ITP001 Axioms: ITP140+5.ax
%------------------------------------------------------------------------------
% File : ITP140+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 : lift_ieee+2.ax [Gau20]
% : HL4140+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 52 ( 2 unt; 0 def)
% Number of atoms : 386 ( 33 equ)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 347 ( 13 ~; 0 |; 97 &)
% ( 7 <=>; 230 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 72 ( 72 usr; 27 con; 0-2 aty)
% Number of variables : 201 ( 191 !; 10 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Elift__ieee_2Eerror,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> mem(c_2Elift__ieee_2Eerror(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) ) ) ).
fof(mem_c_2Elift__ieee_2Enormalizes,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> mem(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),arr(ty_2Erealax_2Ereal,bool))) ) ) ).
fof(ax_thm_2Elift__ieee_2Eerror__def,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),V0x) = ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0x))),V0x) ) ) ) ).
fof(ax_thm_2Elift__ieee_2Enormalizes__def,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),V0x))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))))
& 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_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),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_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__lt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ! [V1y] :
( mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V1y)) )
=> ( p(ap(ap(c_2Ebinary__ieee_2Efloat__less__than(A_27a,A_27b),V0x),V1y))
<=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V1y))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__le,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ! [V1y] :
( mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V1y)) )
=> ( p(ap(ap(c_2Ebinary__ieee_2Efloat__less__equal(A_27a,A_27b),V0x),V1y))
<=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V1y))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__gt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ! [V1y] :
( mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V1y)) )
=> ( p(ap(ap(c_2Ebinary__ieee_2Efloat__greater__than(A_27a,A_27b),V0x),V1y))
<=> p(ap(ap(c_2Ereal_2Ereal__gt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V1y))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__ge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ! [V1y] :
( mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V1y)) )
=> ( p(ap(ap(c_2Ebinary__ieee_2Efloat__greater__equal(A_27a,A_27b),V0x),V1y))
<=> p(ap(ap(c_2Ereal_2Ereal__ge,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V1y))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ! [V1y] :
( mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0x))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V1y)) )
=> ( p(ap(ap(c_2Ebinary__ieee_2Efloat__equal(A_27a,A_27b),V0x),V1y))
<=> ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x) = ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V1y) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__eq__refl,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( p(ap(ap(c_2Ebinary__ieee_2Efloat__equal(A_27a,A_27b),V0x),V0x))
<=> ~ p(ap(c_2Ebinary__ieee_2Efloat__is__nan(A_27a,A_27b),V0x)) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Eis__closest__exits,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1s] :
( mem(V1s,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V1s))
=> ( V1s != c_2Epred__set_2EEMPTY(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ? [V2a] :
( mem(V2a,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
& p(ap(ap(ap(c_2Ebinary__ieee_2Eis__closest(A_27a,A_27b),V1s),V0x),V2a)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Eclosest__is__everything,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0p] :
( mem(V0p,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ! [V1s] :
( mem(V1s,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V1s))
=> ( V1s != c_2Epred__set_2EEMPTY(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( p(ap(ap(ap(c_2Ebinary__ieee_2Eis__closest(A_27a,A_27b),V1s),V2x),ap(ap(ap(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),V0p),V1s),V2x)))
& ( ? [V3b] :
( mem(V3b,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
& p(ap(ap(ap(c_2Ebinary__ieee_2Eis__closest(A_27a,A_27b),V1s),V2x),V3b))
& p(ap(V0p,V3b)) )
=> p(ap(V0p,ap(ap(ap(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),V0p),V1s),V2x))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Eclosest__in__set,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0p] :
( mem(V0p,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ! [V1s] :
( mem(V1s,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V1s))
=> ( V1s != c_2Epred__set_2EEMPTY(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> p(ap(ap(c_2Ebool_2EIN(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),ap(ap(ap(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),V0p),V1s),V2x)),V1s)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Eclosest__is__closest,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0p] :
( mem(V0p,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ! [V1s] :
( mem(V1s,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ! [V2x] :
( mem(V2x,ty_2Erealax_2Ereal)
=> ( p(ap(c_2Epred__set_2EFINITE(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),V1s))
=> ( V1s != c_2Epred__set_2EEMPTY(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> p(ap(ap(ap(c_2Ebinary__ieee_2Eis__closest(A_27a,A_27b),V1s),V2x),ap(ap(ap(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),V0p),V1s),V2x))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> p(ap(c_2Epred__set_2EFINITE(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epred__set_2EUNIV(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))) ) ) ).
fof(lameq_f3133,axiom,
! [A_27a,A_27b,V0a] : ap(f3133(A_27a,A_27b),V0a) = ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool),V0a),ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0a)) ).
fof(conj_thm_2Elift__ieee_2Eis__finite__finite,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> p(ap(c_2Epred__set_2EFINITE(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),ap(c_2Epred__set_2EGSPEC(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),f3133(A_27a,A_27b)))) ) ) ).
fof(conj_thm_2Elift__ieee_2Eis__finite__nonempty,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(c_2Epred__set_2EGSPEC(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),f3133(A_27a,A_27b)) != c_2Epred__set_2EEMPTY(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) ) ) ).
fof(lameq_f3134,axiom,
! [A_27a,A_27b,V2a] : ap(f3134(A_27a,A_27b),V2a) = ap(ap(c_2Epair_2E_2C(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool),V2a),ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V2a)) ).
fof(conj_thm_2Elift__ieee_2Eis__finite__closest,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0p] :
( mem(V0p,arr(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),bool))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),ap(ap(ap(c_2Ebinary__ieee_2Eclosest__such(A_27a,A_27b),V0p),ap(c_2Epred__set_2EGSPEC(ty_2Ebinary__ieee_2Efloat(A_27a,A_27b),ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)),f3134(A_27a,A_27b))),V1x))) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__to__real__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0x))
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x))),ap(c_2Ebinary__ieee_2Elargest(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__to__real__threshold,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0x))
=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Eerror__at__worst__lemma,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V1x)),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a)) )
=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),V1x))),ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),V1x)))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Eerror__is__zero,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a) = V1x )
=> ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),V1x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Erelative__error,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2Eround(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),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_2Elift__ieee_2Efloat__round__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0b] :
( mem(V0b,bool)
=> ! [V1x] :
( mem(V1x,ty_2Erealax_2Ereal)
=> ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V1x)),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0b),V1x))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__add,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__sub,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__mul,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__div,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& ~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2E_2F,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__div(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__div(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__sqrt,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0a) = ap(c_2Ewords_2En2w(ty_2Eone_2Eone),c_2Enum_2E0)
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a))) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a))),ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__mul__add,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V2c] :
( mem(V2c,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V2c))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c))),ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__mul__sub,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V2c] :
( mem(V2c,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V2c))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c))),ap(ap(c_2Elift__ieee_2Eerror(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__add__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b)))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__sub__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b)))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__mul__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b)))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__div__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& ~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V1b))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2E_2F,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__div(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b)))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__sqrt__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0a) = ap(c_2Ewords_2En2w(ty_2Eone_2Eone),c_2Enum_2E0)
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a)))) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__mul__add__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V2c] :
( mem(V2c,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V2c))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__mul__sub__finite,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V2c] :
( mem(V2c,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V2c))
& p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) )
=> p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__add__relative,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),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_2Elift__ieee_2Efloat__sub__relative,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),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_2Elift__ieee_2Efloat__mul__relative,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),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_2Elift__ieee_2Efloat__div__relative,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& ~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V1b))
& p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b)))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__div(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(c_2Ebinary__ieee_2Efloat__div(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b))) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),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_2Elift__ieee_2Efloat__sqrt__relative,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0a) = ap(c_2Ewords_2En2w(ty_2Eone_2Eone),c_2Enum_2E0)
& p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a))))
& ? [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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a))) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a))),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_2Elift__ieee_2Efloat__mul__add__relative,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V2c] :
( mem(V2c,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V2c))
& p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))))
& ? [V3e] :
( mem(V3e,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V3e)),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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__add(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3e)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__mul__sub__relative,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ! [V0a] :
( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V1b] :
( mem(V1b,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ! [V2c] :
( mem(V2c,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V1b))
& p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V2c))
& p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c)))) )
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))))
& ? [V3e] :
( mem(V3e,ty_2Erealax_2Ereal)
& p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V3e)),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(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))
& ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(ap(ap(c_2Ebinary__ieee_2Efloat__mul__sub(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a),V1b),V2c))) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1b))),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V2c))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3e)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efinite__float__within__threshold,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0f))
=> ( ~ p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0f)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Ethreshold(A_27a,A_27b),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27a,A_27b))))))
& ~ p(ap(ap(c_2Ereal_2Ereal__ge,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0f)),ap(c_2Ebinary__ieee_2Ethreshold(A_27a,A_27b),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27a,A_27b))))) ) ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Eround__finite__normal__float__id,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0f))
& ~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0f)) )
=> ap(ap(c_2Ebinary__ieee_2Eround(A_27a,A_27b),c_2Ebinary__ieee_2EroundTiesToEven),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0f)) = V0f ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Ereal__to__float__finite__normal__id,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27a,A_27b),V0f))
& ~ p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0f)) )
=> ap(ap(c_2Ebinary__ieee_2Ereal__to__float(A_27a,A_27b),c_2Ebinary__ieee_2EroundTiesToEven),ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0f)) = V0f ) ) ) ) ).
fof(conj_thm_2Elift__ieee_2Efloat__to__real__real__to__float__zero__id,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),ap(ap(c_2Ebinary__ieee_2Ereal__to__float(A_27a,A_27b),c_2Ebinary__ieee_2EroundTiesToEven),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ).
fof(conj_thm_2Elift__ieee_2Enon__representable__float__is__zero,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0ff] :
( mem(V0ff,ty_2Erealax_2Ereal)
=> ! [V1P] :
( mem(V1P,bool)
=> ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Ereal_2Eabs,V0ff))),ap(c_2Ebinary__ieee_2Eulp(A_27a,A_27b),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),ap(ap(ap(c_2Ebinary__ieee_2Efloat__round(A_27a,A_27b),c_2Ebinary__ieee_2EroundTiesToEven),V1P),V0ff)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ) ).
%------------------------------------------------------------------------------