%   ORIGINAL: h4/float/FLOAT__INFINITIES
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/OR__CLAUSES_c4: !t. t \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__ID: !t b. h4/bool/COND b t t = t
% Assm: h4/bool/FORALL__AND__THM: !Q P. (!x. P x /\ Q x) <=> (!x. P x) /\ (!x. Q x)
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/arithmetic/TWO: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/LE_c0: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm: h4/arithmetic/LE_c1: !n m. h4/arithmetic/_3C_3D m (h4/num/SUC n) <=> m = h4/num/SUC n \/ h4/arithmetic/_3C_3D m n
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/ieee/ccode__distinct_c1: ~(h4/ieee/Gt = h4/ieee/Eq)
% Assm: h4/ieee/ccode__distinct_c3: ~(h4/ieee/Lt = h4/ieee/Eq)
% Assm: h4/ieee/ccode__distinct_c5: ~(h4/ieee/Eq = h4/ieee/Un)
% Assm: h4/ieee/fcompare0: !b a X. h4/ieee/fcompare X a b = h4/bool/COND (h4/ieee/is__nan X a \/ h4/ieee/is__nan X b) h4/ieee/Un (h4/bool/COND (h4/ieee/is__infinity X a /\ h4/ieee/sign a = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/bool/COND (h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/ieee/Eq h4/ieee/Lt) (h4/bool/COND (h4/ieee/is__infinity X a /\ h4/ieee/sign a = h4/num/0) (h4/bool/COND (h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/num/0) h4/ieee/Eq h4/ieee/Gt) (h4/bool/COND (h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/ieee/Gt (h4/bool/COND (h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/num/0) h4/ieee/Lt (h4/bool/COND (h4/realax/real__lt (h4/ieee/valof X a) (h4/ieee/valof X b)) h4/ieee/Lt (h4/bool/COND (h4/ieee/valof X a = h4/ieee/valof X b) h4/ieee/Eq h4/ieee/Gt))))))
% Assm: h4/ieee/feq0: !b a X. h4/ieee/feq X a b <=> h4/ieee/fcompare X a b = h4/ieee/Eq
% Assm: h4/ieee/Isnan0: !a. h4/ieee/Isnan a <=> h4/ieee/is__nan h4/ieee/float__format (h4/ieee/defloat a)
% Assm: h4/ieee/Infinity0: !a. h4/ieee/Infinity a <=> h4/ieee/is__infinity h4/ieee/float__format (h4/ieee/defloat a)
% Assm: h4/ieee/float__eq0: !b a. h4/ieee/float__eq a b <=> h4/ieee/feq h4/ieee/float__format (h4/ieee/defloat a) (h4/ieee/defloat b)
% Assm: h4/float/IS__VALID: !a X. h4/ieee/is__valid X a <=> h4/prim__rec/_3C (h4/ieee/sign a) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) /\ h4/prim__rec/_3C (h4/ieee/exponent a) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/ieee/expwidth X)) /\ h4/prim__rec/_3C (h4/ieee/fraction a) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/ieee/fracwidth X))
% Assm: h4/float/IS__VALID__DEFLOAT: !a. h4/ieee/is__valid h4/ieee/float__format (h4/ieee/defloat a)
% Assm: h4/float/LT__SUC__LE: !n m. h4/prim__rec/_3C m (h4/num/SUC n) <=> h4/arithmetic/_3C_3D m n
% Assm: h4/float/FLOAT__CASES__FINITE: !a. h4/ieee/Isnan a \/ h4/ieee/Infinity a \/ h4/ieee/Finite a
% Assm: h4/float/FLOAT__DISTINCT__FINITE_c0: !a. ~(h4/ieee/Isnan a /\ h4/ieee/Infinity a)
% Assm: h4/float/FLOAT__DISTINCT__FINITE_c1: !a. ~(h4/ieee/Isnan a /\ h4/ieee/Finite a)
% Assm: h4/float/FLOAT__DISTINCT__FINITE_c2: !a. ~(h4/ieee/Infinity a /\ h4/ieee/Finite a)
% Assm: h4/float/FLOAT__INFINITIES__SIGNED_c0: h4/ieee/sign (h4/ieee/defloat h4/ieee/Plus__infinity) = h4/num/0
% Assm: h4/float/FLOAT__INFINITIES__SIGNED_c1: h4/ieee/sign (h4/ieee/defloat h4/ieee/Minus__infinity) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/float/INFINITY__IS__INFINITY_c0: h4/ieee/Infinity h4/ieee/Plus__infinity
% Assm: h4/float/INFINITY__IS__INFINITY_c1: h4/ieee/Infinity h4/ieee/Minus__infinity
% Assm: h4/float/INFINITY__NOT__NAN_c0: ~h4/ieee/Isnan h4/ieee/Plus__infinity
% Assm: h4/float/INFINITY__NOT__NAN_c1: ~h4/ieee/Isnan h4/ieee/Minus__infinity
% Goal: !a. h4/ieee/Infinity a <=> h4/ieee/float__eq a h4/ieee/Plus__infinity \/ h4/ieee/float__eq a h4/ieee/Minus__infinity
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c4]: !t. t \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_CONDu_u_ID]: !t b. h4/bool/COND b t t = t
% Assm [h4s_bools_FORALLu_u_ANDu_u_THM]: !Q P. (!x. happ P x /\ happ Q x) <=> (!x. happ P x) /\ (!x. happ Q x)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_arithmetics_TWO]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_LEu_c0]: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm [h4s_arithmetics_LEu_c1]: !n m. h4/arithmetic/_3C_3D m (h4/num/SUC n) <=> m = h4/num/SUC n \/ h4/arithmetic/_3C_3D m n
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_ieees_ccodeu_u_distinctu_c1]: ~(h4/ieee/Gt = h4/ieee/Eq)
% Assm [h4s_ieees_ccodeu_u_distinctu_c3]: ~(h4/ieee/Lt = h4/ieee/Eq)
% Assm [h4s_ieees_ccodeu_u_distinctu_c5]: ~(h4/ieee/Eq = h4/ieee/Un)
% Assm [h4s_ieees_fcompare0]: !b a X. ?v. (v <=> h4/ieee/valof X a = h4/ieee/valof X b) /\ (?v'. (v' <=> h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/num/0) /\ (?v''. (v'' <=> h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ (?v'''. (v''' <=> h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/num/0) /\ (?v''''. (v'''' <=> h4/ieee/is__infinity X a /\ h4/ieee/sign a = h4/num/0) /\ (?v'''''. (v''''' <=> h4/ieee/is__infinity X b /\ h4/ieee/sign b = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ (?v''''''. (v'''''' <=> h4/ieee/is__infinity X a /\ h4/ieee/sign a = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ (?v'''''''. (v''''''' <=> h4/ieee/is__nan X a \/ h4/ieee/is__nan X b) /\ h4/ieee/fcompare X a b = h4/bool/COND v''''''' h4/ieee/Un (h4/bool/COND v'''''' (h4/bool/COND v''''' h4/ieee/Eq h4/ieee/Lt) (h4/bool/COND v'''' (h4/bool/COND v''' h4/ieee/Eq h4/ieee/Gt) (h4/bool/COND v'' h4/ieee/Gt (h4/bool/COND v' h4/ieee/Lt (h4/bool/COND (h4/realax/real__lt (h4/ieee/valof X a) (h4/ieee/valof X b)) h4/ieee/Lt (h4/bool/COND v h4/ieee/Eq h4/ieee/Gt)))))))))))))
% Assm [h4s_ieees_feq0]: !b a X. h4/ieee/feq X a b <=> h4/ieee/fcompare X a b = h4/ieee/Eq
% Assm [h4s_ieees_Isnan0]: !a. h4/ieee/Isnan a <=> h4/ieee/is__nan h4/ieee/float__format (h4/ieee/defloat a)
% Assm [h4s_ieees_Infinity0]: !a. h4/ieee/Infinity a <=> h4/ieee/is__infinity h4/ieee/float__format (h4/ieee/defloat a)
% Assm [h4s_ieees_floatu_u_eq0]: !b a. h4/ieee/float__eq a b <=> h4/ieee/feq h4/ieee/float__format (h4/ieee/defloat a) (h4/ieee/defloat b)
% Assm [h4s_floats_ISu_u_VALID]: !a X. h4/ieee/is__valid X a <=> h4/prim__rec/_3C (h4/ieee/sign a) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) /\ h4/prim__rec/_3C (h4/ieee/exponent a) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/ieee/expwidth X)) /\ h4/prim__rec/_3C (h4/ieee/fraction a) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/ieee/fracwidth X))
% Assm [h4s_floats_ISu_u_VALIDu_u_DEFLOAT]: !a. h4/ieee/is__valid h4/ieee/float__format (h4/ieee/defloat a)
% Assm [h4s_floats_LTu_u_SUCu_u_LE]: !n m. h4/prim__rec/_3C m (h4/num/SUC n) <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_floats_FLOATu_u_CASESu_u_FINITE]: !a. h4/ieee/Isnan a \/ h4/ieee/Infinity a \/ h4/ieee/Finite a
% Assm [h4s_floats_FLOATu_u_DISTINCTu_u_FINITEu_c0]: !a. ~(h4/ieee/Isnan a /\ h4/ieee/Infinity a)
% Assm [h4s_floats_FLOATu_u_DISTINCTu_u_FINITEu_c1]: !a. ~(h4/ieee/Isnan a /\ h4/ieee/Finite a)
% Assm [h4s_floats_FLOATu_u_DISTINCTu_u_FINITEu_c2]: !a. ~(h4/ieee/Infinity a /\ h4/ieee/Finite a)
% Assm [h4s_floats_FLOATu_u_INFINITIESu_u_SIGNEDu_c0]: h4/ieee/sign (h4/ieee/defloat h4/ieee/Plus__infinity) = h4/num/0
% Assm [h4s_floats_FLOATu_u_INFINITIESu_u_SIGNEDu_c1]: h4/ieee/sign (h4/ieee/defloat h4/ieee/Minus__infinity) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_floats_INFINITYu_u_ISu_u_INFINITYu_c0]: h4/ieee/Infinity h4/ieee/Plus__infinity
% Assm [h4s_floats_INFINITYu_u_ISu_u_INFINITYu_c1]: h4/ieee/Infinity h4/ieee/Minus__infinity
% Assm [h4s_floats_INFINITYu_u_NOTu_u_NANu_c0]: ~h4/ieee/Isnan h4/ieee/Plus__infinity
% Assm [h4s_floats_INFINITYu_u_NOTu_u_NANu_c1]: ~h4/ieee/Isnan h4/ieee/Minus__infinity
% Goal: !a. h4/ieee/Infinity a <=> h4/ieee/float__eq a h4/ieee/Plus__infinity \/ h4/ieee/float__eq a h4/ieee/Minus__infinity
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q97670,TV_Q97666]: ![V_f, V_g]: (![V_x]: s(TV_Q97666,happ(s(t_fun(TV_Q97670,TV_Q97666),V_f),s(TV_Q97670,V_x))) = s(TV_Q97666,happ(s(t_fun(TV_Q97670,TV_Q97666),V_g),s(TV_Q97670,V_x))) => s(t_fun(TV_Q97670,TV_Q97666),V_f) = s(t_fun(TV_Q97670,TV_Q97666),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_CONDu_u_ID, axiom, ![TV_u_27a]: ![V_t, V_b]: s(TV_u_27a,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27a,V_t),s(TV_u_27a,V_t))) = s(TV_u_27a,V_t)).
fof(ah4s_bools_FORALLu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_arithmetics_ONE, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_TWO, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_LEu_c0, axiom, ![V_n]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0)))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_arithmetics_LEu_c1, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))) <=> (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_distribu_c17, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_numerals_numeralu_u_distribu_c18, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_ieees_ccodeu_u_distinctu_c1, axiom, ~ (s(t_h4s_ieees_ccode,h4s_ieees_gt) = s(t_h4s_ieees_ccode,h4s_ieees_eq))).
fof(ah4s_ieees_ccodeu_u_distinctu_c3, axiom, ~ (s(t_h4s_ieees_ccode,h4s_ieees_lt) = s(t_h4s_ieees_ccode,h4s_ieees_eq))).
fof(ah4s_ieees_ccodeu_u_distinctu_c5, axiom, ~ (s(t_h4s_ieees_ccode,h4s_ieees_eq) = s(t_h4s_ieees_ccode,h4s_ieees_un))).
fof(ah4s_ieees_fcompare0, axiom, ![V_b, V_a, V_X]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_realaxs_real,h4s_ieees_valof(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a))) = s(t_h4s_realaxs_real,h4s_ieees_valof(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b)))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> (p(s(t_bool,h4s_ieees_isu_u_infinity(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b)))) & s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b))) = s(t_h4s_nums_num,h4s_nums_0))) & ?[V_vi_i_]: ((p(s(t_bool,V_vi_i_)) <=> (p(s(t_bool,h4s_ieees_isu_u_infinity(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b)))) & s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) & ?[V_vi_i_i_]: ((p(s(t_bool,V_vi_i_i_)) <=> (p(s(t_bool,h4s_ieees_isu_u_infinity(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b)))) & s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b))) = s(t_h4s_nums_num,h4s_nums_0))) & ?[V_vi_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_)) <=> (p(s(t_bool,h4s_ieees_isu_u_infinity(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a)))) & s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a))) = s(t_h4s_nums_num,h4s_nums_0))) & ?[V_vi_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_)) <=> (p(s(t_bool,h4s_ieees_isu_u_infinity(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b)))) & s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) & ?[V_vi_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_)) <=> (p(s(t_bool,h4s_ieees_isu_u_infinity(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a)))) & s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) & ?[V_vi_i_i_i_i_i_i_]: ((p(s(t_bool,V_vi_i_i_i_i_i_i_)) <=> (p(s(t_bool,h4s_ieees_isu_u_nan(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a)))) | p(s(t_bool,h4s_ieees_isu_u_nan(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b)))))) & s(t_h4s_ieees_ccode,h4s_ieees_fcompare(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b))) = s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_i_),s(t_h4s_ieees_ccode,h4s_ieees_un),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_i_),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_),s(t_h4s_ieees_ccode,h4s_ieees_eq),s(t_h4s_ieees_ccode,h4s_ieees_lt))),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_vi_i_i_i_),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_vi_i_i_),s(t_h4s_ieees_ccode,h4s_ieees_eq),s(t_h4s_ieees_ccode,h4s_ieees_gt))),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_vi_i_),s(t_h4s_ieees_ccode,h4s_ieees_gt),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_ieees_ccode,h4s_ieees_lt),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_ieees_valof(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a))),s(t_h4s_realaxs_real,h4s_ieees_valof(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b))))),s(t_h4s_ieees_ccode,h4s_ieees_lt),s(t_h4s_ieees_ccode,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_ieees_ccode,h4s_ieees_eq),s(t_h4s_ieees_ccode,h4s_ieees_gt)))))))))))))))))))))))).
fof(ah4s_ieees_feq0, axiom, ![V_b, V_a, V_X]: (p(s(t_bool,h4s_ieees_feq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b)))) <=> s(t_h4s_ieees_ccode,h4s_ieees_fcompare(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_b))) = s(t_h4s_ieees_ccode,h4s_ieees_eq))).
fof(ah4s_ieees_Isnan0, axiom, ![V_a]: s(t_bool,h4s_ieees_isnan(s(t_h4s_ieees_float,V_a))) = s(t_bool,h4s_ieees_isu_u_nan(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_ieees_floatu_u_format),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_defloat(s(t_h4s_ieees_float,V_a)))))).
fof(ah4s_ieees_Infinity0, axiom, ![V_a]: s(t_bool,h4s_ieees_infinity(s(t_h4s_ieees_float,V_a))) = s(t_bool,h4s_ieees_isu_u_infinity(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_ieees_floatu_u_format),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_defloat(s(t_h4s_ieees_float,V_a)))))).
fof(ah4s_ieees_floatu_u_eq0, axiom, ![V_b, V_a]: s(t_bool,h4s_ieees_floatu_u_eq(s(t_h4s_ieees_float,V_a),s(t_h4s_ieees_float,V_b))) = s(t_bool,h4s_ieees_feq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_ieees_floatu_u_format),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_defloat(s(t_h4s_ieees_float,V_a))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_defloat(s(t_h4s_ieees_float,V_b)))))).
fof(ah4s_floats_ISu_u_VALID, axiom, ![V_a, V_X]: (p(s(t_bool,h4s_ieees_isu_u_valid(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) & (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_ieees_exponent(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_ieees_expwidth(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X)))))))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_ieees_fraction(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_a))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_ieees_fracwidth(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_X)))))))))))).
fof(ah4s_floats_ISu_u_VALIDu_u_DEFLOAT, axiom, ![V_a]: p(s(t_bool,h4s_ieees_isu_u_valid(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_ieees_floatu_u_format),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_defloat(s(t_h4s_ieees_float,V_a))))))).
fof(ah4s_floats_LTu_u_SUCu_u_LE, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_floats_FLOATu_u_CASESu_u_FINITE, axiom, ![V_a]: (p(s(t_bool,h4s_ieees_isnan(s(t_h4s_ieees_float,V_a)))) | (p(s(t_bool,h4s_ieees_infinity(s(t_h4s_ieees_float,V_a)))) | p(s(t_bool,h4s_ieees_finite(s(t_h4s_ieees_float,V_a))))))).
fof(ah4s_floats_FLOATu_u_DISTINCTu_u_FINITEu_c0, axiom, ![V_a]: ~ ((p(s(t_bool,h4s_ieees_isnan(s(t_h4s_ieees_float,V_a)))) & p(s(t_bool,h4s_ieees_infinity(s(t_h4s_ieees_float,V_a))))))).
fof(ah4s_floats_FLOATu_u_DISTINCTu_u_FINITEu_c1, axiom, ![V_a]: ~ ((p(s(t_bool,h4s_ieees_isnan(s(t_h4s_ieees_float,V_a)))) & p(s(t_bool,h4s_ieees_finite(s(t_h4s_ieees_float,V_a))))))).
fof(ah4s_floats_FLOATu_u_DISTINCTu_u_FINITEu_c2, axiom, ![V_a]: ~ ((p(s(t_bool,h4s_ieees_infinity(s(t_h4s_ieees_float,V_a)))) & p(s(t_bool,h4s_ieees_finite(s(t_h4s_ieees_float,V_a))))))).
fof(ah4s_floats_FLOATu_u_INFINITIESu_u_SIGNEDu_c0, axiom, s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_defloat(s(t_h4s_ieees_float,h4s_ieees_plusu_u_infinity))))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_floats_FLOATu_u_INFINITIESu_u_SIGNEDu_c1, axiom, s(t_h4s_nums_num,h4s_ieees_sign(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_defloat(s(t_h4s_ieees_float,h4s_ieees_minusu_u_infinity))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_floats_INFINITYu_u_ISu_u_INFINITYu_c0, axiom, p(s(t_bool,h4s_ieees_infinity(s(t_h4s_ieees_float,h4s_ieees_plusu_u_infinity))))).
fof(ah4s_floats_INFINITYu_u_ISu_u_INFINITYu_c1, axiom, p(s(t_bool,h4s_ieees_infinity(s(t_h4s_ieees_float,h4s_ieees_minusu_u_infinity))))).
fof(ah4s_floats_INFINITYu_u_NOTu_u_NANu_c0, axiom, ~ (p(s(t_bool,h4s_ieees_isnan(s(t_h4s_ieees_float,h4s_ieees_plusu_u_infinity)))))).
fof(ah4s_floats_INFINITYu_u_NOTu_u_NANu_c1, axiom, ~ (p(s(t_bool,h4s_ieees_isnan(s(t_h4s_ieees_float,h4s_ieees_minusu_u_infinity)))))).
fof(ch4s_floats_FLOATu_u_INFINITIES, conjecture, ![V_a]: (p(s(t_bool,h4s_ieees_infinity(s(t_h4s_ieees_float,V_a)))) <=> (p(s(t_bool,h4s_ieees_floatu_u_eq(s(t_h4s_ieees_float,V_a),s(t_h4s_ieees_float,h4s_ieees_plusu_u_infinity)))) | p(s(t_bool,h4s_ieees_floatu_u_eq(s(t_h4s_ieees_float,V_a),s(t_h4s_ieees_float,h4s_ieees_minusu_u_infinity))))))).
