%   ORIGINAL: h4/binary__ieee/float__values_c4
% 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/binary__ieee/float__values_c3: h4/binary__ieee/float__value0 (h4/binary__ieee/float__plus__zero h4/bool/the__value) = h4/binary__ieee/Float (h4/real/real__of__num h4/num/0)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/itself__Axiom: !e. ?f. f h4/bool/the__value = e
% Assm: h4/binary__ieee/float__components_c11: h4/binary__ieee/float__Significand (h4/binary__ieee/float__minus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c10: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__minus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c9: h4/binary__ieee/float__Sign (h4/binary__ieee/float__minus__zero h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/words/n2w__11: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm: h4/binary__ieee/Float0: h4/binary__ieee/Float = h4/binary__ieee/_20_40ind__typebinary__ieee3
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/binary__ieee/float__div__def: !y x mode. h4/binary__ieee/float__div mode x y = h4/pair/pair__CASE (h4/pair/_2C (h4/binary__ieee/float__value0 x) (h4/binary__ieee/float__value0 y)) (\v v1. h4/binary__ieee/float__value__CASE v (\r1. h4/binary__ieee/float__value__CASE v1 (\r2. h4/bool/COND (r2 = h4/real/real__of__num h4/num/0) (h4/bool/COND (r1 = h4/real/real__of__num h4/num/0) (h4/binary__ieee/float__some__nan h4/bool/the__value) (h4/bool/COND (h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y) (h4/binary__ieee/float__plus__infinity h4/bool/the__value) (h4/binary__ieee/float__minus__infinity h4/bool/the__value))) (h4/binary__ieee/float__round mode (~(h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y)) (h4/real/_2F r1 r2))) (h4/bool/COND (h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y) (h4/binary__ieee/float__plus__zero h4/bool/the__value) (h4/binary__ieee/float__minus__zero h4/bool/the__value)) (h4/binary__ieee/float__some__nan h4/bool/the__value)) (h4/binary__ieee/float__value__CASE v1 (\v7. h4/bool/COND (h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y) (h4/binary__ieee/float__plus__infinity h4/bool/the__value) (h4/binary__ieee/float__minus__infinity h4/bool/the__value)) (h4/binary__ieee/float__some__nan h4/bool/the__value) (h4/binary__ieee/float__some__nan h4/bool/the__value)) (h4/binary__ieee/float__some__nan h4/bool/the__value))
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/words/WORD__NEG__1: h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/word__T
% Assm: h4/binary__ieee/float__value__def: !x. h4/binary__ieee/float__value0 x = h4/bool/COND (h4/binary__ieee/float__Exponent x = h4/words/word__T) (h4/bool/COND (h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0) h4/binary__ieee/Infinity h4/binary__ieee/NaN) (h4/binary__ieee/Float (h4/binary__ieee/float__to__real x))
% Assm: h4/binary__ieee/float__minus__zero__def: h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__zero h4/bool/the__value)
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/binary__ieee/datatype__float__value: !float__value. h4/bool/DATATYPE (float__value h4/binary__ieee/Float h4/binary__ieee/Infinity h4/binary__ieee/NaN)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/binary__ieee/float__component__equality: !f2 f1. f1 = f2 <=> h4/binary__ieee/float__Sign f1 = h4/binary__ieee/float__Sign f2 /\ h4/binary__ieee/float__Exponent f1 = h4/binary__ieee/float__Exponent f2 /\ h4/binary__ieee/float__Significand f1 = h4/binary__ieee/float__Significand f2
% Assm: h4/words/word__T__not__zero: ~(h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/n2w h4/num/0)
% Assm: h4/binary__ieee/float__mul__add__def: !z y x mode. h4/binary__ieee/float__mul__add mode x y z = h4/bool/LET (\signP. h4/bool/LET (\infP. h4/bool/COND (h4/binary__ieee/float__is__nan x \/ h4/binary__ieee/float__is__nan y \/ h4/binary__ieee/float__is__nan z \/ h4/binary__ieee/float__is__infinite x /\ h4/binary__ieee/float__is__zero y \/ h4/binary__ieee/float__is__zero x /\ h4/binary__ieee/float__is__infinite y \/ h4/binary__ieee/float__is__infinite z /\ infP /\ ~(h4/binary__ieee/float__Sign z = signP)) (h4/binary__ieee/float__some__nan h4/bool/the__value) (h4/bool/COND (h4/binary__ieee/float__is__infinite z /\ h4/binary__ieee/float__Sign z = h4/words/n2w h4/num/0 \/ infP /\ signP = h4/words/n2w h4/num/0) (h4/binary__ieee/float__plus__infinity h4/bool/the__value) (h4/bool/COND (h4/binary__ieee/float__is__infinite z /\ h4/binary__ieee/float__Sign z = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) \/ infP /\ signP = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/binary__ieee/float__minus__infinity h4/bool/the__value) (h4/bool/COND (h4/binary__ieee/float__is__zero z /\ (h4/binary__ieee/float__is__zero x \/ h4/binary__ieee/float__is__zero y) /\ h4/binary__ieee/float__Sign x = signP) (h4/bool/COND (h4/binary__ieee/float__Sign x = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/binary__ieee/float__minus__zero h4/bool/the__value) (h4/binary__ieee/float__plus__zero h4/bool/the__value)) (h4/binary__ieee/float__round mode (mode = h4/binary__ieee/roundTowardNegative) (h4/realax/real__add (h4/binary__ieee/float__to__real z) (h4/realax/real__mul (h4/binary__ieee/float__to__real x) (h4/binary__ieee/float__to__real y)))))))) (h4/binary__ieee/float__is__infinite x \/ h4/binary__ieee/float__is__infinite y)) (h4/words/word__xor (h4/binary__ieee/float__Sign x) (h4/binary__ieee/float__Sign y))
% Assm: h4/binary__ieee/float__round__def: !toneg r mode. h4/binary__ieee/float__round mode toneg r = h4/bool/LET (\x. h4/bool/COND (h4/binary__ieee/float__is__zero x) (h4/bool/COND toneg (h4/binary__ieee/float__minus__zero h4/bool/the__value) (h4/binary__ieee/float__plus__zero h4/bool/the__value)) x) (h4/binary__ieee/round mode r)
% Assm: h4/binary__ieee/float__distinct_c2: ~(h4/binary__ieee/float__plus__infinity h4/bool/the__value = h4/binary__ieee/float__minus__zero h4/bool/the__value)
% Assm: h4/binary__ieee/float__distinct_c25: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__some__nan h4/bool/the__value)
% Assm: h4/binary__ieee/float__distinct_c22: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__bottom h4/bool/the__value)
% Assm: h4/binary__ieee/float__distinct_c24: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__minus__min h4/bool/the__value)
% Assm: h4/binary__ieee/float__distinct_c9: ~(h4/binary__ieee/float__minus__infinity h4/bool/the__value = h4/binary__ieee/float__minus__zero h4/bool/the__value)
% Assm: h4/binary__ieee/float__distinct_c23: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__plus__min h4/bool/the__value)
% Assm: h4/binary__ieee/float__distinct_c15: ~(h4/binary__ieee/float__plus__zero h4/bool/the__value = h4/binary__ieee/float__minus__zero h4/bool/the__value)
% Assm: h4/binary__ieee/float__distinct_c21: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__top h4/bool/the__value)
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/binary__ieee/float__plus__zero__def: h4/binary__ieee/float__plus__zero h4/bool/the__value = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Significand__fupd (h4/combin/K (h4/words/n2w h4/num/0)) h4/bool/ARB))
% Assm: h4/binary__ieee/float__accfupds_c6: !f0 f. h4/binary__ieee/float__Sign (h4/binary__ieee/float__Sign__fupd f0 f) = f0 (h4/binary__ieee/float__Sign f)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/words/ZERO__LT__dimword: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/arithmetic/ZERO__MOD: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm: h4/binary__ieee/float__value__size__def_c0: !a. h4/binary__ieee/float__value__size (h4/binary__ieee/Float a) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/words/ONE__LT__dimword: h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/words/dimword h4/bool/the__value)
% Assm: h4/arithmetic/LESS__MOD: !n k. h4/prim__rec/_3C k n ==> h4/arithmetic/MOD k n = k
% Assm: h4/binary__ieee/float__accfupds_c7: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Exponent__fupd f0 f) = f0 (h4/binary__ieee/float__Exponent f)
% Assm: h4/binary__ieee/float__accfupds_c2: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm: h4/binary__ieee/float__accfupds_c5: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Exponent__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm: h4/binary__ieee/float__accfupds_c8: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Significand__fupd f0 f) = f0 (h4/binary__ieee/float__Significand f)
% Assm: h4/binary__ieee/float__accfupds_c4: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm: h4/numeral/numeral__distrib_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/binary__ieee/hidden____20__40ind____typebinary____ieee3____def: h4/binary__ieee/_20_40ind__typebinary__ieee3 = (\a. h4/binary__ieee/_20_40ind__typebinary__ieee6 ((\a0. h4/ind__type/CONSTR h4/num/0 a0 (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/binary__ieee/NaN0: h4/binary__ieee/NaN = h4/binary__ieee/_20_40ind__typebinary__ieee5
% Assm: h4/binary__ieee/Infinity0: h4/binary__ieee/Infinity = h4/binary__ieee/_20_40ind__typebinary__ieee4
% Assm: h4/binary__ieee/hidden____20__40ind____typebinary____ieee5____def: h4/binary__ieee/_20_40ind__typebinary__ieee5 = h4/binary__ieee/_20_40ind__typebinary__ieee6 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/binary__ieee/float__value__repfns_c1: !r. (\a0. !_27float__value_27. (!a00. (?a. a00 = (\a1. h4/ind__type/CONSTR h4/num/0 a1 (\n. h4/ind__type/BOTTOM)) a) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM) ==> _27float__value_27 a00) ==> _27float__value_27 a0) r <=> h4/binary__ieee/_20_40ind__typebinary__ieee7 (h4/binary__ieee/_20_40ind__typebinary__ieee6 r) = r
% Assm: h4/binary__ieee/hidden____20__40ind____typebinary____ieee4____def: h4/binary__ieee/_20_40ind__typebinary__ieee4 = h4/binary__ieee/_20_40ind__typebinary__ieee6 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/binary__ieee/float__negate__def: !x. h4/binary__ieee/float__negate x = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/word__1comp (h4/binary__ieee/float__Sign x))) x
% Assm: h4/binary__ieee/float__fupdfupds_c0: !g f0 f. h4/binary__ieee/float__Sign__fupd f0 (h4/binary__ieee/float__Sign__fupd g f) = h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g) f
% Assm: h4/words/WORD__NOT__0: h4/words/word__1comp (h4/words/n2w h4/num/0) = h4/words/word__T
% Assm: h4/combin/K__o__THM_c0: !v f. h4/combin/o (h4/combin/K v) f = h4/combin/K v
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/real/REAL__MUL__RID: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/real/eq__ints_c0: !n m. h4/real/real__of__num n = h4/real/real__of__num m <=> n = m
% Assm: h4/binary__ieee/float__to__real__def: !x. h4/binary__ieee/float__to__real x = h4/bool/COND (h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0) (h4/realax/real__mul (h4/realax/real__mul (h4/real/pow (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/words/w2n (h4/binary__ieee/float__Sign x))) (h4/real/_2F (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/words/INT__MAX h4/bool/the__value)))) (h4/real/_2F (h4/real/real__of__num (h4/words/w2n (h4/binary__ieee/float__Significand x))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/fcp/dimindex h4/bool/the__value)))) (h4/realax/real__mul (h4/realax/real__mul (h4/real/pow (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/words/w2n (h4/binary__ieee/float__Sign x))) (h4/real/_2F (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/words/w2n (h4/binary__ieee/float__Exponent x))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/words/INT__MAX h4/bool/the__value)))) (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/real/_2F (h4/real/real__of__num (h4/words/w2n (h4/binary__ieee/float__Significand x))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/fcp/dimindex h4/bool/the__value)))))
% Assm: h4/words/word__0__n2w: h4/words/w2n (h4/words/n2w h4/num/0) = h4/num/0
% Assm: h4/real/pow__rat_c0: !x. h4/real/pow x h4/num/0 = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/REAL__ADD__RID: !x. h4/realax/real__add x (h4/real/real__of__num h4/num/0) = x
% Assm: h4/real/REAL__MUL__RZERO: !x. h4/realax/real__mul x (h4/real/real__of__num h4/num/0) = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__MUL__LID: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm: h4/real/REAL__DIV__LZERO: !x. h4/real/_2F (h4/real/real__of__num h4/num/0) x = h4/real/real__of__num h4/num/0
% 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/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/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/words/WORD__LITERAL__ADD_c0: !n m. h4/words/word__add (h4/words/word__2comp (h4/words/n2w m)) (h4/words/word__2comp (h4/words/n2w n)) = h4/words/word__2comp (h4/words/n2w (h4/arithmetic/_2B m n))
% Assm: h4/words/word__sub__def: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/binary__ieee/float__components_c24: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__some__nan h4/bool/the__value) = h4/words/word__T
% Assm: h4/binary__ieee/float__components_c25: ~(h4/binary__ieee/float__Significand (h4/binary__ieee/float__some__nan h4/bool/the__value) = h4/words/n2w h4/num/0)
% Assm: h4/binary__ieee/float__components_c3: h4/binary__ieee/float__Sign (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/float__components_c4: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/words/word__T
% Assm: h4/binary__ieee/float__components_c5: h4/binary__ieee/float__Significand (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c16: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c15: h4/binary__ieee/float__Sign (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/float__components_c17: h4/binary__ieee/float__Significand (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/float__components_c8: h4/binary__ieee/float__Significand (h4/binary__ieee/float__plus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c7: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c6: h4/binary__ieee/float__Sign (h4/binary__ieee/float__plus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c13: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c14: h4/binary__ieee/float__Significand (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/float__components_c12: h4/binary__ieee/float__Sign (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c2: h4/binary__ieee/float__Significand (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c0: h4/binary__ieee/float__Sign (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/binary__ieee/float__components_c1: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/words/word__T
% Assm: h4/binary__ieee/float__components_c22: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__bottom h4/bool/the__value) = h4/words/word__sub h4/words/word__T (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/binary__ieee/float__components_c21: h4/binary__ieee/float__Sign (h4/binary__ieee/float__bottom h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/float__components_c23: h4/binary__ieee/float__Significand (h4/binary__ieee/float__bottom h4/bool/the__value) = h4/words/word__T
% Assm: h4/binary__ieee/float__components_c20: h4/binary__ieee/float__Significand (h4/binary__ieee/float__top h4/bool/the__value) = h4/words/word__T
% Assm: h4/binary__ieee/float__components_c19: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__top h4/bool/the__value) = h4/words/word__sub h4/words/word__T (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/binary__ieee/float__components_c18: h4/binary__ieee/float__Sign (h4/binary__ieee/float__top h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/bool/LET__DEF: h4/bool/LET = (\f x. f x)
% 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/words/dimword__1: h4/words/dimword h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/words/word__2comp__n2w: !n. h4/words/word__2comp (h4/words/n2w n) = h4/words/n2w (h4/arithmetic/_2D (h4/words/dimword h4/bool/the__value) (h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)))
% Assm: h4/numeral/numeral__sub: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm: h4/numeral/iSUB__THM_c8: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c22: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__distrib_c8: !n m. h4/arithmetic/_2D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m)
% Assm: h4/numeral/numeral__distrib_c3: !n. h4/arithmetic/_2A h4/num/0 n = h4/num/0
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/numeral/numeral__distrib_c0: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm: h4/arithmetic/DIVMOD__ID: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/DIV n n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) /\ h4/arithmetic/MOD n n = h4/num/0
% Assm: h4/arithmetic/MOD__UNIQUE: !r n k. (?q. k = h4/arithmetic/_2B (h4/arithmetic/_2A q n) r /\ h4/prim__rec/_3C r n) ==> h4/arithmetic/MOD k n = r
% Assm: h4/arithmetic/SUB__0_c1: !m. h4/arithmetic/_2D m h4/num/0 = m
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Goal: h4/binary__ieee/float__value0 (h4/binary__ieee/float__minus__zero h4/bool/the__value) = h4/binary__ieee/Float (h4/real/real__of__num h4/num/0)
%   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_binaryu_u_ieees_floatu_u_valuesu_c3]: h4/binary__ieee/float__value0 (h4/binary__ieee/float__plus__zero h4/bool/the__value) = happ h4/binary__ieee/Float (h4/real/real__of__num h4/num/0)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_itselfu_u_Axiom]: !e. ?f. happ f h4/bool/the__value = e
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c11]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__minus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c10]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__minus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c9]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__minus__zero h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_wordss_n2wu_u_11]: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_Float0]: h4/binary__ieee/Float = h4/binary__ieee/_20_40ind__typebinary__ieee3
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_binaryu_u_ieees_floatu_u_divu_u_def]: !_4. (!x y v7. ?v. (v <=> h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y) /\ happ (happ (happ _4 x) y) v7 = h4/bool/COND v (h4/binary__ieee/float__plus__infinity h4/bool/the__value) (h4/binary__ieee/float__minus__infinity h4/bool/the__value)) ==> (!_3. (!mode x y r1 r2. ?v. (v <=> ~(h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y)) /\ (?v'. (v' <=> h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y) /\ (?v''. (v'' <=> r1 = h4/real/real__of__num h4/num/0) /\ (?v'''. (v''' <=> r2 = h4/real/real__of__num h4/num/0) /\ happ (happ (happ (happ (happ _3 mode) x) y) r1) r2 = h4/bool/COND v''' (h4/bool/COND v'' (h4/binary__ieee/float__some__nan h4/bool/the__value) (h4/bool/COND v' (h4/binary__ieee/float__plus__infinity h4/bool/the__value) (h4/binary__ieee/float__minus__infinity h4/bool/the__value))) (h4/binary__ieee/float__round mode v (h4/real/_2F r1 r2)))))) ==> (!_2. (!v1 mode x y r1. ?v. (v <=> h4/binary__ieee/float__Sign x = h4/binary__ieee/float__Sign y) /\ happ (happ (happ (happ (happ _2 v1) mode) x) y) r1 = h4/binary__ieee/float__value__CASE v1 (happ (happ (happ (happ _3 mode) x) y) r1) (h4/bool/COND v (h4/binary__ieee/float__plus__zero h4/bool/the__value) (h4/binary__ieee/float__minus__zero h4/bool/the__value)) (h4/binary__ieee/float__some__nan h4/bool/the__value)) ==> (!_1. (!v mode x y v1. happ (happ (happ (happ (happ _1 v) mode) x) y) v1 = h4/binary__ieee/float__value__CASE v (happ (happ (happ (happ _2 v1) mode) x) y) (h4/binary__ieee/float__value__CASE v1 (happ (happ _4 x) y) (h4/binary__ieee/float__some__nan h4/bool/the__value) (h4/binary__ieee/float__some__nan h4/bool/the__value)) (h4/binary__ieee/float__some__nan h4/bool/the__value)) ==> (!_0. (!mode x y v. happ (happ (happ (happ _0 mode) x) y) v = happ (happ (happ (happ _1 v) mode) x) y) ==> (!y x mode. h4/binary__ieee/float__div mode x y = h4/pair/pair__CASE (h4/pair/_2C (h4/binary__ieee/float__value0 x) (h4/binary__ieee/float__value0 y)) (happ (happ (happ _0 mode) x) y))))))
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_wordss_WORDu_u_NEGu_u_1]: h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/word__T
% Assm [h4s_binaryu_u_ieees_floatu_u_valueu_u_def]: !x. ?v. (v <=> h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0) /\ (?v'. (v' <=> h4/binary__ieee/float__Exponent x = h4/words/word__T) /\ h4/binary__ieee/float__value0 x = h4/bool/COND v' (h4/bool/COND v h4/binary__ieee/Infinity h4/binary__ieee/NaN) (happ h4/binary__ieee/Float (h4/binary__ieee/float__to__real x)))
% Assm [h4s_binaryu_u_ieees_floatu_u_minusu_u_zerou_u_def]: h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__zero h4/bool/the__value)
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_binaryu_u_ieees_datatypeu_u_floatu_u_value]: !float__value. h4/bool/DATATYPE (happ (happ (happ float__value h4/binary__ieee/Float) h4/binary__ieee/Infinity) h4/binary__ieee/NaN)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_binaryu_u_ieees_floatu_u_componentu_u_equality]: !f2 f1. f1 = f2 <=> h4/binary__ieee/float__Sign f1 = h4/binary__ieee/float__Sign f2 /\ h4/binary__ieee/float__Exponent f1 = h4/binary__ieee/float__Exponent f2 /\ h4/binary__ieee/float__Significand f1 = h4/binary__ieee/float__Significand f2
% Assm [h4s_wordss_wordu_u_Tu_u_notu_u_zero]: ~(h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/n2w h4/num/0)
% Assm [h4s_binaryu_u_ieees_floatu_u_mulu_u_addu_u_def]: !_1. (!signP mode z x y infP. ?v. (v <=> mode = h4/binary__ieee/roundTowardNegative) /\ (?v'. (v' <=> h4/binary__ieee/float__Sign x = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ (?v''. (v'' <=> h4/binary__ieee/float__is__zero z /\ (h4/binary__ieee/float__is__zero x \/ h4/binary__ieee/float__is__zero y) /\ h4/binary__ieee/float__Sign x = signP) /\ (?v'''. (v''' <=> h4/binary__ieee/float__is__infinite z /\ h4/binary__ieee/float__Sign z = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) \/ infP /\ signP = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ (?v''''. (v'''' <=> h4/binary__ieee/float__is__infinite z /\ h4/binary__ieee/float__Sign z = h4/words/n2w h4/num/0 \/ infP /\ signP = h4/words/n2w h4/num/0) /\ (?v'''''. (v''''' <=> h4/binary__ieee/float__is__nan x \/ h4/binary__ieee/float__is__nan y \/ h4/binary__ieee/float__is__nan z \/ h4/binary__ieee/float__is__infinite x /\ h4/binary__ieee/float__is__zero y \/ h4/binary__ieee/float__is__zero x /\ h4/binary__ieee/float__is__infinite y \/ h4/binary__ieee/float__is__infinite z /\ infP /\ ~(h4/binary__ieee/float__Sign z = signP)) /\ happ (happ (happ (happ (happ (happ _1 signP) mode) z) x) y) infP = h4/bool/COND v''''' (h4/binary__ieee/float__some__nan h4/bool/the__value) (h4/bool/COND v'''' (h4/binary__ieee/float__plus__infinity h4/bool/the__value) (h4/bool/COND v''' (h4/binary__ieee/float__minus__infinity h4/bool/the__value) (h4/bool/COND v'' (h4/bool/COND v' (h4/binary__ieee/float__minus__zero h4/bool/the__value) (h4/binary__ieee/float__plus__zero h4/bool/the__value)) (h4/binary__ieee/float__round mode v (h4/realax/real__add (h4/binary__ieee/float__to__real z) (h4/realax/real__mul (h4/binary__ieee/float__to__real x) (h4/binary__ieee/float__to__real y))))))))))))) ==> (!_0. (!mode z x y signP. ?v. (v <=> h4/binary__ieee/float__is__infinite x \/ h4/binary__ieee/float__is__infinite y) /\ happ (happ (happ (happ (happ _0 mode) z) x) y) signP = h4/bool/LET (happ (happ (happ (happ (happ _1 signP) mode) z) x) y) v) ==> (!z y x mode. h4/binary__ieee/float__mul__add mode x y z = h4/bool/LET (happ (happ (happ (happ _0 mode) z) x) y) (h4/words/word__xor (h4/binary__ieee/float__Sign x) (h4/binary__ieee/float__Sign y))))
% Assm [h4s_binaryu_u_ieees_floatu_u_roundu_u_def]: !_0. (!toneg x. happ (happ _0 toneg) x = h4/bool/COND (h4/binary__ieee/float__is__zero x) (h4/bool/COND toneg (h4/binary__ieee/float__minus__zero h4/bool/the__value) (h4/binary__ieee/float__plus__zero h4/bool/the__value)) x) ==> (!toneg r mode. h4/binary__ieee/float__round mode toneg r = h4/bool/LET (happ _0 toneg) (h4/binary__ieee/round mode r))
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c2]: ~(h4/binary__ieee/float__plus__infinity h4/bool/the__value = h4/binary__ieee/float__minus__zero h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c25]: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__some__nan h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c22]: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__bottom h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c24]: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__minus__min h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c9]: ~(h4/binary__ieee/float__minus__infinity h4/bool/the__value = h4/binary__ieee/float__minus__zero h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c23]: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__plus__min h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c15]: ~(h4/binary__ieee/float__plus__zero h4/bool/the__value = h4/binary__ieee/float__minus__zero h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_distinctu_c21]: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__top h4/bool/the__value)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_binaryu_u_ieees_floatu_u_plusu_u_zerou_u_def]: h4/binary__ieee/float__plus__zero h4/bool/the__value = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Exponent__fupd (h4/combin/K (h4/words/n2w h4/num/0)) (h4/binary__ieee/float__Significand__fupd (h4/combin/K (h4/words/n2w h4/num/0)) h4/bool/ARB))
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c6]: !f0 f. h4/binary__ieee/float__Sign (h4/binary__ieee/float__Sign__fupd f0 f) = happ f0 (h4/binary__ieee/float__Sign f)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_wordss_ZEROu_u_LTu_u_dimword]: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_arithmetics_ZEROu_u_MOD]: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_valueu_u_sizeu_u_defu_c0]: !a. h4/binary__ieee/float__value__size (happ h4/binary__ieee/Float a) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_wordss_ONEu_u_LTu_u_dimword]: h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/words/dimword h4/bool/the__value)
% Assm [h4s_arithmetics_LESSu_u_MOD]: !n k. h4/prim__rec/_3C k n ==> h4/arithmetic/MOD k n = k
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c7]: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Exponent__fupd f0 f) = happ f0 (h4/binary__ieee/float__Exponent f)
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c2]: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c5]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Exponent__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c8]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Significand__fupd f0 f) = happ f0 (h4/binary__ieee/float__Significand f)
% Assm [h4s_binaryu_u_ieees_floatu_u_accfupdsu_c4]: !f0 f. h4/binary__ieee/float__Significand (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Significand f
% Assm [h4s_numerals_numeralu_u_distribu_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm [h4s_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee3u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/binary__ieee/_20_40ind__typebinary__ieee3 x = h4/binary__ieee/_20_40ind__typebinary__ieee6 (h4/ind__type/CONSTR h4/num/0 x _0))
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = happ f n
% Assm [h4s_binaryu_u_ieees_NaN0]: h4/binary__ieee/NaN = h4/binary__ieee/_20_40ind__typebinary__ieee5
% Assm [h4s_binaryu_u_ieees_Infinity0]: h4/binary__ieee/Infinity = h4/binary__ieee/_20_40ind__typebinary__ieee4
% Assm [h4s_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/binary__ieee/_20_40ind__typebinary__ieee5 = h4/binary__ieee/_20_40ind__typebinary__ieee6 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0)
% Assm [h4s_binaryu_u_ieees_floatu_u_valueu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27float__value_27. (!a00. (?a. a00 = h4/ind__type/CONSTR h4/num/0 a _0) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB _0 \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0 ==> happ _27float__value_27 a00) ==> happ _27float__value_27 r) <=> h4/binary__ieee/_20_40ind__typebinary__ieee7 (h4/binary__ieee/_20_40ind__typebinary__ieee6 r) = r)
% Assm [h4s_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/binary__ieee/_20_40ind__typebinary__ieee4 = h4/binary__ieee/_20_40ind__typebinary__ieee6 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB _0)
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_binaryu_u_ieees_floatu_u_negateu_u_def]: !x. h4/binary__ieee/float__negate x = h4/binary__ieee/float__Sign__fupd (h4/combin/K (h4/words/word__1comp (h4/binary__ieee/float__Sign x))) x
% Assm [h4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c0]: !g f0 f. h4/binary__ieee/float__Sign__fupd f0 (h4/binary__ieee/float__Sign__fupd g f) = h4/binary__ieee/float__Sign__fupd (h4/combin/o f0 g) f
% Assm [h4s_wordss_WORDu_u_NOTu_u_0]: h4/words/word__1comp (h4/words/n2w h4/num/0) = h4/words/word__T
% Assm [h4s_combins_Ku_u_ou_u_THMu_c0]: !v f. h4/combin/o (h4/combin/K v) f = h4/combin/K v
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_reals_REALu_u_MULu_u_RID]: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_reals_equ_u_intsu_c0]: !n m. h4/real/real__of__num n = h4/real/real__of__num m <=> n = m
% Assm [h4s_binaryu_u_ieees_floatu_u_tou_u_realu_u_def]: !x. ?v. (v <=> h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0) /\ h4/binary__ieee/float__to__real x = h4/bool/COND v (h4/realax/real__mul (h4/realax/real__mul (h4/real/pow (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/words/w2n (h4/binary__ieee/float__Sign x))) (h4/real/_2F (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/words/INT__MAX h4/bool/the__value)))) (h4/real/_2F (h4/real/real__of__num (h4/words/w2n (h4/binary__ieee/float__Significand x))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/fcp/dimindex h4/bool/the__value)))) (h4/realax/real__mul (h4/realax/real__mul (h4/real/pow (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/words/w2n (h4/binary__ieee/float__Sign x))) (h4/real/_2F (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/words/w2n (h4/binary__ieee/float__Exponent x))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/words/INT__MAX h4/bool/the__value)))) (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/real/_2F (h4/real/real__of__num (h4/words/w2n (h4/binary__ieee/float__Significand x))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/fcp/dimindex h4/bool/the__value)))))
% Assm [h4s_wordss_wordu_u_0u_u_n2w]: h4/words/w2n (h4/words/n2w h4/num/0) = h4/num/0
% Assm [h4s_reals_powu_u_ratu_c0]: !x. h4/real/pow x h4/num/0 = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_reals_REALu_u_ADDu_u_RID]: !x. h4/realax/real__add x (h4/real/real__of__num h4/num/0) = x
% Assm [h4s_reals_REALu_u_MULu_u_RZERO]: !x. h4/realax/real__mul x (h4/real/real__of__num h4/num/0) = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_MULu_u_LID]: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm [h4s_reals_REALu_u_DIVu_u_LZERO]: !x. h4/real/_2F (h4/real/real__of__num h4/num/0) x = h4/real/real__of__num h4/num/0
% 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_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_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_wordss_WORDu_u_LITERALu_u_ADDu_c0]: !n m. h4/words/word__add (h4/words/word__2comp (h4/words/n2w m)) (h4/words/word__2comp (h4/words/n2w n)) = h4/words/word__2comp (h4/words/n2w (h4/arithmetic/_2B m n))
% Assm [h4s_wordss_wordu_u_subu_u_def]: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_addu_c1]: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c24]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__some__nan h4/bool/the__value) = h4/words/word__T
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c25]: ~(h4/binary__ieee/float__Significand (h4/binary__ieee/float__some__nan h4/bool/the__value) = h4/words/n2w h4/num/0)
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c3]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c4]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/words/word__T
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c5]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c16]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c15]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c17]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c8]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__plus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c7]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c6]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__plus__zero h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c13]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c14]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c12]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c2]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c0]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c1]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/words/word__T
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c22]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__bottom h4/bool/the__value) = h4/words/word__sub h4/words/word__T (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c21]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__bottom h4/bool/the__value) = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c23]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__bottom h4/bool/the__value) = h4/words/word__T
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c20]: h4/binary__ieee/float__Significand (h4/binary__ieee/float__top h4/bool/the__value) = h4/words/word__T
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c19]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__top h4/bool/the__value) = h4/words/word__sub h4/words/word__T (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_binaryu_u_ieees_floatu_u_componentsu_c18]: h4/binary__ieee/float__Sign (h4/binary__ieee/float__top h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_bools_LETu_u_DEF]: !x x. h4/bool/LET x x = happ x x
% 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_wordss_dimwordu_u_1]: h4/words/dimword h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm [h4s_wordss_wordu_u_2compu_u_n2w]: !n. h4/words/word__2comp (h4/words/n2w n) = h4/words/n2w (h4/arithmetic/_2D (h4/words/dimword h4/bool/the__value) (h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)))
% Assm [h4s_numerals_numeralu_u_sub]: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm [h4s_numerals_iSUBu_u_THMu_c8]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_distribu_c8]: !n m. h4/arithmetic/_2D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m)
% Assm [h4s_numerals_numeralu_u_distribu_c3]: !n. h4/arithmetic/_2A h4/num/0 n = h4/num/0
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm [h4s_numerals_numeralu_u_distribu_c0]: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm [h4s_arithmetics_DIVMODu_u_ID]: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/DIV n n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) /\ h4/arithmetic/MOD n n = h4/num/0
% Assm [h4s_arithmetics_MODu_u_UNIQUE]: !r n k. (?q. k = h4/arithmetic/_2B (h4/arithmetic/_2A q n) r /\ h4/prim__rec/_3C r n) ==> h4/arithmetic/MOD k n = r
% Assm [h4s_arithmetics_SUBu_u_0u_c1]: !m. h4/arithmetic/_2D m h4/num/0 = m
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Goal: h4/binary__ieee/float__value0 (h4/binary__ieee/float__minus__zero h4/bool/the__value) = happ h4/binary__ieee/Float (h4/real/real__of__num h4/num/0)
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_Q1186068,TV_Q1186064]: ![V_f, V_g]: (![V_x]: s(TV_Q1186064,happ(s(t_fun(TV_Q1186068,TV_Q1186064),V_f),s(TV_Q1186068,V_x))) = s(TV_Q1186064,happ(s(t_fun(TV_Q1186068,TV_Q1186064),V_g),s(TV_Q1186068,V_x))) => s(t_fun(TV_Q1186068,TV_Q1186064),V_f) = s(t_fun(TV_Q1186068,TV_Q1186064),V_g))).
fof(ah4s_binaryu_u_ieees_floatu_u_valuesu_c3, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_binaryu_u_ieees_floatu_u_value,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_float),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_itselfu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_e]: ?[V_f]: s(TV_u_27a,happ(s(t_fun(t_h4s_bools_itself(TV_u_27b),TV_u_27a),V_f),s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))) = s(TV_u_27a,V_e)).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c11, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c10, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c9, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(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_wordss_n2wu_u_11, axiom, ![TV_u_27a]: ![V_n, V_m]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_binaryu_u_ieees_Float0, axiom, s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_float) = s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee3)).
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_binaryu_u_ieees_floatu_u_divu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_4]: (![V_x, V_y, V_v7]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y)))) & s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),V_uu_4),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_realaxs_real,V_v7))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value)))))) => ![V_uu_3]: (![V_mode, V_x, V_y, V_r1, V_r2]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ~ (s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y)))) & ?[V_vi_i_]: ((p(s(t_bool,V_vi_i_)) <=> s(t_h4s_realaxs_real,V_r1) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & ?[V_vi_i_i_]: ((p(s(t_bool,V_vi_i_i_)) <=> s(t_h4s_realaxs_real,V_r2) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_3),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_realaxs_real,V_r1))),s(t_h4s_realaxs_real,V_r2))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_i_i_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_i_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_bool,V_v),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_r1),s(t_h4s_realaxs_real,V_r2))))))))))) => ![V_uu_2]: (![V_v1, V_mode, V_x, V_y, V_r1]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y)))) & s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_2),s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v1))),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_realaxs_real,V_r1))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v1),s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_3),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_realaxs_real,V_r1))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value)))))) => ![V_uu_1]: (![V_v, V_mode, V_x, V_y, V_v1]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_1),s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v))),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v1))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v),s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_2),s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v1))),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v1),s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),V_uu_4),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) => ![V_uu_0]: (![V_mode, V_x, V_y, V_v]: s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_0),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v))) = s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_1),s(t_h4s_binaryu_u_ieees_floatu_u_value,V_v))),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))) => ![V_y, V_x, V_mode]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_div(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_pairs_u_2c(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))))),s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_0),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))))))))))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_wordss_WORDu_u_NEGu_u_1, axiom, ![TV_u_27a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(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_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_binaryu_u_ieees_floatu_u_valueu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_x]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_t)) & s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_infinity),s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_nan))),s(t_h4s_binaryu_u_ieees_floatu_u_value,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_float),s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_minusu_u_zerou_u_def, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_negate(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value)))))).
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_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_binaryu_u_ieees_datatypeu_u_floatu_u_value, axiom, ![V_floatu_u_value]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_bool),happ(s(t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_bool)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_fun(t_h4s_binaryu_u_ieees_floatu_u_value,t_bool))),V_floatu_u_value),s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_float))),s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_infinity))),s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_nan))))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentu_u_equality, axiom, ![TV_u_27t,TV_u_27w]: ![V_f2, V_f1]: (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2) <=> (s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2))) & (s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2))) & s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f1))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f2))))))).
fof(ah4s_wordss_wordu_u_Tu_u_notu_u_zero, axiom, ![TV_u_27a]: ~ (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(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_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_binaryu_u_ieees_floatu_u_mulu_u_addu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_1]: (![V_signP, V_mode, V_z, V_x, V_y, V_infP]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_binaryu_u_ieees_rounding,V_mode) = s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtowardnegative)) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(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_]: ((p(s(t_bool,V_vi_i_)) <=> (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z)))) & ((p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))) | p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))))) & s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_signP)))) & ?[V_vi_i_i_]: ((p(s(t_bool,V_vi_i_i_)) <=> ((p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_infinite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z)))) & s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))) | (p(s(t_bool,V_infP)) & s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_signP) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(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_]: ((p(s(t_bool,V_vi_i_i_i_)) <=> ((p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_infinite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z)))) & s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) | (p(s(t_bool,V_infP)) & s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_signP) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_isu_u_nan(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))) | (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_nan(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y)))) | (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_nan(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z)))) | ((p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_infinite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))) & p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))))) | ((p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))) & p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_infinite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))))) | (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_infinite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z)))) & (p(s(t_bool,V_infP)) & ~ (s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_signP)))))))))) & s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))))),V_uu_1),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_signP))),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_bool,V_infP))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_i_i_i_i_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_i_i_i_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_i_i_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_i_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_bool,V_v),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))))))))))))))))))))))) => ![V_uu_0]: (![V_mode, V_z, V_x, V_y, V_signP]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_infinite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))) | p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_infinite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y)))))) & s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_0),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_signP))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_let(s(t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_bool,t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))))),V_uu_1),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_signP))),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_bool,V_v)))) => ![V_z, V_y, V_x, V_mode]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_mulu_u_add(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_rounding,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)))))),V_uu_0),s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_z))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y))),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_y)))))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_roundu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_0]: (![V_toneg, V_x]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_bool,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),V_uu_0),s(t_bool,V_toneg))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_zero(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_cond(s(t_bool,V_toneg),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) => ![V_toneg, V_r, V_mode]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_bool,V_toneg),s(t_h4s_realaxs_real,V_r))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_let(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w)),happ(s(t_fun(t_bool,t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w))),V_uu_0),s(t_bool,V_toneg))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_round(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_realaxs_real,V_r))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c2, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c25, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c22, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_bottom(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c24, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c9, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c23, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c15, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
fof(ah4s_binaryu_u_ieees_floatu_u_distinctu_c21, axiom, ![TV_u_27t,TV_u_27w]: ~ (s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_top(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))).
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_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_binaryu_u_ieees_floatu_u_plusu_u_zerou_u_def, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_bools_arb)))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c6, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
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_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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_wordss_ZEROu_u_LTu_u_dimword, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
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_arithmetics_ZEROu_u_MOD, axiom, ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(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_binaryu_u_ieees_floatu_u_valueu_u_sizeu_u_defu_c0, axiom, ![V_a]: s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_valueu_u_size(s(t_h4s_binaryu_u_ieees_floatu_u_value,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_float),s(t_h4s_realaxs_real,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)))))).
fof(ah4s_wordss_ONEu_u_LTu_u_dimword, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(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_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_arithmetics_LESSu_u_MOD, axiom, ![V_n, V_k]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_k))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c7, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c2, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c5, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponentu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_fcps_cart(t_bool,TV_u_27w)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c8, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_significandu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27t),t_h4s_fcps_cart(t_bool,TV_u_27t)),V_f0),s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_accfupdsu_c4, axiom, ![TV_u_27t,TV_u_27w]: ![V_f0, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
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_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee3u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_binaryu_u_ieees_floatu_u_value,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee3),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee6(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_realaxs_real,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))))).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_binaryu_u_ieees_NaN0, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_nan) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee5)).
fof(ah4s_binaryu_u_ieees_Infinity0, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_infinity) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee4)).
fof(ah4s_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee5u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee5) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee6(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_valueu_u_repfnsu_c1, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27floatu_u_valueu_27]: (![V_a00]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_realaxs_real,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))) | (s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))) | s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_27floatu_u_valueu_27),s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_27floatu_u_valueu_27),s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee7(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee6(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_r)))).
fof(ah4s_binaryu_u_ieees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typebinaryu_u_u_u_ieee4u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee4) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_u_20u_40indu_u_typebinaryu_u_ieee6(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => 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,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_negateu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_x]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_negate(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_k(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))))))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x)))).
fof(ah4s_binaryu_u_ieees_floatu_u_fupdfupdsu_c0, axiom, ![TV_u_27t,TV_u_27w]: ![V_g, V_f0, V_f]: s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f))))) = s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_signu_u_fupd(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_f0),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),t_h4s_fcps_cart(t_bool,t_h4s_ones_one)),V_g))),s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_f)))).
fof(ah4s_wordss_WORDu_u_NOTu_u_0, axiom, ![TV_u_27a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_combins_Ku_u_ou_u_THMu_c0, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_v, V_f]: s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),h4s_combins_k(s(TV_u_27c,V_v))),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_k(s(TV_u_27c,V_v)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_reals_REALu_u_MULu_u_RID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,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_reals_equ_u_intsu_c0, axiom, ![V_n, V_m]: (s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_binaryu_u_ieees_floatu_u_tou_u_realu_u_def, axiom, ![TV_u_27w,TV_u_27t]: ![V_x]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) & s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_h4s_realaxs_real,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_wordss_w2n(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))))))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_wordss_intu_u_max(s(t_h4s_bools_itself(TV_u_27w),h4s_bools_theu_u_value))))))))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27t),h4s_bools_theu_u_value))))))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_wordss_w2n(s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))))))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_wordss_intu_u_max(s(t_h4s_bools_itself(TV_u_27w),h4s_bools_theu_u_value))))))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27t),h4s_bools_theu_u_value))))))))))))))).
fof(ah4s_wordss_wordu_u_0u_u_n2w, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_reals_powu_u_ratu_c0, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_reals_REALu_u_ADDu_u_RID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_MULu_u_RZERO, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_reals_REALu_u_MULu_u_LID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_DIVu_u_LZERO, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
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_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_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_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_wordss_WORDu_u_LITERALu_u_ADDu_c0, axiom, ![TV_u_27a]: ![V_n, V_m]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_wordss_wordu_u_subu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_addu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c24, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_t)).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c25, axiom, ![TV_u_27w,TV_u_27t]: ~ (s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_someu_u_nan(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c3, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_componentsu_c4, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_t)).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c5, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c16, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c15, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_componentsu_c17, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_componentsu_c8, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c7, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c6, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c13, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c14, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_componentsu_c12, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c2, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c0, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c1, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_infinity(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_t)).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c22, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_bottom(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_t),s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_componentsu_c21, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_bottom(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_componentsu_c23, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_bottom(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_wordu_u_t)).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c20, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_binaryu_u_ieees_floatu_u_significand(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_top(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27t),h4s_wordss_wordu_u_t)).
fof(ah4s_binaryu_u_ieees_floatu_u_componentsu_c19, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_exponent(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_top(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_wordu_u_t),s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(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_binaryu_u_ieees_floatu_u_componentsu_c18, axiom, ![TV_u_27t,TV_u_27w]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_binaryu_u_ieees_floatu_u_sign(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_top(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_bools_LETu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0)))).
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_wordss_dimwordu_u_1, axiom, s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(t_h4s_ones_one),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_wordss_wordu_u_2compu_u_n2w, axiom, ![TV_u_27a]: ![V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))))).
fof(ah4s_numerals_numeralu_u_sub, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_numerals_iSUBu_u_THMu_c8, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_distribu_c8, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_numeralu_u_distribu_c3, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m)))))) <=> ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_distribu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_DIVMODu_u_ID, axiom, ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => (s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n))) = 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_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_MODu_u_UNIQUE, axiom, ![V_r, V_n, V_k]: (?[V_q]: (s(t_h4s_nums_num,V_k) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_q),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_r))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_r),s(t_h4s_nums_num,V_n))))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_arithmetics_SUBu_u_0u_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_numerals_iSUBu_u_THMu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ch4s_binaryu_u_ieees_floatu_u_valuesu_c4, conjecture, ![TV_u_27t,TV_u_27w]: s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_zero(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_binaryu_u_ieees_floatu_u_value,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_binaryu_u_ieees_floatu_u_value),h4s_binaryu_u_ieees_float),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
