%   ORIGINAL: h4/bitstring/length__bitify__null
% 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/bitstring/v2n__def: !l. h4/bitstring/v2n l = h4/numposrep/num__from__bin__list (h4/bitstring/bitify h4/list/NIL l)
% Assm: h4/bitstring/every__bit__bitify: !v. h4/list/EVERY (h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/bitstring/bitify h4/list/NIL v)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bitstring/bitify__reverse__map: !v a. h4/bitstring/bitify a v = h4/list/APPEND (h4/list/REVERSE (h4/list/MAP (\b. h4/bool/COND b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/num/0) v)) a
% Assm: h4/bitstring/length__bitify: !v l. h4/list/LENGTH (h4/bitstring/bitify l v) = h4/arithmetic/_2B (h4/list/LENGTH l) (h4/list/LENGTH v)
% Assm: h4/bitstring/bitify__curried__def: !x1 x. h4/bitstring/bitify x x1 = h4/bitstring/bitify__tupled (h4/pair/_2C x x1)
% Assm: h4/bitstring/fixwidth__def: !v n. h4/bitstring/fixwidth n v = h4/bool/LET (\l. h4/bool/COND (h4/prim__rec/_3C l n) (h4/bitstring/zero__extend n v) (h4/list/DROP (h4/arithmetic/_2D l n) v)) (h4/list/LENGTH v)
% Assm: h4/bitstring/bitify__def_c1: !l a. h4/bitstring/bitify a (h4/list/CONS F l) = h4/bitstring/bitify (h4/list/CONS h4/num/0 a) l
% Assm: h4/bitstring/bitify__def_c2: !l a. h4/bitstring/bitify a (h4/list/CONS T l) = h4/bitstring/bitify (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bitstring/extend0_c0: !v n. h4/bitstring/zero__extend n v = h4/bitstring/extend F (h4/arithmetic/_2D n (h4/list/LENGTH v)) v
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bitstring/bitify__def_c0: !a. h4/bitstring/bitify a h4/list/NIL = a
% Assm: h4/bitstring/fixwidth__id: !w. h4/bitstring/fixwidth (h4/list/LENGTH w) w = w
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bitstring/fixwidth0: !v n. h4/bitstring/fixwidth n v = h4/bool/LET (\l. h4/bool/COND (h4/prim__rec/_3C l n) (h4/bitstring/extend F (h4/arithmetic/_2D n l) v) (h4/list/DROP (h4/arithmetic/_2D l n) v)) (h4/list/LENGTH v)
% Assm: h4/bitstring/length__zero__extend: !v n. h4/prim__rec/_3C (h4/list/LENGTH v) n ==> h4/list/LENGTH (h4/bitstring/zero__extend n v) = n
% Assm: h4/bitstring/bitwise__def: !v2 v1 f. h4/bitstring/bitwise f v1 v2 = h4/bool/LET (\m. h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C (h4/bitstring/fixwidth m v1) (h4/bitstring/fixwidth m v2)))) (h4/arithmetic/MAX (h4/list/LENGTH v1) (h4/list/LENGTH v2))
% Assm: h4/bitstring/fixwidth__id__imp: !w n. n = h4/list/LENGTH w ==> h4/bitstring/fixwidth n w = w
% Assm: h4/bitstring/add__def: !b a. h4/bitstring/add a b = h4/bool/LET (\m. h4/bitstring/zero__extend m (h4/bitstring/n2v (h4/arithmetic/_2B (h4/bitstring/v2n a) (h4/bitstring/v2n b)))) (h4/arithmetic/MAX (h4/list/LENGTH a) (h4/list/LENGTH b))
% Assm: h4/bitstring/modify__def: !v f. h4/bitstring/modify f v = h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C (h4/bitstring/rev__count__list (h4/list/LENGTH v)) v))
% Assm: h4/bitstring/rotate__def: !v m. h4/bitstring/rotate v m = h4/bool/LET (\l. h4/bool/LET (\x. h4/list/APPEND (h4/bitstring/field (h4/arithmetic/_2D x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h4/num/0 v) (h4/bitstring/field (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x v)) (h4/arithmetic/MOD m l)) (h4/list/LENGTH v)
% Assm: h4/bitstring/shiftl__def: !v m. h4/bitstring/shiftl v m = h4/list/PAD__RIGHT F (h4/arithmetic/_2B (h4/list/LENGTH v) m) v
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/rich__list/EVERY__REVERSE: !l P. h4/list/EVERY P (h4/list/REVERSE l) <=> h4/list/EVERY P l
% Assm: h4/list/EVERY__EL: !l P. h4/list/EVERY P l <=> (!n. h4/prim__rec/_3C n (h4/list/LENGTH l) ==> P (h4/list/EL n l))
% Assm: h4/list/APPEND__NIL: !l. h4/list/APPEND l h4/list/NIL = l
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/numeral/numeral__distrib_c25: !n m. h4/arithmetic/_3E (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C m n
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/list/EVERY__MAP: !l f P. h4/list/EVERY P (h4/list/MAP f l) <=> h4/list/EVERY (\x. P (f x)) l
% Assm: h4/numeral/numeral__distrib_c24: !n. h4/arithmetic/_3E (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% 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__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bitstring/zero__extend__def: !v n. h4/bitstring/zero__extend n v = h4/list/PAD__LEFT F n v
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/bitstring/sign__extend__def: !v n. h4/bitstring/sign__extend n v = h4/list/PAD__LEFT (h4/list/HD v) n v
% Assm: h4/bitstring/pad__left__extend: !n l c. h4/list/PAD__LEFT c n l = h4/bitstring/extend c (h4/arithmetic/_2D n (h4/list/LENGTH l)) l
% Assm: h4/bitstring/length__fixwidth: !v n. h4/list/LENGTH (h4/bitstring/fixwidth n v) = n
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/list/LENGTH__REVERSE: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm: h4/list/LENGTH__APPEND: !l2 l1. h4/list/LENGTH (h4/list/APPEND l1 l2) = h4/arithmetic/_2B (h4/list/LENGTH l1) (h4/list/LENGTH l2)
% Assm: h4/list/LENGTH__MAP: !l f. h4/list/LENGTH (h4/list/MAP f l) = h4/list/LENGTH l
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bitstring/bitify__tupled__primitive__def: h4/bitstring/bitify__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!l a. R (h4/pair/_2C (h4/list/CONS h4/num/0 a) l) (h4/pair/_2C a (h4/list/CONS F l))) /\ (!l a. R (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l) (h4/pair/_2C a (h4/list/CONS T l))))) (\bitify__tupled a_27. h4/pair/pair__CASE a_27 (\a v1. h4/list/list__CASE v1 (h4/combin/I a) (\v2 l. h4/bool/COND v2 (h4/combin/I (bitify__tupled (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l))) (h4/combin/I (bitify__tupled (h4/pair/_2C (h4/list/CONS h4/num/0 a) l))))))
% Assm: h4/list/list__size__def_c1: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/list/list__size f a1))
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/basicSize/bool__size__def: !b. h4/basicSize/bool__size b = h4/num/0
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bitstring/length__pad__left: !x n a. h4/list/LENGTH (h4/list/PAD__LEFT x n a) = h4/bool/COND (h4/prim__rec/_3C (h4/list/LENGTH a) n) n (h4/list/LENGTH a)
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bitstring/length__field: !v l h. h4/list/LENGTH (h4/bitstring/field h l v) = h4/arithmetic/_2D (h4/num/SUC h) l
% Assm: h4/list/DROP__0: !l. h4/list/DROP h4/num/0 l = l
% Assm: h4/arithmetic/SUB__EQUAL__0: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm: h4/prim__rec/LESS__REFL: !n. ~h4/prim__rec/_3C n n
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/bitstring/field__def: !v l h. h4/bitstring/field h l v = h4/bitstring/fixwidth (h4/arithmetic/_2D (h4/num/SUC h) l) (h4/bitstring/shiftr v l)
% Assm: h4/list/REVERSE__DEF_c1: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% Assm: h4/list/REVERSE__DEF_c0: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/APPEND__ASSOC: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/list/LENGTH__DROP: !n l. h4/list/LENGTH (h4/list/DROP n l) = h4/arithmetic/_2D (h4/list/LENGTH l) n
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/arithmetic/SUB__RIGHT__EQ: !p n m. h4/arithmetic/_2D m n = p <=> m = h4/arithmetic/_2B n p \/ h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D p h4/num/0
% Goal: !v. h4/list/LENGTH (h4/bitstring/bitify h4/list/NIL v) = h4/list/LENGTH v
%   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_bitstrings_v2nu_u_def]: !l. h4/bitstring/v2n l = h4/numposrep/num__from__bin__list (h4/bitstring/bitify h4/list/NIL l)
% Assm [h4s_bitstrings_everyu_u_bitu_u_bitify]: !v. h4/list/EVERY (h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/bitstring/bitify h4/list/NIL v)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bitstrings_bitifyu_u_reverseu_u_map]: !_0. (!b. happ _0 b = h4/bool/COND b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/num/0) ==> (!v a. h4/bitstring/bitify a v = h4/list/APPEND (h4/list/REVERSE (h4/list/MAP _0 v)) a)
% Assm [h4s_bitstrings_lengthu_u_bitify]: !v l. h4/list/LENGTH (h4/bitstring/bitify l v) = h4/arithmetic/_2B (h4/list/LENGTH l) (h4/list/LENGTH v)
% Assm [h4s_bitstrings_bitifyu_u_curriedu_u_def]: !x1 x. h4/bitstring/bitify x x1 = happ h4/bitstring/bitify__tupled (h4/pair/_2C x x1)
% Assm [h4s_bitstrings_fixwidthu_u_def]: !_0. (!n v l. happ (happ (happ _0 n) v) l = h4/bool/COND (happ (happ h4/prim__rec/_3C l) n) (h4/bitstring/zero__extend n v) (h4/list/DROP (h4/arithmetic/_2D l n) v)) ==> (!v n. h4/bitstring/fixwidth n v = h4/bool/LET (happ (happ _0 n) v) (h4/list/LENGTH v))
% Assm [h4s_bitstrings_bitifyu_u_defu_c1]: !l a. h4/bitstring/bitify a (h4/list/CONS F l) = h4/bitstring/bitify (h4/list/CONS h4/num/0 a) l
% Assm [h4s_bitstrings_bitifyu_u_defu_c2]: !l a. h4/bitstring/bitify a (h4/list/CONS T l) = h4/bitstring/bitify (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bitstrings_extend0u_c0]: !v n. h4/bitstring/zero__extend n v = h4/bitstring/extend F (h4/arithmetic/_2D n (h4/list/LENGTH v)) v
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bitstrings_bitifyu_u_defu_c0]: !a. h4/bitstring/bitify a h4/list/NIL = a
% Assm [h4s_bitstrings_fixwidthu_u_id]: !w. h4/bitstring/fixwidth (h4/list/LENGTH w) w = w
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bitstrings_fixwidth0]: !_0. (!n v l. happ (happ (happ _0 n) v) l = h4/bool/COND (happ (happ h4/prim__rec/_3C l) n) (h4/bitstring/extend F (h4/arithmetic/_2D n l) v) (h4/list/DROP (h4/arithmetic/_2D l n) v)) ==> (!v n. h4/bitstring/fixwidth n v = h4/bool/LET (happ (happ _0 n) v) (h4/list/LENGTH v))
% Assm [h4s_bitstrings_lengthu_u_zerou_u_extend]: !v n. happ (happ h4/prim__rec/_3C (h4/list/LENGTH v)) n ==> h4/list/LENGTH (h4/bitstring/zero__extend n v) = n
% Assm [h4s_bitstrings_bitwiseu_u_def]: !_0. (!f v1 v2 m. happ (happ (happ (happ _0 f) v1) v2) m = h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C (h4/bitstring/fixwidth m v1) (h4/bitstring/fixwidth m v2)))) ==> (!v2 v1 f. h4/bitstring/bitwise f v1 v2 = h4/bool/LET (happ (happ (happ _0 f) v1) v2) (h4/arithmetic/MAX (h4/list/LENGTH v1) (h4/list/LENGTH v2)))
% Assm [h4s_bitstrings_fixwidthu_u_idu_u_imp]: !w n. n = h4/list/LENGTH w ==> h4/bitstring/fixwidth n w = w
% Assm [h4s_bitstrings_addu_u_def]: !_0. (!a b m. happ (happ (happ _0 a) b) m = h4/bitstring/zero__extend m (h4/bitstring/n2v (h4/arithmetic/_2B (h4/bitstring/v2n a) (h4/bitstring/v2n b)))) ==> (!b a. h4/bitstring/add a b = h4/bool/LET (happ (happ _0 a) b) (h4/arithmetic/MAX (h4/list/LENGTH a) (h4/list/LENGTH b)))
% Assm [h4s_bitstrings_modifyu_u_def]: !v f. h4/bitstring/modify f v = h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C (h4/bitstring/rev__count__list (h4/list/LENGTH v)) v))
% Assm [h4s_bitstrings_rotateu_u_def]: !_1. (!l v x. happ (happ (happ _1 l) v) x = h4/list/APPEND (h4/bitstring/field (h4/arithmetic/_2D x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h4/num/0 v) (h4/bitstring/field (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x v)) ==> (!_0. (!v m l. happ (happ (happ _0 v) m) l = h4/bool/LET (happ (happ _1 l) v) (h4/arithmetic/MOD m l)) ==> (!v m. h4/bitstring/rotate v m = h4/bool/LET (happ (happ _0 v) m) (h4/list/LENGTH v)))
% Assm [h4s_bitstrings_shiftlu_u_def]: !v m. h4/bitstring/shiftl v m = h4/list/PAD__RIGHT F (h4/arithmetic/_2B (h4/list/LENGTH v) m) v
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_richu_u_lists_EVERYu_u_REVERSE]: !l P. h4/list/EVERY P (h4/list/REVERSE l) <=> h4/list/EVERY P l
% Assm [h4s_lists_EVERYu_u_EL]: !l P. h4/list/EVERY P l <=> (!n. happ (happ h4/prim__rec/_3C n) (h4/list/LENGTH l) ==> happ P (h4/list/EL n l))
% Assm [h4s_lists_APPENDu_u_NIL]: !l. h4/list/APPEND l h4/list/NIL = l
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT2 m) <=> ~happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_numerals_numeralu_u_distribu_c25]: !n m. happ (h4/arithmetic/_3E (h4/arithmetic/NUMERAL n)) (h4/arithmetic/NUMERAL m) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. happ (happ h4/prim__rec/_3C n) h4/arithmetic/ZERO <=> F
% Assm [h4s_lists_EVERYu_u_MAP]: !_0. (!P f x. happ (happ (happ _0 P) f) x <=> happ P (happ f x)) ==> (!l f P. h4/list/EVERY P (h4/list/MAP f l) <=> h4/list/EVERY (happ (happ _0 P) f) l)
% Assm [h4s_numerals_numeralu_u_distribu_c24]: !n. happ (h4/arithmetic/_3E (h4/arithmetic/NUMERAL n)) h4/num/0 <=> happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) n
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% 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_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bitstrings_zerou_u_extendu_u_def]: !v n. h4/bitstring/zero__extend n v = h4/list/PAD__LEFT F n v
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_bitstrings_signu_u_extendu_u_def]: !v n. h4/bitstring/sign__extend n v = h4/list/PAD__LEFT (h4/list/HD v) n v
% Assm [h4s_bitstrings_padu_u_leftu_u_extend]: !n l c. h4/list/PAD__LEFT c n l = h4/bitstring/extend c (h4/arithmetic/_2D n (h4/list/LENGTH l)) l
% Assm [h4s_bitstrings_lengthu_u_fixwidth]: !v n. h4/list/LENGTH (h4/bitstring/fixwidth n v) = n
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_lists_LENGTHu_u_REVERSE]: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm [h4s_lists_LENGTHu_u_APPEND]: !l2 l1. h4/list/LENGTH (h4/list/APPEND l1 l2) = h4/arithmetic/_2B (h4/list/LENGTH l1) (h4/list/LENGTH l2)
% Assm [h4s_lists_LENGTHu_u_MAP]: !l f. h4/list/LENGTH (h4/list/MAP f l) = h4/list/LENGTH l
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bitstrings_bitifyu_u_tupledu_u_primitiveu_u_def]: !_6. (!v2 bitify__tupled a l. happ (happ (happ (happ _6 v2) bitify__tupled) a) l = h4/bool/COND v2 (h4/combin/I (happ bitify__tupled (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l))) (h4/combin/I (happ bitify__tupled (h4/pair/_2C (h4/list/CONS h4/num/0 a) l)))) ==> (!_5. (!bitify__tupled a v2. happ (happ (happ _5 bitify__tupled) a) v2 = happ (happ (happ _6 v2) bitify__tupled) a) ==> (!_4. (!bitify__tupled a v1. happ (happ (happ _4 bitify__tupled) a) v1 = h4/list/list__CASE v1 (h4/combin/I a) (happ (happ _5 bitify__tupled) a)) ==> (!_3. (!bitify__tupled a. happ (happ _3 bitify__tupled) a = happ (happ _4 bitify__tupled) a) ==> (!_2. (!bitify__tupled a_27. happ (happ _2 bitify__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 bitify__tupled)) ==> (!_1. (!bitify__tupled. happ _1 bitify__tupled = happ _2 bitify__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!l a. happ (happ R (h4/pair/_2C (h4/list/CONS h4/num/0 a) l)) (h4/pair/_2C a (h4/list/CONS F l))) /\ (!l a. happ (happ R (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l)) (h4/pair/_2C a (h4/list/CONS T l)))) ==> h4/bitstring/bitify__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))
% Assm [h4s_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/list/list__size f a1))
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = happ (happ f a0) a1
% Assm [h4s_basicSizes_boolu_u_sizeu_u_def]: !b. h4/basicSize/bool__size b = h4/num/0
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. happ (happ h4/prim__rec/_3C h4/num/0) (h4/arithmetic/NUMERAL n) <=> happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) n
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bitstrings_lengthu_u_padu_u_left]: !x n a. h4/list/LENGTH (h4/list/PAD__LEFT x n a) = h4/bool/COND (happ (happ h4/prim__rec/_3C (h4/list/LENGTH a)) n) n (h4/list/LENGTH a)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bitstrings_lengthu_u_field]: !v l h. h4/list/LENGTH (h4/bitstring/field h l v) = h4/arithmetic/_2D (h4/num/SUC h) l
% Assm [h4s_lists_DROPu_u_0]: !l. h4/list/DROP h4/num/0 l = l
% Assm [h4s_arithmetics_SUBu_u_EQUALu_u_0]: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm [h4s_primu_u_recs_LESSu_u_REFL]: !n. ~happ (happ h4/prim__rec/_3C n) n
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_bitstrings_fieldu_u_def]: !v l h. h4/bitstring/field h l v = h4/bitstring/fixwidth (h4/arithmetic/_2D (h4/num/SUC h) l) (h4/bitstring/shiftr v l)
% Assm [h4s_lists_REVERSEu_u_DEFu_c1]: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% Assm [h4s_lists_REVERSEu_u_DEFu_c0]: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_lists_APPENDu_u_ASSOC]: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (happ f h) (h4/list/MAP f t)
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_lists_LENGTHu_u_DROP]: !n l. h4/list/LENGTH (h4/list/DROP n l) = h4/arithmetic/_2D (h4/list/LENGTH l) n
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_EQ]: !p n m. h4/arithmetic/_2D m n = p <=> m = h4/arithmetic/_2B n p \/ h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D p h4/num/0
% Goal: !v. h4/list/LENGTH (h4/bitstring/bitify h4/list/NIL v) = h4/list/LENGTH v
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_Q1165549,TV_Q1165545]: ![V_f, V_g]: (![V_x]: s(TV_Q1165545,happ(s(t_fun(TV_Q1165549,TV_Q1165545),V_f),s(TV_Q1165549,V_x))) = s(TV_Q1165545,happ(s(t_fun(TV_Q1165549,TV_Q1165545),V_g),s(TV_Q1165549,V_x))) => s(t_fun(TV_Q1165549,TV_Q1165545),V_f) = s(t_fun(TV_Q1165549,TV_Q1165545),V_g))).
fof(ah4s_bitstrings_v2nu_u_def, axiom, ![V_l]: s(t_h4s_nums_num,h4s_bitstrings_v2n(s(t_h4s_lists_list(t_bool),V_l))) = s(t_h4s_nums_num,h4s_numposreps_numu_u_fromu_u_binu_u_list(s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil),s(t_h4s_lists_list(t_bool),V_l)))))).
fof(ah4s_bitstrings_everyu_u_bitu_u_bitify, axiom, ![V_v]: p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil),s(t_h4s_lists_list(t_bool),V_v))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bitstrings_bitifyu_u_reverseu_u_map, axiom, ![V_uu_0]: (![V_b]: s(t_h4s_nums_num,happ(s(t_fun(t_bool,t_h4s_nums_num),V_uu_0),s(t_bool,V_b))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_nums_0))) => ![V_v, V_a]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_append(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_map(s(t_fun(t_bool,t_h4s_nums_num),V_uu_0),s(t_h4s_lists_list(t_bool),V_v))))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))))).
fof(ah4s_bitstrings_lengthu_u_bitify, axiom, ![V_v, V_l]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_l),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),V_l))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v)))))).
fof(ah4s_bitstrings_bitifyu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_x),s(t_h4s_lists_list(t_bool),V_x1))) = s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),h4s_bitstrings_bitifyu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),V_x),s(t_h4s_lists_list(t_bool),V_x1)))))).
fof(ah4s_bitstrings_fixwidthu_u_def, axiom, ![V_uu_0]: (![V_n, V_v, V_l]: s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_l))) = s(t_h4s_lists_list(t_bool),h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),h4s_bitstrings_zerou_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_lists_list(t_bool),h4s_lists_drop(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),V_v))))) => ![V_v, V_n]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))))))).
fof(ah4s_bitstrings_bitifyu_u_defu_c1, axiom, ![V_l, V_a]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,f),s(t_h4s_lists_list(t_bool),V_l))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l)))).
fof(ah4s_bitstrings_bitifyu_u_defu_c2, axiom, ![V_l, V_a]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,t),s(t_h4s_lists_list(t_bool),V_l))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(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_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bitstrings_extend0u_c0, axiom, ![V_v, V_n]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_zerou_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_bitstrings_extend(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))))),s(t_h4s_lists_list(t_bool),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_bitstrings_bitifyu_u_defu_c0, axiom, ![V_a]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_nums_num),V_a)).
fof(ah4s_bitstrings_fixwidthu_u_id, axiom, ![V_w]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_w))),s(t_h4s_lists_list(t_bool),V_w))) = s(t_h4s_lists_list(t_bool),V_w)).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bitstrings_fixwidth0, axiom, ![V_uu_0]: (![V_n, V_v, V_l]: s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_l))) = s(t_h4s_lists_list(t_bool),h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),h4s_bitstrings_extend(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_l))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_lists_list(t_bool),h4s_lists_drop(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),V_v))))) => ![V_v, V_n]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))))))).
fof(ah4s_bitstrings_lengthu_u_zerou_u_extend, axiom, ![V_v, V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))))),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),h4s_bitstrings_zerou_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,V_n))).
fof(ah4s_bitstrings_bitwiseu_u_def, axiom, ![V_uu_0]: (![V_f, V_v1, V_v2, V_m]: s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))))),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_bool),V_v1))),s(t_h4s_lists_list(t_bool),V_v2))),s(t_h4s_nums_num,V_m))) = s(t_h4s_lists_list(t_bool),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_bool,t_bool)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(t_bool),V_v1))),s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(t_bool),V_v2))))))))) => ![V_v2, V_v1, V_f]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_bitwise(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_h4s_lists_list(t_bool),V_v1),s(t_h4s_lists_list(t_bool),V_v2))) = s(t_h4s_lists_list(t_bool),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))))),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_bool),V_v1))),s(t_h4s_lists_list(t_bool),V_v2))),s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v1))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v2))))))))).
fof(ah4s_bitstrings_fixwidthu_u_idu_u_imp, axiom, ![V_w, V_n]: (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_w))) => s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_w))) = s(t_h4s_lists_list(t_bool),V_w))).
fof(ah4s_bitstrings_addu_u_def, axiom, ![V_uu_0]: (![V_a, V_b, V_m]: s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_lists_list(t_bool),V_a))),s(t_h4s_lists_list(t_bool),V_b))),s(t_h4s_nums_num,V_m))) = s(t_h4s_lists_list(t_bool),h4s_bitstrings_zerou_u_extend(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(t_bool),h4s_bitstrings_n2v(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bitstrings_v2n(s(t_h4s_lists_list(t_bool),V_a))),s(t_h4s_nums_num,h4s_bitstrings_v2n(s(t_h4s_lists_list(t_bool),V_b))))))))) => ![V_b, V_a]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_add(s(t_h4s_lists_list(t_bool),V_a),s(t_h4s_lists_list(t_bool),V_b))) = s(t_h4s_lists_list(t_bool),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_lists_list(t_bool),V_a))),s(t_h4s_lists_list(t_bool),V_b))),s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_a))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_b))))))))).
fof(ah4s_bitstrings_modifyu_u_def, axiom, ![V_v, V_f]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_modify(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_bool),t_bool),h4s_pairs_uncurry(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_bool)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_revu_u_countu_u_list(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))))),s(t_h4s_lists_list(t_bool),V_v)))))))).
fof(ah4s_bitstrings_rotateu_u_def, axiom, ![V_uu_1]: (![V_l, V_v, V_x]: s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_1),s(t_h4s_nums_num,V_l))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_x))) = s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),h4s_bitstrings_field(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_lists_list(t_bool),h4s_bitstrings_field(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_l),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,V_x),s(t_h4s_lists_list(t_bool),V_v))))) => ![V_uu_0]: (![V_v, V_m, V_l]: s(t_h4s_lists_list(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_l))) = s(t_h4s_lists_list(t_bool),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_1),s(t_h4s_nums_num,V_l))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_l))))) => ![V_v, V_m]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_rotate(s(t_h4s_lists_list(t_bool),V_v),s(t_h4s_nums_num,V_m))) = s(t_h4s_lists_list(t_bool),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool))),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)))),V_uu_0),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v)))))))).
fof(ah4s_bitstrings_shiftlu_u_def, axiom, ![V_v, V_m]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_shiftl(s(t_h4s_lists_list(t_bool),V_v),s(t_h4s_nums_num,V_m))) = s(t_h4s_lists_list(t_bool),h4s_lists_padu_u_right(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_m))),s(t_h4s_lists_list(t_bool),V_v)))).
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_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_CONDu_u_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_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_richu_u_lists_EVERYu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l, V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_EVERYu_u_EL, axiom, ![TV_u_27a]: ![V_l, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
fof(ah4s_lists_APPENDu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_distribu_c25, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(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,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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_c2, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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_lists_EVERYu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_P, V_f, V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))) => ![V_l, V_f, V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27b,t_bool),V_P),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ah4s_numerals_numeralu_u_distribu_c24, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(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_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n)))).
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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bitstrings_zerou_u_extendu_u_def, axiom, ![V_v, V_n]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_zerou_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_lists_padu_u_left(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v)))).
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_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,V_n)))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(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_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_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_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_bitstrings_signu_u_extendu_u_def, axiom, ![TV_u_27a]: ![V_v, V_n]: s(t_h4s_lists_list(TV_u_27a),h4s_bitstrings_signu_u_extend(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_v))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_padu_u_left(s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_v))),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_v)))).
fof(ah4s_bitstrings_padu_u_leftu_u_extend, axiom, ![TV_u_27a]: ![V_n, V_l, V_c]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_padu_u_left(s(TV_u_27a,V_c),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_bitstrings_extend(s(TV_u_27a,V_c),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_bitstrings_lengthu_u_fixwidth, axiom, ![V_v, V_n]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_lists_LENGTHu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_LENGTHu_u_APPEND, axiom, ![TV_u_27a]: ![V_l2, V_l1]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_LENGTHu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_f]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_bitstrings_bitifyu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_6]: (![V_v2, V_bitifyu_u_tupled, V_a, V_l]: s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_6),s(t_bool,V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_v2),s(t_h4s_lists_list(t_h4s_nums_num),h4s_combins_i(s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(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_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_combins_i(s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))))))) => ![V_uu_5]: (![V_bitifyu_u_tupled, V_a, V_v2]: s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_bool,V_v2))) = s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_6),s(t_bool,V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))) => ![V_uu_4]: (![V_bitifyu_u_tupled, V_a, V_v1]: s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_v1))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_bool),V_v1),s(t_h4s_lists_list(t_h4s_nums_num),h4s_combins_i(s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))))) => ![V_uu_3]: (![V_bitifyu_u_tupled, V_a]: s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))) = s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))) => ![V_uu_2]: (![V_bitifyu_u_tupled, V_au_27]: s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),V_au_27))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),V_au_27),s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))))) => ![V_uu_1]: (![V_bitifyu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R)))) & (![V_l, V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,f),s(t_h4s_lists_list(t_bool),V_l)))))))) & ![V_l, V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(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_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,t),s(t_h4s_lists_list(t_bool),V_l))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),h4s_bitstrings_bitifyu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_1))))))))))).
fof(ah4s_lists_listu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),V_a1)))))))).
fof(ah4s_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
fof(ah4s_basicSizes_boolu_u_sizeu_u_def, axiom, ![V_b]: s(t_h4s_nums_num,h4s_basicsizes_boolu_u_size(s(t_bool,V_b))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),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_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![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),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),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_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bitstrings_lengthu_u_padu_u_left, axiom, ![TV_u_27a]: ![V_x, V_n, V_a]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_padu_u_left(s(TV_u_27a,V_x),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_a))))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_a)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bitstrings_lengthu_u_field, axiom, ![V_v, V_l, V_h]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),h4s_bitstrings_field(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_h))),s(t_h4s_nums_num,V_l)))).
fof(ah4s_lists_DROPu_u_0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_drop(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_arithmetics_SUBu_u_EQUALu_u_0, axiom, ![V_c]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_c),s(t_h4s_nums_num,V_c))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_primu_u_recs_LESSu_u_REFL, axiom, ![V_n]: ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_bitstrings_fieldu_u_def, axiom, ![V_v, V_l, V_h]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_field(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_h))),s(t_h4s_nums_num,V_l))),s(t_h4s_lists_list(t_bool),h4s_bitstrings_shiftr(s(t_h4s_lists_list(t_bool),V_v),s(t_h4s_nums_num,V_l)))))).
fof(ah4s_lists_REVERSEu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_t))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))))).
fof(ah4s_lists_REVERSEu_u_DEFu_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_APPENDu_u_ASSOC, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l3))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),V_l3)))).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
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_lists_LENGTHu_u_DROP, axiom, ![TV_u_27a]: ![V_n, V_l]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_drop(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,V_n)))).
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_arithmetics_SUBu_u_RIGHTu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_p) <=> (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))) | (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ch4s_bitstrings_lengthu_u_bitifyu_u_null, conjecture, ![V_v]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v)))).
