%   ORIGINAL: h4/bitstring/word__lsl__v2w
% 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/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/bitstring/shiftl__replicate__F: !v n. h4/bitstring/shiftl v n = h4/list/APPEND v (h4/bitstring/replicate (h4/list/CONS F h4/list/NIL) n)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bitstring/bit__v2w: !v n. h4/words/word__bit n (h4/bitstring/v2w v) <=> h4/prim__rec/_3C n (h4/fcp/dimindex h4/bool/the__value) /\ h4/bitstring/testbit n v
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/bitstring/v2w__def: !v. h4/bitstring/v2w v = h4/fcp/FCP (\i. h4/bitstring/testbit i v)
% Assm: h4/list/GENLIST__CONS: !n f. h4/list/GENLIST f (h4/num/SUC n) = h4/list/CONS (f h4/num/0) (h4/list/GENLIST (h4/combin/o f h4/num/SUC) n)
% Assm: h4/list/FLAT0_c1: !t h. h4/list/FLAT (h4/list/CONS h t) = h4/list/APPEND h (h4/list/FLAT t)
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/list/PAD__RIGHT0: !s n c. h4/list/PAD__RIGHT c n s = h4/list/APPEND s (h4/list/GENLIST (h4/combin/K c) (h4/arithmetic/_2D n (h4/list/LENGTH s)))
% 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/list/APPEND__11_c0: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm: h4/arithmetic/ADD__SUB: !c a. h4/arithmetic/_2D (h4/arithmetic/_2B a c) c = a
% Assm: h4/bitstring/replicate__def: !v n. h4/bitstring/replicate v n = h4/list/FLAT (h4/list/GENLIST (h4/combin/K v) n)
% Assm: h4/list/FLAT0_c0: h4/list/FLAT h4/list/NIL = h4/list/NIL
% Assm: h4/list/GENLIST__NUMERALS_c0: !f. h4/list/GENLIST f h4/num/0 = h4/list/NIL
% Assm: h4/combin/K__o__THM_c0: !v f. h4/combin/o (h4/combin/K v) f = h4/combin/K v
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/bitstring/word__index__v2w: !v index_20too_20large i. h4/fcp/fcp__index (h4/bitstring/v2w v) i <=> h4/bool/COND (h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value)) (h4/bitstring/testbit i v) (h4/combin/FAIL h4/fcp/fcp__index index_20too_20large (h4/bitstring/v2w v) i)
% Assm: h4/bitstring/v2w__11: !w v. h4/bitstring/v2w v = h4/bitstring/v2w w <=> h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v = h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) w
% Assm: h4/bitstring/sw2sw__v2w: !v. h4/words/sw2sw (h4/bitstring/v2w v) = h4/bool/COND (h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/bitstring/v2w (h4/bitstring/sign__extend (h4/fcp/dimindex h4/bool/the__value) (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v))) (h4/bitstring/v2w (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v))
% Assm: h4/bitstring/w2w__v2w: !v. h4/words/w2w (h4/bitstring/v2w v) = h4/bitstring/v2w (h4/bitstring/fixwidth (h4/bool/COND (h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) v)
% Assm: h4/bitstring/w2v__v2w: !v. h4/bitstring/w2v (h4/bitstring/v2w v) = h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/words/word__bit0: !w b. h4/prim__rec/_3C b (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index w b <=> h4/words/word__bit b w)
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/fcp/CART__EQ: !y x. x = y <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index x i = h4/fcp/fcp__index y i)
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__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/bitstring/fixwidth__eq: !w v n. h4/bitstring/fixwidth n v = h4/bitstring/fixwidth n w <=> (!i. h4/prim__rec/_3C i n ==> (h4/bitstring/testbit i v <=> h4/bitstring/testbit i w))
% Assm: h4/combin/FAIL__DEF: h4/combin/FAIL = (\x y. x)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/words/DIMINDEX__GT__0: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> 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__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/SUB__LEFT__LESS__EQ: !p n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2D n p) <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2B m p) n \/ h4/arithmetic/_3C_3D m h4/num/0
% 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/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% 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/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% 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__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% 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__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% 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/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/bitstring/testbit0: !v b. h4/bitstring/testbit b v <=> h4/bool/LET (\n. h4/prim__rec/_3C b n /\ h4/list/EL (h4/arithmetic/_2D (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) b) v) (h4/list/LENGTH v)
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% 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
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/arithmetic/SUB__RIGHT__LESS: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm: h4/arithmetic/SUB__LEFT__EQ: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/SUB__RIGHT__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D m n) p <=> h4/arithmetic/_3C_3D m (h4/arithmetic/_2B n p)
% Assm: h4/arithmetic/SUB__RIGHT__SUB: !p n m. h4/arithmetic/_2D (h4/arithmetic/_2D m n) p = h4/arithmetic/_2D m (h4/arithmetic/_2B n p)
% Assm: h4/arithmetic/SUB__RIGHT__ADD: !p n m. h4/arithmetic/_2B (h4/arithmetic/_2D m n) p = h4/bool/COND (h4/arithmetic/_3C_3D m n) p (h4/arithmetic/_2D (h4/arithmetic/_2B m p) 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/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/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c1: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/arithmetic/SUB__LEFT__ADD: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2D n p) = h4/bool/COND (h4/arithmetic/_3C_3D n p) m (h4/arithmetic/_2D (h4/arithmetic/_2B m n) p)
% Assm: h4/bool/COND__EXPAND: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm: h4/bool/COND__RAND: !y x f b. f (h4/bool/COND b x y) = h4/bool/COND b (f x) (f y)
% Assm: h4/bool/COND__RATOR: !x g f b. h4/bool/COND b f g x = h4/bool/COND b (f x) (g x)
% Assm: h4/words/word__bit__def: !w b. h4/words/word__bit b w <=> h4/arithmetic/_3C_3D b (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ h4/fcp/fcp__index w b
% Assm: h4/fcp/FCP__BETA: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = g i
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bitstring/el__fixwidth: !w n i. h4/prim__rec/_3C i n ==> (h4/list/EL i (h4/bitstring/fixwidth n w) <=> h4/bool/COND (h4/prim__rec/_3C (h4/list/LENGTH w) n) (h4/arithmetic/_3C_3D (h4/arithmetic/_2D n (h4/list/LENGTH w)) i /\ h4/list/EL (h4/arithmetic/_2D i (h4/arithmetic/_2D n (h4/list/LENGTH w))) w) (h4/list/EL (h4/arithmetic/_2B i (h4/arithmetic/_2D (h4/list/LENGTH w) n)) w))
% Assm: h4/bool/F__DEF: F <=> (!t. t)
% Assm: h4/bitstring/length__fixwidth: !v n. h4/list/LENGTH (h4/bitstring/fixwidth n v) = n
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/arithmetic/SUB__LEFT__LESS: !p n m. h4/prim__rec/_3C m (h4/arithmetic/_2D n p) <=> h4/prim__rec/_3C (h4/arithmetic/_2B m p) n
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/words/w2w0: !w i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/w2w w) i <=> h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ h4/fcp/fcp__index w i)
% Assm: h4/numeral/numeral__add_c6: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm: h4/numeral/numeral__add_c4: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__add_c3: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/bitstring/word__msb__v2w: !v. h4/words/word__msb (h4/bitstring/v2w v) <=> h4/bitstring/testbit (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) v
% Assm: h4/words/sw2sw0: !w i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/sw2sw w) i <=> h4/bool/COND (h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) \/ h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/fcp/fcp__index w i) (h4/words/word__msb w))
% Assm: h4/list/EL__restricted_c0: h4/list/EL h4/num/0 = h4/list/HD
% Assm: h4/bitstring/el__sign__extend: !v n i. h4/list/EL i (h4/bitstring/sign__extend n v) = h4/bool/COND (h4/prim__rec/_3C i (h4/arithmetic/_2D n (h4/list/LENGTH v))) (h4/list/EL h4/num/0 v) (h4/list/EL (h4/arithmetic/_2D i (h4/arithmetic/_2D n (h4/list/LENGTH v))) v)
% Assm: h4/arithmetic/LE__LT1: !y x. h4/arithmetic/_3C_3D x y <=> h4/prim__rec/_3C x (h4/arithmetic/_2B y (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/arithmetic/TIMES2: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm: h4/arithmetic/RIGHT__ADD__DISTRIB: !p n m. h4/arithmetic/_2A (h4/arithmetic/_2B m n) p = h4/arithmetic/_2B (h4/arithmetic/_2A m p) (h4/arithmetic/_2A n p)
% Assm: h4/arithmetic/SUB__0_c0: !m. h4/arithmetic/_2D h4/num/0 m = h4/num/0
% Assm: h4/bitstring/length__sign__extend: !v n. h4/prim__rec/_3C (h4/list/LENGTH v) n ==> h4/list/LENGTH (h4/bitstring/sign__extend n v) = n
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/prim__rec/NOT__LESS__0: !n. ~h4/prim__rec/_3C n h4/num/0
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% 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)
% Goal: !v n. h4/words/word__lsl (h4/bitstring/v2w v) n = h4/bitstring/v2w (h4/bitstring/shiftl v n)
%   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_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_bitstrings_shiftlu_u_replicateu_u_F]: !v n. h4/bitstring/shiftl v n = h4/list/APPEND v (h4/bitstring/replicate (h4/list/CONS F h4/list/NIL) n)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bitstrings_bitu_u_v2w]: !v n. h4/words/word__bit n (h4/bitstring/v2w v) <=> h4/prim__rec/_3C n (h4/fcp/dimindex h4/bool/the__value) /\ h4/bitstring/testbit n v
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_bitstrings_v2wu_u_def]: !_0. (!v i. happ (happ _0 v) i <=> h4/bitstring/testbit i v) ==> (!v. h4/bitstring/v2w v = h4/fcp/FCP (happ _0 v))
% Assm [h4s_lists_GENLISTu_u_CONS]: !n f. h4/list/GENLIST f (happ h4/num/SUC n) = h4/list/CONS (happ f h4/num/0) (h4/list/GENLIST (h4/combin/o f h4/num/SUC) n)
% Assm [h4s_lists_FLAT0u_c1]: !t h. h4/list/FLAT (h4/list/CONS h t) = h4/list/APPEND h (h4/list/FLAT t)
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_lists_PADu_u_RIGHT0]: !s n c. h4/list/PAD__RIGHT c n s = h4/list/APPEND s (h4/list/GENLIST (h4/combin/K c) (h4/arithmetic/_2D n (h4/list/LENGTH s)))
% 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_lists_APPENDu_u_11u_c0]: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm [h4s_arithmetics_ADDu_u_SUB]: !c a. h4/arithmetic/_2D (h4/arithmetic/_2B a c) c = a
% Assm [h4s_bitstrings_replicateu_u_def]: !v n. h4/bitstring/replicate v n = h4/list/FLAT (h4/list/GENLIST (h4/combin/K v) n)
% Assm [h4s_lists_FLAT0u_c0]: h4/list/FLAT h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_GENLISTu_u_NUMERALSu_c0]: !f. h4/list/GENLIST f h4/num/0 = h4/list/NIL
% 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_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (happ h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_bitstrings_wordu_u_indexu_u_v2w]: !v index_20too_20large i. happ (happ h4/fcp/fcp__index (h4/bitstring/v2w v)) i <=> h4/bool/COND (h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value)) (h4/bitstring/testbit i v) (happ (happ (h4/combin/FAIL h4/fcp/fcp__index index_20too_20large) (h4/bitstring/v2w v)) i)
% Assm [h4s_bitstrings_v2wu_u_11]: !w v. h4/bitstring/v2w v = h4/bitstring/v2w w <=> h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v = h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) w
% Assm [h4s_bitstrings_sw2swu_u_v2w]: !v. h4/words/sw2sw (h4/bitstring/v2w v) = h4/bool/COND (h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/bitstring/v2w (h4/bitstring/sign__extend (h4/fcp/dimindex h4/bool/the__value) (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v))) (h4/bitstring/v2w (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v))
% Assm [h4s_bitstrings_w2wu_u_v2w]: !v. h4/words/w2w (h4/bitstring/v2w v) = h4/bitstring/v2w (h4/bitstring/fixwidth (h4/bool/COND (h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) v)
% Assm [h4s_bitstrings_w2vu_u_v2w]: !v. h4/bitstring/w2v (h4/bitstring/v2w v) = h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_wordss_wordu_u_bit0]: !w b. h4/prim__rec/_3C b (h4/fcp/dimindex h4/bool/the__value) ==> (happ (happ h4/fcp/fcp__index w) b <=> h4/words/word__bit b w)
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_fcps_CARTu_u_EQ]: !y x. x = y <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> happ (happ h4/fcp/fcp__index x) i = happ (happ h4/fcp/fcp__index y) i)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_CONDu_u_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_bitstrings_fixwidthu_u_eq]: !w v n. h4/bitstring/fixwidth n v = h4/bitstring/fixwidth n w <=> (!i. h4/prim__rec/_3C i n ==> (h4/bitstring/testbit i v <=> h4/bitstring/testbit i w))
% Assm [h4s_combins_FAILu_u_DEF]: !x x. h4/combin/FAIL x x = x
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_wordss_DIMINDEXu_u_GTu_u_0]: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> 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_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2D n p) <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2B m p) n \/ h4/arithmetic/_3C_3D m h4/num/0
% 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_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% 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_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (happ h4/num/SUC m) n
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. happ h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% 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_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (happ h4/num/SUC n) m
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_bitstrings_testbit0]: !_0. (!b v n. happ (happ (happ _0 b) v) n <=> h4/prim__rec/_3C b n /\ happ (h4/list/EL (h4/arithmetic/_2D (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) b)) v) ==> (!v b. h4/bitstring/testbit b v <=> h4/bool/LET (happ (happ _0 b) v) (h4/list/LENGTH v))
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% 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
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESS]: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_EQ]: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D m n) p <=> h4/arithmetic/_3C_3D m (h4/arithmetic/_2B n p)
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_SUB]: !p n m. h4/arithmetic/_2D (h4/arithmetic/_2D m n) p = h4/arithmetic/_2D m (h4/arithmetic/_2B n p)
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_ADD]: !p n m. h4/arithmetic/_2B (h4/arithmetic/_2D m n) p = h4/bool/COND (h4/arithmetic/_3C_3D m n) p (h4/arithmetic/_2D (h4/arithmetic/_2B m p) n)
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (happ h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (happ h4/num/SUC n) m
% 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_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_ADD]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2D n p) = h4/bool/COND (h4/arithmetic/_3C_3D n p) m (h4/arithmetic/_2D (h4/arithmetic/_2B m n) p)
% Assm [h4s_bools_CONDu_u_EXPAND]: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm [h4s_bools_CONDu_u_RAND]: !y x f b. happ f (h4/bool/COND b x y) = h4/bool/COND b (happ f x) (happ f y)
% Assm [h4s_bools_CONDu_u_RATOR]: !x g f b. happ (h4/bool/COND b f g) x = h4/bool/COND b (happ f x) (happ g x)
% Assm [h4s_wordss_wordu_u_bitu_u_def]: !w b. h4/words/word__bit b w <=> h4/arithmetic/_3C_3D b (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ happ (happ h4/fcp/fcp__index w) b
% Assm [h4s_fcps_FCPu_u_BETA]: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> happ (happ h4/fcp/fcp__index (h4/fcp/FCP g)) i = happ g i
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bitstrings_elu_u_fixwidth]: !w n i. h4/prim__rec/_3C i n ==> (?v. (v <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2D n (h4/list/LENGTH w)) i /\ happ (h4/list/EL (h4/arithmetic/_2D i (h4/arithmetic/_2D n (h4/list/LENGTH w)))) w) /\ (happ (h4/list/EL i) (h4/bitstring/fixwidth n w) <=> h4/bool/COND (h4/prim__rec/_3C (h4/list/LENGTH w) n) v (happ (h4/list/EL (h4/arithmetic/_2B i (h4/arithmetic/_2D (h4/list/LENGTH w) n))) w)))
% Assm [h4s_bools_Fu_u_DEF]: F <=> (!t. t)
% Assm [h4s_bitstrings_lengthu_u_fixwidth]: !v n. h4/list/LENGTH (h4/bitstring/fixwidth n v) = n
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_LESS]: !p n m. h4/prim__rec/_3C m (h4/arithmetic/_2D n p) <=> h4/prim__rec/_3C (h4/arithmetic/_2B m p) n
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_wordss_w2w0]: !w i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (happ (happ h4/fcp/fcp__index (h4/words/w2w w)) i <=> h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ happ (happ h4/fcp/fcp__index w) i)
% Assm [h4s_numerals_numeralu_u_addu_c6]: !n. happ h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = happ h4/num/SUC n
% Assm [h4s_numerals_numeralu_u_addu_c4]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (happ h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_addu_c3]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (happ h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_sucu_c0]: happ h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_bitstrings_wordu_u_msbu_u_v2w]: !v. h4/words/word__msb (h4/bitstring/v2w v) <=> h4/bitstring/testbit (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) v
% Assm [h4s_wordss_sw2sw0]: !w i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (?v. (v <=> h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) \/ h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) /\ (happ (happ h4/fcp/fcp__index (h4/words/sw2sw w)) i <=> h4/bool/COND v (happ (happ h4/fcp/fcp__index w) i) (h4/words/word__msb w)))
% Assm [h4s_lists_ELu_u_restrictedu_c0]: h4/list/EL h4/num/0 = h4/list/HD
% Assm [h4s_bitstrings_elu_u_signu_u_extend]: !v n i. happ (h4/list/EL i) (h4/bitstring/sign__extend n v) = h4/bool/COND (h4/prim__rec/_3C i (h4/arithmetic/_2D n (h4/list/LENGTH v))) (happ (h4/list/EL h4/num/0) v) (happ (h4/list/EL (h4/arithmetic/_2D i (h4/arithmetic/_2D n (h4/list/LENGTH v)))) v)
% Assm [h4s_arithmetics_LEu_u_LT1]: !y x. h4/arithmetic/_3C_3D x y <=> h4/prim__rec/_3C x (h4/arithmetic/_2B y (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_arithmetics_TIMES2]: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm [h4s_arithmetics_RIGHTu_u_ADDu_u_DISTRIB]: !p n m. h4/arithmetic/_2A (h4/arithmetic/_2B m n) p = h4/arithmetic/_2B (h4/arithmetic/_2A m p) (h4/arithmetic/_2A n p)
% Assm [h4s_arithmetics_SUBu_u_0u_c0]: !m. h4/arithmetic/_2D h4/num/0 m = h4/num/0
% Assm [h4s_bitstrings_lengthu_u_signu_u_extend]: !v n. h4/prim__rec/_3C (h4/list/LENGTH v) n ==> h4/list/LENGTH (h4/bitstring/sign__extend n v) = n
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_primu_u_recs_NOTu_u_LESSu_u_0]: !n. ~h4/prim__rec/_3C n h4/num/0
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bitstrings_fixwidthu_u_def]: !_0. (!n v l. happ (happ (happ _0 n) v) 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)) ==> (!v n. h4/bitstring/fixwidth n v = h4/bool/LET (happ (happ _0 n) v) (h4/list/LENGTH v))
% Goal: !v n. h4/words/word__lsl (h4/bitstring/v2w v) n = h4/bitstring/v2w (h4/bitstring/shiftl v n)
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_Q1166788,TV_Q1166784]: ![V_f, V_g]: (![V_x]: s(TV_Q1166784,happ(s(t_fun(TV_Q1166788,TV_Q1166784),V_f),s(TV_Q1166788,V_x))) = s(TV_Q1166784,happ(s(t_fun(TV_Q1166788,TV_Q1166784),V_g),s(TV_Q1166788,V_x))) => s(t_fun(TV_Q1166788,TV_Q1166784),V_f) = s(t_fun(TV_Q1166788,TV_Q1166784),V_g))).
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_bitstrings_shiftlu_u_replicateu_u_F, axiom, ![V_v, V_n]: 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_n))) = s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),V_v),s(t_h4s_lists_list(t_bool),h4s_bitstrings_replicate(s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,f),s(t_h4s_lists_list(t_bool),h4s_lists_nil))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_bitu_u_v2w, axiom, ![TV_u_27a]: ![V_v, V_n]: (p(s(t_bool,h4s_wordss_wordu_u_bit(s(t_h4s_nums_num,V_n),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v)))))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) & p(s(t_bool,h4s_bitstrings_testbit(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,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_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_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_bitstrings_v2wu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_v, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bitstrings_testbit(s(t_h4s_nums_num,V_i),s(t_h4s_lists_list(t_bool),V_v))) => ![V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_lists_list(t_bool),V_v))))))).
fof(ah4s_lists_GENLISTu_u_CONS, axiom, ![TV_u_27a]: ![V_n, V_f]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_combins_o(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_lists_FLAT0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_cons(s(t_h4s_lists_list(TV_u_27a),V_h),s(t_h4s_lists_list(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),V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_t)))))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (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_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0u_27),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
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_PADu_u_RIGHT0, axiom, ![TV_u_27a]: ![V_s, V_n, V_c]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_padu_u_right(s(TV_u_27a,V_c),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_s))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_s),s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_combins_k(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_s)))))))))).
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_lists_APPENDu_u_11u_c0, 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),V_l2))) = 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_l3))) <=> s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),V_l3))).
fof(ah4s_arithmetics_ADDu_u_SUB, axiom, ![V_c, V_a]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_c))),s(t_h4s_nums_num,V_c))) = s(t_h4s_nums_num,V_a)).
fof(ah4s_bitstrings_replicateu_u_def, axiom, ![V_v, V_n]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_replicate(s(t_h4s_lists_list(t_bool),V_v),s(t_h4s_nums_num,V_n))) = s(t_h4s_lists_list(t_bool),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(t_bool)),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_bool)),h4s_combins_k(s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_lists_FLAT0u_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_GENLISTu_u_NUMERALSu_c0, axiom, ![TV_u_27a]: ![V_f]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
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_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_bitstrings_wordu_u_indexu_u_v2w, axiom, ![TV_u_27a]: ![V_v, V_indexu_20toou_20large, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))),s(t_bool,h4s_bitstrings_testbit(s(t_h4s_nums_num,V_i),s(t_h4s_lists_list(t_bool),V_v))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_combins_fail(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_bool,V_indexu_20toou_20large))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))))),s(t_h4s_nums_num,V_i)))))).
fof(ah4s_bitstrings_v2wu_u_11, axiom, ![TV_u_27a]: ![V_w, V_v]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_w))) <=> s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_lists_list(t_bool),V_w))))).
fof(ah4s_bitstrings_sw2swu_u_v2w, axiom, ![TV_u_27a,TV_u_27b]: ![V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_sw2sw(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(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,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_signu_u_extend(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_lists_list(t_bool),V_v))))))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),s(t_h4s_lists_list(t_bool),V_v)))))))).
fof(ah4s_bitstrings_w2wu_u_v2w, axiom, ![TV_u_27b,TV_u_27a]: ![V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),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,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))),s(t_h4s_lists_list(t_bool),V_v)))))).
fof(ah4s_bitstrings_w2vu_u_v2w, axiom, ![TV_u_27a]: ![V_v]: s(t_h4s_lists_list(t_bool),h4s_bitstrings_w2v(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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_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_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_wordss_wordu_u_bit0, axiom, ![TV_u_27a]: ![V_w, V_b]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) => s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_b))) = s(t_bool,h4s_wordss_wordu_u_bit(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_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_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_fcps_CARTu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: (s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_y) <=> ![V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_y))),s(t_h4s_nums_num,V_i)))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_CONDu_u_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_bitstrings_fixwidthu_u_eq, axiom, ![V_w, 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_bitstrings_fixwidth(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_w))) <=> ![V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n)))) => s(t_bool,h4s_bitstrings_testbit(s(t_h4s_nums_num,V_i),s(t_h4s_lists_list(t_bool),V_v))) = s(t_bool,h4s_bitstrings_testbit(s(t_h4s_nums_num,V_i),s(t_h4s_lists_list(t_bool),V_w)))))).
fof(ah4s_combins_FAILu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27a,h4s_combins_fail(s(TV_u_27a,V_x),s(TV_u_27b,V_x0))) = s(TV_u_27a,V_x)).
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_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_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_wordss_DIMINDEXu_u_GTu_u_0, 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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
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_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_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_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_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_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_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_SUBu_u_LEFTu_u_LESSu_u_EQ, 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,h4s_arithmetics_u_2d(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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))))))).
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_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_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_arithmetics_NOTu_u_LESS, 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,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_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,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_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_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,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_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
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_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_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_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_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_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_arithmetics_NOTu_u_LEQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
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_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_bitstrings_testbit0, axiom, ![V_uu_0]: (![V_b, V_v, V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,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_bool))),V_uu_0),s(t_h4s_nums_num,V_b))),s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_n)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(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,V_b))))),s(t_h4s_lists_list(t_bool),V_v)))))) => ![V_v, V_b]: s(t_bool,h4s_bitstrings_testbit(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_bool),V_v))) = s(t_bool,h4s_bools_let(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_lists_list(t_bool),t_fun(t_h4s_nums_num,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_bool))),V_uu_0),s(t_h4s_nums_num,V_b))),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_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_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_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
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(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_LESS, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(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)))) <=> (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_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_p))))))).
fof(ah4s_arithmetics_SUBu_u_LEFTu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(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,V_m),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,V_n) | (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0)))) & 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_SUBu_u_RIGHTu_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_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_bool,h4s_arithmetics_u_3cu_3d(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)))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_SUB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(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,h4s_arithmetics_u_2d(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)))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_ADD, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(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,h4s_arithmetics_u_2d(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_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,happ(s(t_fun(t_h4s_nums_num,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,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
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_arithmetics_ADDu_u_COMM, 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_ADDu_u_CLAUSESu_c1, 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_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_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_arithmetics_SUBu_u_LEFTu_u_ADD, 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_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(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_2d(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_bools_CONDu_u_EXPAND, axiom, ![V_t2, V_t1, V_b]: (p(s(t_bool,h4s_bools_cond(s(t_bool,V_b),s(t_bool,V_t1),s(t_bool,V_t2)))) <=> ((~ (p(s(t_bool,V_b))) | p(s(t_bool,V_t1))) & (p(s(t_bool,V_b)) | p(s(t_bool,V_t2)))))).
fof(ah4s_bools_CONDu_u_RAND, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27a,V_x),s(TV_u_27a,V_y))))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_b),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_y)))))).
fof(ah4s_bools_CONDu_u_RATOR, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_g, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_bools_cond(s(t_bool,V_b),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_b),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_wordss_wordu_u_bitu_u_def, axiom, ![TV_u_27a]: ![V_w, V_b]: (p(s(t_bool,h4s_wordss_wordu_u_bit(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_u_2d(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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_b))))))).
fof(ah4s_fcps_FCPu_u_BETA, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_g]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g))))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,V_i))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bitstrings_elu_u_fixwidth, axiom, ![V_w, V_n, V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n)))) => ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(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_w))))),s(t_h4s_nums_num,V_i)))) & p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_i),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_w))))))))),s(t_h4s_lists_list(t_bool),V_w)))))) & s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_lists_el(s(t_h4s_nums_num,V_i))),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_bool,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_w))),s(t_h4s_nums_num,V_n))),s(t_bool,V_v),s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_w))),s(t_h4s_nums_num,V_n))))))),s(t_h4s_lists_list(t_bool),V_w)))))))).
fof(ah4s_bools_Fu_u_DEF, axiom, (p(s(t_bool,f)) <=> ![V_t]: p(s(t_bool,V_t)))).
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_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_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_arithmetics_SUBu_u_LEFTu_u_LESS, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_primu_u_recs_u_3c(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_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_wordss_w2w0, axiom, ![TV_u_27b,TV_u_27a]: ![V_w, V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))))))).
fof(ah4s_numerals_numeralu_u_addu_c6, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_addu_c4, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_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,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_addu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_sucu_c0, axiom, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_bitstrings_wordu_u_msbu_u_v2w, axiom, ![TV_u_27a]: ![V_v]: s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))))) = s(t_bool,h4s_bitstrings_testbit(s(t_h4s_nums_num,h4s_arithmetics_u_2d(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,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_bool),V_v)))).
fof(ah4s_wordss_sw2sw0, axiom, ![TV_u_27b,TV_u_27a]: ![V_w, V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) | p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))) & s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_sw2sw(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bools_cond(s(t_bool,V_v),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))),s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))))).
fof(ah4s_lists_ELu_u_restrictedu_c0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0))) = s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_hd)).
fof(ah4s_bitstrings_elu_u_signu_u_extend, axiom, ![TV_u_27a]: ![V_v, V_n, V_i]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_el(s(t_h4s_nums_num,V_i))),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(TV_u_27a,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),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_v))))))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_lists_list(TV_u_27a),V_v))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_i),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_v))))))))),s(t_h4s_lists_list(TV_u_27a),V_v)))))).
fof(ah4s_arithmetics_LEu_u_LT1, axiom, ![V_y, V_x]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_y),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_TIMES2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_RIGHTu_u_ADDu_u_DISTRIB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_SUBu_u_0u_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bitstrings_lengthu_u_signu_u_extend, axiom, ![TV_u_27a]: ![V_v, V_n]: (p(s(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_v))),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_lists_length(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_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_primu_u_recs_NOTu_u_LESSu_u_0, axiom, ![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_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_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,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(ch4s_bitstrings_wordu_u_lslu_u_v2w, conjecture, ![TV_u_27a]: ![V_v, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))),s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(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_n)))))).
