%   ORIGINAL: h4/binary__ieee/zero__properties_c13
% 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__is__infinite__def: !x. h4/binary__ieee/float__is__infinite x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) (\v1. F) T F
% Assm: h4/bool/TRUTH: T
% Assm: h4/binary__ieee/float__sets_c1: h4/binary__ieee/float__is__infinite = h4/pred__set/INSERT (h4/binary__ieee/float__minus__infinity h4/bool/the__value) (h4/pred__set/INSERT (h4/binary__ieee/float__plus__infinity h4/bool/the__value) h4/pred__set/EMPTY)
% 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__value__case__def_c1: !v1 v f. h4/binary__ieee/float__value__CASE h4/binary__ieee/Infinity f v v1 = v
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/binary__ieee/zero__properties_c12: ~h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__plus__zero h4/bool/the__value)
% Assm: h4/binary__ieee/infinity__properties_c13: h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__minus__infinity h4/bool/the__value)
% Assm: h4/binary__ieee/infinity__properties_c12: h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__plus__infinity h4/bool/the__value)
% Assm: h4/binary__ieee/float__value__case__def_c0: !v1 v f a. h4/binary__ieee/float__value__CASE (h4/binary__ieee/Float a) f v v1 = f a
% Assm: h4/binary__ieee/float__values_c1: h4/binary__ieee/float__value0 (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/binary__ieee/Infinity
% Assm: h4/binary__ieee/float__values_c0: h4/binary__ieee/float__value0 (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/binary__ieee/Infinity
% 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/zero__properties_c7: ~h4/binary__ieee/float__is__nan (h4/binary__ieee/float__minus__zero 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_c21: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__top 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/zero__properties_c11: ~h4/binary__ieee/float__is__subnormal (h4/binary__ieee/float__minus__zero h4/bool/the__value)
% 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/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/bool/REFL__CLAUSE: !x. x = x <=> T
% 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/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/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/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__values_c4: 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)
% Assm: h4/binary__ieee/float__is__nan__def: !x. h4/binary__ieee/float__is__nan x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) (\v1. F) F T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% 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/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/numeral/numeral__distrib_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% 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/bool/NOT__CLAUSES_c1: ~T <=> F
% 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/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/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/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_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_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_c2: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/words/WORD__NOT__0: h4/words/word__1comp (h4/words/n2w h4/num/0) = h4/words/word__T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% 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_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_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_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_c13: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% 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/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__is__subnormal__def: !x. h4/binary__ieee/float__is__subnormal x <=> h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0 /\ ~(h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0)
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/bool/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/bool/LET__DEF: h4/bool/LET = (\f x. f x)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/binary__ieee/float__minus__infinity__def: h4/binary__ieee/float__minus__infinity h4/bool/the__value = h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__infinity h4/bool/the__value)
% Assm: h4/binary__ieee/float__plus__infinity__def: h4/binary__ieee/float__plus__infinity 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/word__T) (h4/binary__ieee/float__Significand__fupd (h4/combin/K (h4/words/n2w h4/num/0)) h4/bool/ARB))
% 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/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__value__case__def_c2: !v1 v f. h4/binary__ieee/float__value__CASE h4/binary__ieee/NaN f v v1 = v1
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/words/dimword__1: h4/words/dimword h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/words/dimindex__1: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/words/word__eq__n2w_c0: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/bit/MOD__2EXP__EQ (h4/fcp/dimindex h4/bool/the__value) m n
% Assm: h4/words/NUMERAL__LESS__THM_c0: !n m. h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) <=> m = h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) \/ h4/prim__rec/_3C m (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/words/ranged__word__nchotomy: !w. ?n. w = h4/words/n2w n /\ h4/prim__rec/_3C n (h4/words/dimword h4/bool/the__value)
% Assm: h4/numeral__bit/MOD__2EXP__EQ_c0: !b a. h4/bit/MOD__2EXP__EQ h4/num/0 a b <=> T
% Assm: h4/pred__set/IN__INSERT: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm: h4/pred__set/INSERT__applied: !y x s. h4/pred__set/INSERT y s x <=> x = y \/ h4/bool/IN x s
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% 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/words/NUMERAL__LESS__THM_c1: !n m. h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) <=> m = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) \/ h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))
% 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__bit/MOD__2EXP__EQ_c1: !n b a. h4/bit/MOD__2EXP__EQ (h4/num/SUC n) a b <=> (h4/arithmetic/ODD a <=> h4/arithmetic/ODD b) /\ h4/bit/MOD__2EXP__EQ n (h4/arithmetic/DIV2 a) (h4/arithmetic/DIV2 b)
% Assm: h4/numeral__bit/MOD__2EXP__EQ_c2: !n a. h4/bit/MOD__2EXP__EQ n a a <=> T
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% 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/numeral__evenodd_c5: !n. h4/arithmetic/ODD (h4/arithmetic/BIT1 n)
% 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__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__evenodd_c3: ~h4/arithmetic/ODD h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c20: !n. h4/prim__rec/_3C n h4/num/0 <=> F
% 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/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/numeral/numeral__distrib_c0: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm: h4/arithmetic/SUC__ELIM__NUMERALS: !g f. (!n. g (h4/num/SUC n) = f n (h4/num/SUC n)) <=> (!n. g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = f (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) /\ (!n. g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 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/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_c3: !n. h4/arithmetic/_2A h4/num/0 n = h4/num/0
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/arithmetic/SUB__0_c1: !m. h4/arithmetic/_2D m h4/num/0 = m
% Assm: h4/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/arithmetic/PRE__SUB1: !m. h4/prim__rec/PRE m = h4/arithmetic/_2D m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% 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/ALT__ZERO: h4/arithmetic/ZERO = h4/num/0
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% 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/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~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/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/words/word__sub__def: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% 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))
% Goal: ~h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__minus__zero h4/bool/the__value)
%   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_isu_u_infiniteu_u_def]: !_0. (!v1. happ _0 v1 <=> F) ==> (!x. happ h4/binary__ieee/float__is__infinite x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) _0 T F)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_binaryu_u_ieees_floatu_u_setsu_c1]: h4/binary__ieee/float__is__infinite = h4/pred__set/INSERT (h4/binary__ieee/float__minus__infinity h4/bool/the__value) (h4/pred__set/INSERT (h4/binary__ieee/float__plus__infinity h4/bool/the__value) h4/pred__set/EMPTY)
% 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''' <=> happ 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'''' <=> happ 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 \/ happ h4/binary__ieee/float__is__infinite x /\ h4/binary__ieee/float__is__zero y \/ h4/binary__ieee/float__is__zero x /\ happ h4/binary__ieee/float__is__infinite y \/ happ 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 <=> happ h4/binary__ieee/float__is__infinite x \/ happ 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_valueu_u_caseu_u_defu_c1]: !v1 v f. h4/binary__ieee/float__value__CASE h4/binary__ieee/Infinity f v v1 = v
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_binaryu_u_ieees_zerou_u_propertiesu_c12]: ~happ h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__plus__zero h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_infinityu_u_propertiesu_c13]: happ h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__minus__infinity h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_infinityu_u_propertiesu_c12]: happ h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__plus__infinity h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_valueu_u_caseu_u_defu_c0]: !v1 v f a. h4/binary__ieee/float__value__CASE (h4/binary__ieee/Float a) f v v1 = happ f a
% Assm [h4s_binaryu_u_ieees_floatu_u_valuesu_c1]: h4/binary__ieee/float__value0 (h4/binary__ieee/float__minus__infinity h4/bool/the__value) = h4/binary__ieee/Infinity
% Assm [h4s_binaryu_u_ieees_floatu_u_valuesu_c0]: h4/binary__ieee/float__value0 (h4/binary__ieee/float__plus__infinity h4/bool/the__value) = h4/binary__ieee/Infinity
% 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_zerou_u_propertiesu_c7]: ~h4/binary__ieee/float__is__nan (h4/binary__ieee/float__minus__zero 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_c21]: ~(h4/binary__ieee/float__minus__zero h4/bool/the__value = h4/binary__ieee/float__top 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_zerou_u_propertiesu_c11]: ~h4/binary__ieee/float__is__subnormal (h4/binary__ieee/float__minus__zero h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_valuesu_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 [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_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% 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_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_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_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_valuesu_c4]: 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)
% Assm [h4s_binaryu_u_ieees_floatu_u_isu_u_nanu_u_def]: !_0. (!v1. happ _0 v1 <=> F) ==> (!x. h4/binary__ieee/float__is__nan x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) _0 F T)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% 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_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% 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_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% 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_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_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_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_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_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_c2]: !f0 f. h4/binary__ieee/float__Exponent (h4/binary__ieee/float__Sign__fupd f0 f) = h4/binary__ieee/float__Exponent f
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_wordss_WORDu_u_NOTu_u_0]: h4/words/word__1comp (h4/words/n2w h4/num/0) = h4/words/word__T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> 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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_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_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_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_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_c13]: h4/binary__ieee/float__Exponent (h4/binary__ieee/float__plus__min h4/bool/the__value) = h4/words/n2w h4/num/0
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% 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_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_isu_u_subnormalu_u_def]: !x. h4/binary__ieee/float__is__subnormal x <=> h4/binary__ieee/float__Exponent x = h4/words/n2w h4/num/0 /\ ~(h4/binary__ieee/float__Significand x = h4/words/n2w h4/num/0)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_bools_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_bools_LETu_u_DEF]: !x x. h4/bool/LET x x = happ x x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_binaryu_u_ieees_floatu_u_minusu_u_infinityu_u_def]: h4/binary__ieee/float__minus__infinity h4/bool/the__value = h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__infinity h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_floatu_u_plusu_u_infinityu_u_def]: h4/binary__ieee/float__plus__infinity 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/word__T) (h4/binary__ieee/float__Significand__fupd (h4/combin/K (h4/words/n2w h4/num/0)) h4/bool/ARB))
% 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_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) (h4/binary__ieee/Float (h4/binary__ieee/float__to__real x)))
% Assm [h4s_binaryu_u_ieees_floatu_u_valueu_u_caseu_u_defu_c2]: !v1 v f. h4/binary__ieee/float__value__CASE h4/binary__ieee/NaN f v v1 = v1
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% 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_dimindexu_u_1]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_wordss_wordu_u_equ_u_n2wu_c0]: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/bit/MOD__2EXP__EQ (h4/fcp/dimindex h4/bool/the__value) m n
% Assm [h4s_wordss_NUMERALu_u_LESSu_u_THMu_c0]: !n m. h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) <=> m = h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) \/ h4/prim__rec/_3C m (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_wordss_rangedu_u_wordu_u_nchotomy]: !w. ?n. w = h4/words/n2w n /\ h4/prim__rec/_3C n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_numeralu_u_bits_MODu_u_2EXPu_u_EQu_c0]: !b a. h4/bit/MOD__2EXP__EQ h4/num/0 a b <=> T
% Assm [h4s_predu_u_sets_INu_u_INSERT]: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm [h4s_predu_u_sets_INSERTu_u_applied]: !y x s. happ (h4/pred__set/INSERT y s) x <=> x = y \/ h4/bool/IN x s
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% 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_wordss_NUMERALu_u_LESSu_u_THMu_c1]: !n m. h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) <=> m = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n) \/ h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))
% 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_numeralu_u_bits_MODu_u_2EXPu_u_EQu_c1]: !n b a. h4/bit/MOD__2EXP__EQ (h4/num/SUC n) a b <=> (h4/arithmetic/ODD a <=> h4/arithmetic/ODD b) /\ h4/bit/MOD__2EXP__EQ n (h4/arithmetic/DIV2 a) (h4/arithmetic/DIV2 b)
% Assm [h4s_numeralu_u_bits_MODu_u_2EXPu_u_EQu_c2]: !n a. h4/bit/MOD__2EXP__EQ n a a <=> T
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% 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_numeralu_u_evenoddu_c5]: !n. h4/arithmetic/ODD (h4/arithmetic/BIT1 n)
% 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_ltu_c3]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_evenoddu_c3]: ~h4/arithmetic/ODD h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c20]: !n. h4/prim__rec/_3C n h4/num/0 <=> F
% 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_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_numerals_numeralu_u_distribu_c0]: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm [h4s_arithmetics_SUCu_u_ELIMu_u_NUMERALS]: !g f. (!n. happ g (h4/num/SUC n) = happ (happ f n) (h4/num/SUC n)) <=> (!n. happ g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = happ (happ f (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) /\ (!n. happ g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = happ (happ f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 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_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_c3]: !n. h4/arithmetic/_2A h4/num/0 n = h4/num/0
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_arithmetics_SUBu_u_0u_c1]: !m. h4/arithmetic/_2D m h4/num/0 = m
% Assm [h4s_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_arithmetics_PREu_u_SUB1]: !m. h4/prim__rec/PRE m = h4/arithmetic/_2D m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% 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_ALTu_u_ZERO]: h4/arithmetic/ZERO = h4/num/0
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% 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_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~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_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_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_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))
% Goal: ~happ h4/binary__ieee/float__is__infinite (h4/binary__ieee/float__minus__zero h4/bool/the__value)
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_Q1187468,TV_Q1187464]: ![V_f, V_g]: (![V_x]: s(TV_Q1187464,happ(s(t_fun(TV_Q1187468,TV_Q1187464),V_f),s(TV_Q1187468,V_x))) = s(TV_Q1187464,happ(s(t_fun(TV_Q1187468,TV_Q1187464),V_g),s(TV_Q1187468,V_x))) => s(t_fun(TV_Q1187468,TV_Q1187464),V_f) = s(t_fun(TV_Q1187468,TV_Q1187464),V_g))).
fof(ah4s_binaryu_u_ieees_floatu_u_isu_u_infiniteu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_0]: (![V_v1]: s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_h4s_realaxs_real,V_v1))) = s(t_bool,f) => ![V_x]: s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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))) = s(t_bool,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(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_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_bool,t),s(t_bool,f))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_binaryu_u_ieees_floatu_u_setsu_c1, axiom, ![TV_u_27t,TV_u_27w]: s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_binaryu_u_ieees_floatu_u_isu_u_infinite) = s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_predu_u_sets_insert(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_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_predu_u_sets_insert(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_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_predu_u_sets_empty)))))).
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,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),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_valueu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f]: s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_infinity),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(TV_u_27a,V_v),s(TV_u_27a,V_v1))) = s(TV_u_27a,V_v)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_binaryu_u_ieees_zerou_u_propertiesu_c12, axiom, ![TV_u_27t,TV_u_27w]: ~ (p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_binaryu_u_ieees_floatu_u_isu_u_infinite),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_binaryu_u_ieees_infinityu_u_propertiesu_c13, axiom, ![TV_u_27t,TV_u_27w]: p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_binaryu_u_ieees_floatu_u_isu_u_infinite),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))))))).
fof(ah4s_binaryu_u_ieees_infinityu_u_propertiesu_c12, axiom, ![TV_u_27t,TV_u_27w]: p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_binaryu_u_ieees_floatu_u_isu_u_infinite),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))))))).
fof(ah4s_binaryu_u_ieees_floatu_u_valueu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f, V_a]: s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_float(s(t_h4s_realaxs_real,V_a))),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(TV_u_27a,V_v),s(TV_u_27a,V_v1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(t_h4s_realaxs_real,V_a)))).
fof(ah4s_binaryu_u_ieees_floatu_u_valuesu_c1, 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_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_floatu_u_value,h4s_binaryu_u_ieees_infinity)).
fof(ah4s_binaryu_u_ieees_floatu_u_valuesu_c0, 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_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_floatu_u_value,h4s_binaryu_u_ieees_infinity)).
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_zerou_u_propertiesu_c7, axiom, ![TV_u_27t,TV_u_27w]: ~ (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),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_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_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_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_zerou_u_propertiesu_c11, axiom, ![TV_u_27t,TV_u_27w]: ~ (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_subnormal(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_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,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_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_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_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_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_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_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_valuesu_c4, 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_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,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_binaryu_u_ieees_floatu_u_isu_u_nanu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_0]: (![V_v1]: s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_h4s_realaxs_real,V_v1))) = s(t_bool,f) => ![V_x]: 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))) = s(t_bool,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(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_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_bool,f),s(t_bool,t))))).
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_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_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_numerals_numeralu_u_distribu_c18, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_numerals_numeralu_u_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_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_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
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_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_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_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_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_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_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_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_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_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_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_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_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_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_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_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_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_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_isu_u_subnormalu_u_def, axiom, ![TV_u_27w,TV_u_27t]: ![V_x]: (p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_subnormal(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_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_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))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_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_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![V_x]: s(TV_u_27b,happ(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_g),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_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_binaryu_u_ieees_floatu_u_minusu_u_infinityu_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_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_negate(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)))))).
fof(ah4s_binaryu_u_ieees_floatu_u_plusu_u_infinityu_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_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_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_wordu_u_t))),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_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_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,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_valueu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f]: s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_nan),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(TV_u_27a,V_v),s(TV_u_27a,V_v1))) = s(TV_u_27a,V_v1)).
fof(ah4s_bools_CONJu_u_ASSOC, 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_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_dimindexu_u_1, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(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_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_wordss_wordu_u_equ_u_n2wu_c0, 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))) <=> p(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_wordss_NUMERALu_u_LESSu_u_THMu_c0, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))))))) <=> (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(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))))))) | p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(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))))))))))))).
fof(ah4s_wordss_rangedu_u_wordu_u_nchotomy, axiom, ![TV_u_27a]: ![V_w]: ?[V_n]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) & p(s(t_bool,h4s_primu_u_recs_u_3c(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_numeralu_u_bits_MODu_u_2EXPu_u_EQu_c0, axiom, ![V_b, V_a]: s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b))) = s(t_bool,t)).
fof(ah4s_predu_u_sets_INu_u_INSERT, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s)))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_INSERTu_u_applied, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27a,V_x)))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
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_wordss_NUMERALu_u_LESSu_u_THMu_c1, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n)))))))) <=> (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) | p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))))))).
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_numeralu_u_bits_MODu_u_2EXPu_u_EQu_c1, axiom, ![V_n, V_b, V_a]: (p(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b)))) <=> (s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_a))) = s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_b))) & p(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_b))))))))).
fof(ah4s_numeralu_u_bits_MODu_u_2EXPu_u_EQu_c2, axiom, ![V_n, V_a]: s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_a))) = s(t_bool,t)).
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_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
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_numeralu_u_evenoddu_c5, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))).
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_ltu_c3, axiom, ![V_n, V_m]: 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_bit1(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_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_evenoddu_c3, axiom, ~ (p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_numerals_numeralu_u_distribu_c20, 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_nums_0))) = s(t_bool,f)).
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_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_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_SUCu_u_ELIMu_u_NUMERALS, axiom, ![TV_u_27a]: ![V_g, V_f]: (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),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),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) <=> (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) & ![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(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_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_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_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_arithmetics_PREu_u_SUB1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_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_ALTu_u_ZERO, axiom, s(t_h4s_nums_num,h4s_arithmetics_zero) = s(t_h4s_nums_num,h4s_nums_0)).
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_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_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(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_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_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_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(ch4s_binaryu_u_ieees_zerou_u_propertiesu_c13, conjecture, ![TV_u_27t,TV_u_27w]: ~ (p(s(t_bool,happ(s(t_fun(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),t_bool),h4s_binaryu_u_ieees_floatu_u_isu_u_infinite),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)))))))).
