),V0rep)) ) ).
fof(ax_thm_2Eieee_2Efloat__tybij,axiom,
( ! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2Efloat,ap(c_2Eieee_2Edefloat,V0a)) = V0a )
& ! [V1r] :
( mem(V1r,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__valid,c_2Eieee_2Efloat__format),V1r))
<=> ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,V1r)) = V1r ) ) ) ).
fof(ax_thm_2Eieee_2EVal,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2EVal,V0a) = ap(ap(c_2Eieee_2Evalof,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a)) ) ).
fof(ax_thm_2Eieee_2EFloat,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Eieee_2EFloat,V0x) = ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)) ) ).
fof(ax_thm_2Eieee_2ESign,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2ESign,V0a) = ap(c_2Eieee_2Esign,ap(c_2Eieee_2Edefloat,V0a)) ) ).
fof(ax_thm_2Eieee_2EExponent,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2EExponent,V0a) = ap(c_2Eieee_2Eexponent,ap(c_2Eieee_2Edefloat,V0a)) ) ).
fof(ax_thm_2Eieee_2EFraction,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2EFraction,V0a) = ap(c_2Eieee_2Efraction,ap(c_2Eieee_2Edefloat,V0a)) ) ).
fof(ax_thm_2Eieee_2EUlp,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2EUlp,V0a) = ap(ap(c_2Eieee_2Eulp,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a)) ) ).
fof(ax_thm_2Eieee_2EIsnan,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EIsnan,V0a))
<=> p(ap(ap(c_2Eieee_2Eis__nan,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).
fof(ax_thm_2Eieee_2EInfinity,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EInfinity,V0a))
<=> p(ap(ap(c_2Eieee_2Eis__infinity,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).
fof(ax_thm_2Eieee_2EIsnormal,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EIsnormal,V0a))
<=> p(ap(ap(c_2Eieee_2Eis__normal,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).
fof(ax_thm_2Eieee_2EIsdenormal,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EIsdenormal,V0a))
<=> p(ap(ap(c_2Eieee_2Eis__denormal,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).
fof(ax_thm_2Eieee_2EIszero,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EIszero,V0a))
<=> p(ap(ap(c_2Eieee_2Eis__zero,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).
fof(ax_thm_2Eieee_2EFinite,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EFinite,V0a))
<=> ( p(ap(c_2Eieee_2EIsnormal,V0a))
| p(ap(c_2Eieee_2EIsdenormal,V0a))
| p(ap(c_2Eieee_2EIszero,V0a)) ) ) ) ).
fof(ax_thm_2Eieee_2EIsintegral,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EIsintegral,V0a))
<=> p(ap(ap(c_2Eieee_2Eis__integral,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).
fof(ax_thm_2Eieee_2EPlus__zero,axiom,
c_2Eieee_2EPlus__zero = ap(c_2Eieee_2Efloat,ap(c_2Eieee_2Eplus__zero,c_2Eieee_2Efloat__format)) ).
fof(ax_thm_2Eieee_2EMinus__zero,axiom,
c_2Eieee_2EMinus__zero = ap(c_2Eieee_2Efloat,ap(c_2Eieee_2Eminus__zero,c_2Eieee_2Efloat__format)) ).
fof(ax_thm_2Eieee_2EMinus__infinity,axiom,
c_2Eieee_2EMinus__infinity = ap(c_2Eieee_2Efloat,ap(c_2Eieee_2Eminus__infinity,c_2Eieee_2Efloat__format)) ).
fof(ax_thm_2Eieee_2EPlus__infinity,axiom,
c_2Eieee_2EPlus__infinity = ap(c_2Eieee_2Efloat,ap(c_2Eieee_2Eplus__infinity,c_2Eieee_2Efloat__format)) ).
fof(ax_thm_2Eieee_2Efloat__add,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ap(ap(c_2Eieee_2Efloat__add,V0a),V1b) = ap(c_2Eieee_2Efloat,ap(ap(ap(ap(c_2Eieee_2Efadd,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ).
fof(ax_thm_2Eieee_2Efloat__sub,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b) = ap(c_2Eieee_2Efloat,ap(ap(ap(ap(c_2Eieee_2Efsub,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ).
fof(ax_thm_2Eieee_2Efloat__mul,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b) = ap(c_2Eieee_2Efloat,ap(ap(ap(ap(c_2Eieee_2Efmul,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ).
fof(ax_thm_2Eieee_2Efloat__div,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ap(ap(c_2Eieee_2Efloat__div,V0a),V1b) = ap(c_2Eieee_2Efloat,ap(ap(ap(ap(c_2Eieee_2Efdiv,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ).
fof(ax_thm_2Eieee_2Efloat__rem,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ap(ap(c_2Eieee_2Efloat__rem,V0a),V1b) = ap(c_2Eieee_2Efloat,ap(ap(ap(ap(c_2Eieee_2Efrem,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ).
fof(ax_thm_2Eieee_2Efloat__sqrt,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2Efloat__sqrt,V0a) = ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Efsqrt,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a))) ) ).
fof(ax_thm_2Eieee_2EROUNDFLOAT,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2EROUNDFLOAT,V0a) = ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Efintrnd,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a))) ) ).
fof(ax_thm_2Eieee_2Efloat__lt,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( p(ap(ap(c_2Eieee_2Efloat__lt,V0a),V1b))
<=> p(ap(ap(ap(c_2Eieee_2Eflt,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ) ).
fof(ax_thm_2Eieee_2Efloat__le,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( p(ap(ap(c_2Eieee_2Efloat__le,V0a),V1b))
<=> p(ap(ap(ap(c_2Eieee_2Efle,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ) ).
fof(ax_thm_2Eieee_2Efloat__gt,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( p(ap(ap(c_2Eieee_2Efloat__gt,V0a),V1b))
<=> p(ap(ap(ap(c_2Eieee_2Efgt,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ) ).
fof(ax_thm_2Eieee_2Efloat__ge,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( p(ap(ap(c_2Eieee_2Efloat__ge,V0a),V1b))
<=> p(ap(ap(ap(c_2Eieee_2Efge,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ) ).
fof(ax_thm_2Eieee_2Efloat__eq,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),V1b))
<=> p(ap(ap(ap(c_2Eieee_2Efeq,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a)),ap(c_2Eieee_2Edefloat,V1b))) ) ) ) ).
fof(ax_thm_2Eieee_2Efloat__neg,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2Efloat__neg,V0a) = ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Efneg,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),ap(c_2Eieee_2Edefloat,V0a))) ) ).
fof(ax_thm_2Eieee_2Efloat__abs,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ap(c_2Eieee_2Efloat__abs,V0a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eieee_2Efloat),ap(ap(c_2Eieee_2Efloat__ge,V0a),c_2Eieee_2EPlus__zero)),V0a),ap(c_2Eieee_2Efloat__neg,V0a)) ) ).
%------------------------------------------------------------------------------