ITP001 Axioms: ITP139+5.ax
%------------------------------------------------------------------------------
% File : ITP139+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 : float+2.ax [Gau20]
% : HL4139+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 4 unt; 0 def)
% Number of atoms : 316 ( 33 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 275 ( 27 ~; 7 |; 97 &)
% ( 11 <=>; 133 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 130 ( 7 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 90 ( 90 usr; 73 con; 0-2 aty)
% Number of variables : 112 ( 103 !; 9 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Efloat_2Eerror,axiom,
mem(c_2Efloat_2Eerror,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ).
fof(mem_c_2Efloat_2Enormalizes,axiom,
mem(c_2Efloat_2Enormalizes,arr(ty_2Erealax_2Ereal,bool)) ).
fof(conj_thm_2Efloat_2ESIGN,axiom,
! [V0a] :
( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(c_2Eieee_2Esign,V0a) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a) ) ).
fof(conj_thm_2Efloat_2EEXPONENT,axiom,
! [V0a] :
( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(c_2Eieee_2Eexponent,V0a) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a)) ) ).
fof(conj_thm_2Efloat_2EFRACTION,axiom,
! [V0a] :
( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(c_2Eieee_2Efraction,V0a) = ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a)) ) ).
fof(conj_thm_2Efloat_2EIS__VALID,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__valid,V0X),V1a))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Esign,V1a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Eexponent,V1a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Eexpwidth,V0X))))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Efraction,V1a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Eieee_2Efracwidth,V0X)))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EVALOF,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] :
( mem(V1a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ap(ap(c_2Eieee_2Evalof,V0X),V1a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Eieee_2Eexponent,V1a)),c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Eieee_2Esign,V1a))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Eieee_2Efraction,V1a))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Efracwidth,V0X))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Eieee_2Esign,V1a))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Eexponent,V1a))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Ebias,V0X))))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Eieee_2Efraction,V1a))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Eieee_2Efracwidth,V0X)))))) ) ) ).
fof(conj_thm_2Efloat_2EIS__VALID__DEFLOAT,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> p(ap(ap(c_2Eieee_2Eis__valid,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ).
fof(conj_thm_2Efloat_2EIS__FINITE__EXPLICIT,axiom,
! [V0a] :
( mem(V0a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(c_2Eieee_2Eis__finite,c_2Eieee_2Efloat__format),V0a))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Esign,V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Eexponent,V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))
& p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eieee_2Efraction,V0a)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))))))))))))))))) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__CASES,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EIsnan,V0a))
| p(ap(c_2Eieee_2EInfinity,V0a))
| p(ap(c_2Eieee_2EIsnormal,V0a))
| p(ap(c_2Eieee_2EIsdenormal,V0a))
| p(ap(c_2Eieee_2EIszero,V0a)) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__CASES__FINITE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EIsnan,V0a))
| p(ap(c_2Eieee_2EInfinity,V0a))
| p(ap(c_2Eieee_2EFinite,V0a)) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__DISTINCT,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
& p(ap(c_2Eieee_2EInfinity,V0a)) )
& ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
& p(ap(c_2Eieee_2EIsnormal,V0a)) )
& ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
& p(ap(c_2Eieee_2EIsdenormal,V0a)) )
& ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
& p(ap(c_2Eieee_2EIszero,V0a)) )
& ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
& p(ap(c_2Eieee_2EIsnormal,V0a)) )
& ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
& p(ap(c_2Eieee_2EIsdenormal,V0a)) )
& ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
& p(ap(c_2Eieee_2EIszero,V0a)) )
& ~ ( p(ap(c_2Eieee_2EIsnormal,V0a))
& p(ap(c_2Eieee_2EIsdenormal,V0a)) )
& ~ ( p(ap(c_2Eieee_2EIsnormal,V0a))
& p(ap(c_2Eieee_2EIszero,V0a)) )
& ~ ( p(ap(c_2Eieee_2EIsdenormal,V0a))
& p(ap(c_2Eieee_2EIszero,V0a)) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__DISTINCT__FINITE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
& p(ap(c_2Eieee_2EInfinity,V0a)) )
& ~ ( p(ap(c_2Eieee_2EIsnan,V0a))
& p(ap(c_2Eieee_2EFinite,V0a)) )
& ~ ( p(ap(c_2Eieee_2EInfinity,V0a))
& p(ap(c_2Eieee_2EFinite,V0a)) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__INFINITIES__SIGNED,axiom,
( ap(c_2Eieee_2Esign,ap(c_2Eieee_2Edefloat,c_2Eieee_2EPlus__infinity)) = c_2Enum_2E0
& ap(c_2Eieee_2Esign,ap(c_2Eieee_2Edefloat,c_2Eieee_2EMinus__infinity)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ).
fof(conj_thm_2Efloat_2EINFINITY__IS__INFINITY,axiom,
( p(ap(c_2Eieee_2EInfinity,c_2Eieee_2EPlus__infinity))
& p(ap(c_2Eieee_2EInfinity,c_2Eieee_2EMinus__infinity)) ) ).
fof(conj_thm_2Efloat_2EZERO__IS__ZERO,axiom,
( p(ap(c_2Eieee_2EIszero,c_2Eieee_2EPlus__zero))
& p(ap(c_2Eieee_2EIszero,c_2Eieee_2EMinus__zero)) ) ).
fof(conj_thm_2Efloat_2EINFINITY__NOT__NAN,axiom,
( ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EPlus__infinity))
& ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EMinus__infinity)) ) ).
fof(conj_thm_2Efloat_2EZERO__NOT__NAN,axiom,
( ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EPlus__zero))
& ~ p(ap(c_2Eieee_2EIsnan,c_2Eieee_2EMinus__zero)) ) ).
fof(conj_thm_2Efloat_2EFLOAT__INFINITIES,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EInfinity,V0a))
<=> ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EPlus__infinity))
| p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EMinus__infinity)) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__INFINITES__DISTINCT,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ~ ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EPlus__infinity))
& p(ap(ap(c_2Eieee_2Efloat__eq,V0a),c_2Eieee_2EMinus__infinity)) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__LT,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b)) )
=> ( p(ap(ap(c_2Eieee_2Efloat__lt,V0a),V1b))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__GT,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b)) )
=> ( p(ap(ap(c_2Eieee_2Efloat__gt,V0a),V1b))
<=> p(ap(ap(c_2Ereal_2Ereal__gt,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__LE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b)) )
=> ( p(ap(ap(c_2Eieee_2Efloat__le,V0a),V1b))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__GE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b)) )
=> ( p(ap(ap(c_2Eieee_2Efloat__ge,V0a),V1b))
<=> p(ap(ap(c_2Ereal_2Ereal__ge,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__EQ,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b)) )
=> ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),V1b))
<=> ap(c_2Eieee_2EVal,V0a) = ap(c_2Eieee_2EVal,V1b) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__EQ__REFL,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(ap(c_2Eieee_2Efloat__eq,V0a),V0a))
<=> ~ p(ap(c_2Eieee_2EIsnan,V0a)) ) ) ).
fof(conj_thm_2Efloat_2EIS__VALID__SPECIAL,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ( p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eminus__infinity,V0X)))
& p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eplus__infinity,V0X)))
& p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Etopfloat,V0X)))
& p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Ebottomfloat,V0X)))
& p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eplus__zero,V0X)))
& p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(c_2Eieee_2Eminus__zero,V0X))) ) ) ).
fof(conj_thm_2Efloat_2EIS__CLOSEST__EXISTS,axiom,
! [V0v] :
( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ! [V2s] :
( mem(V2s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V2s))
=> ( V2s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ? [V3a] :
( mem(V3a,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
& p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V2s),V1x),V3a)) ) ) ) ) ) ) ).
fof(conj_thm_2Efloat_2ECLOSEST__IS__EVERYTHING,axiom,
! [V0v] :
( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
=> ! [V1p] :
( mem(V1p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ! [V2s] :
( mem(V2s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V2s))
=> ( V2s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> ( p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V2s),V3x),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V2s),V3x)))
& ( ? [V4b] :
( mem(V4b,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
& p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V2s),V3x),V4b))
& p(ap(V1p,V4b)) )
=> p(ap(V1p,ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V2s),V3x))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efloat_2ECLOSEST__IN__SET,axiom,
! [V0v] :
( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
=> ! [V1p] :
( mem(V1p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ! [V3s] :
( mem(V3s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V3s))
=> ( V3s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V3s),V2x)),V3s)) ) ) ) ) ) ) ).
fof(conj_thm_2Efloat_2ECLOSEST__IS__CLOSEST,axiom,
! [V0v] :
( mem(V0v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
=> ! [V1p] :
( mem(V1p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ! [V3s] :
( mem(V3s,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V3s))
=> ( V3s != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
=> p(ap(ap(ap(ap(c_2Eieee_2Eis__closest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V3s),V2x),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V0v),V1p),V3s),V2x))) ) ) ) ) ) ) ).
fof(lameq_f3150,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] : ap(f3150(V0X),V1a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V1a),ap(ap(c_2Eieee_2Eis__valid,V0X),V1a)) ) ).
fof(conj_thm_2Efloat_2EIS__VALID__FINITE,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3150(V0X)))) ) ).
fof(lameq_f3151,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1a] : ap(f3151(V0X),V1a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V1a),ap(ap(c_2Eieee_2Eis__finite,V0X),V1a)) ) ).
fof(conj_thm_2Efloat_2EIS__FINITE__FINITE,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> p(ap(c_2Epred__set_2EFINITE(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3151(V0X)))) ) ).
fof(conj_thm_2Efloat_2EIS__VALID__NONEMPTY,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3150(V0X)) != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ) ).
fof(conj_thm_2Efloat_2EIS__FINITE__NONEMPTY,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3151(V0X)) != c_2Epred__set_2EEMPTY(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ) ).
fof(lameq_f3152,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V4a] : ap(f3152(V0X),V4a) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool),V4a),ap(ap(c_2Eieee_2Eis__finite,V0X),V4a)) ) ).
fof(conj_thm_2Efloat_2EIS__FINITE__CLOSEST,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1v] :
( mem(V1v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
=> ! [V2p] :
( mem(V2p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eieee_2Eis__finite,V0X),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V1v),V2p),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3152(V0X))),V3x))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EIS__VALID__CLOSEST,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1v] :
( mem(V1v,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Erealax_2Ereal))
=> ! [V2p] :
( mem(V2p,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),bool))
=> ! [V3x] :
( mem(V3x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(ap(ap(ap(c_2Eieee_2Eclosest(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),V1v),V2p),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))),f3152(V0X))),V3x))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EIS__VALID__ROUND,axiom,
! [V0X] :
( mem(V0X,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Eieee_2Eis__valid,V0X),ap(ap(ap(c_2Eieee_2Eround,V0X),c_2Eieee_2ETo__nearest),V1x))) ) ) ).
fof(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ROUND,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x))) = ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x) ) ).
fof(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V1b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)))) = ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V1b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)) ) ) ).
fof(conj_thm_2Efloat_2EVALOF__DEFLOAT__FLOAT__ZEROSIGN__ROUND,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1b] :
( mem(V1b,ty_2Enum_2Enum)
=> ap(ap(c_2Eieee_2Evalof,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V1b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x))))) = ap(ap(c_2Eieee_2Evalof,c_2Eieee_2Efloat__format),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)) ) ) ).
fof(conj_thm_2Efloat_2EISFINITE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EFinite,V0a))
<=> p(ap(ap(c_2Eieee_2Eis__finite,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,V0a))) ) ) ).
fof(conj_thm_2Efloat_2EVAL__FINITE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EFinite,V0a))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Eieee_2EVal,V0a))),ap(c_2Eieee_2Elargest,c_2Eieee_2Efloat__format))) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__THRESHOLD__EXPLICIT,axiom,
ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).
fof(conj_thm_2Efloat_2EFLOAT__LARGEST__EXPLICIT,axiom,
ap(c_2Eieee_2Elargest,c_2Eieee_2Efloat__format) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ).
fof(conj_thm_2Efloat_2EVAL__THRESHOLD,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ( p(ap(c_2Eieee_2EFinite,V0a))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(c_2Eieee_2EVal,V0a))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) ) ) ).
fof(ax_thm_2Efloat_2Eerror__def,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(c_2Efloat_2Eerror,V0x) = ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x)))),V0x) ) ).
fof(conj_thm_2Efloat_2EERROR__IS__ZERO,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& ap(c_2Eieee_2EVal,V0a) = V1x )
=> ap(c_2Efloat_2Eerror,V1x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Efloat_2EERROR__BOUND__NORM__STRONG,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1j] :
( mem(V1j,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,V1j))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Efloat_2Eerror,V0x))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1j)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ) ) ).
fof(ax_thm_2Efloat_2Enormalizes__def,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Efloat_2Enormalizes,V0x))
<=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Ebias,c_2Eieee_2Efloat__format)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Eabs,V0x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) ) ) ) ).
fof(conj_thm_2Efloat_2EREAL__IN__BINADE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Efloat_2Enormalizes,V0x))
=> ? [V1j] :
( mem(V1j,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V1j),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eieee_2Eemax,c_2Eieee_2Efloat__format)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1j)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))),ap(c_2Ereal_2Eabs,V0x)))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,V1j))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))) ) ) ) ).
fof(conj_thm_2Efloat_2EERROR__BOUND__NORM__STRONG__NORMALIZE,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Efloat_2Enormalizes,V0x))
=> ? [V1j] :
( mem(V1j,ty_2Enum_2Enum)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Efloat_2Eerror,V0x))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1j)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))) ) ) ) ).
fof(conj_thm_2Efloat_2ERELATIVE__ERROR,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Efloat_2Enormalizes,V0x))
=> ? [V1e] :
( mem(V1e,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V1e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
& ap(c_2Eieee_2EVal,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V0x))) = ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1e)) ) ) ) ).
fof(conj_thm_2Efloat_2EDEFLOAT__FLOAT__ZEROSIGN__ROUND__FINITE,axiom,
! [V0b] :
( mem(V0b,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V1x)),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format)))
=> p(ap(ap(c_2Eieee_2Eis__finite,c_2Eieee_2Efloat__format),ap(c_2Eieee_2Edefloat,ap(c_2Eieee_2Efloat,ap(ap(ap(c_2Eieee_2Ezerosign,c_2Eieee_2Efloat__format),V0b),ap(ap(ap(c_2Eieee_2Eround,c_2Eieee_2Efloat__format),c_2Eieee_2ETo__nearest),V1x)))))) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__ADD,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__SUB,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__MUL,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__DIV,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& ~ p(ap(c_2Eieee_2EIszero,V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(c_2Efloat_2Eerror,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__ADD__FINITE,axiom,
! [V0b] :
( mem(V0b,ty_2Eieee_2Efloat)
=> ! [V1a] :
( mem(V1a,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V1a))
& p(ap(c_2Eieee_2EFinite,V0b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V1a)),ap(c_2Eieee_2EVal,V0b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
=> p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__add,V1a),V0b))) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__SUB__FINITE,axiom,
! [V0b] :
( mem(V0b,ty_2Eieee_2Efloat)
=> ! [V1a] :
( mem(V1a,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V1a))
& p(ap(c_2Eieee_2EFinite,V0b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V1a)),ap(c_2Eieee_2EVal,V0b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
=> p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__sub,V1a),V0b))) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__MUL__FINITE,axiom,
! [V0b] :
( mem(V0b,ty_2Eieee_2Efloat)
=> ! [V1a] :
( mem(V1a,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V1a))
& p(ap(c_2Eieee_2EFinite,V0b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V1a)),ap(c_2Eieee_2EVal,V0b)))),ap(c_2Eieee_2Ethreshold,c_2Eieee_2Efloat__format))) )
=> p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__mul,V1a),V0b))) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__ADD__RELATIVE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)))
& ? [V2e] :
( mem(V2e,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__add,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__SUB__RELATIVE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)))
& ? [V2e] :
( mem(V2e,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__sub,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__MUL__RELATIVE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)))
& ? [V2e] :
( mem(V2e,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__mul,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).
fof(conj_thm_2Efloat_2EFLOAT__DIV__RELATIVE,axiom,
! [V0a] :
( mem(V0a,ty_2Eieee_2Efloat)
=> ! [V1b] :
( mem(V1b,ty_2Eieee_2Efloat)
=> ( ( p(ap(c_2Eieee_2EFinite,V0a))
& p(ap(c_2Eieee_2EFinite,V1b))
& ~ p(ap(c_2Eieee_2EIszero,V1b))
& p(ap(c_2Efloat_2Enormalizes,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b)))) )
=> ( p(ap(c_2Eieee_2EFinite,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)))
& ? [V2e] :
( mem(V2e,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V2e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))
& ap(c_2Eieee_2EVal,ap(ap(c_2Eieee_2Efloat__div,V0a),V1b)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(c_2Eieee_2EVal,V0a)),ap(c_2Eieee_2EVal,V1b))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2e)) ) ) ) ) ) ).
%------------------------------------------------------------------------------