%   ORIGINAL: h4/words/WORD__OR__ABSORB
% 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/words/word__or__def: !w v. h4/words/word__or v w = h4/fcp/FCP (\i. h4/fcp/fcp__index v i \/ h4/fcp/fcp__index w i)
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/TRUTH: T
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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/words/WORD__DE__MORGAN__THM_c1: !b a. h4/words/word__1comp (h4/words/word__or a b) = h4/words/word__and (h4/words/word__1comp a) (h4/words/word__1comp b)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/words/word__and__def: !w v. h4/words/word__and v w = h4/fcp/FCP (\i. h4/fcp/fcp__index v i /\ h4/fcp/fcp__index w i)
% Assm: h4/words/WORD__OR__ASSOC: !c b a. h4/words/word__or (h4/words/word__or a b) c = h4/words/word__or a (h4/words/word__or b c)
% Assm: h4/words/WORD__OR__IDEM: !a. h4/words/word__or a a = a
% Assm: h4/words/WORD__OR__CLAUSES_c4: !a. h4/words/word__or a a = a
% Assm: h4/words/WORD__OR__COMM: !b a. h4/words/word__or a b = h4/words/word__or b a
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/fcp/FCP__ETA: !g. h4/fcp/FCP (\i. h4/fcp/fcp__index g i) = g
% Assm: h4/list/list__Axiom: !f1 f0. ?fn. fn h4/list/NIL = f0 /\ (!a0 a1. fn (h4/list/CONS a0 a1) = f1 a0 a1 (fn a1))
% Assm: h4/words/WORD__DE__MORGAN__THM_c0: !b a. h4/words/word__1comp (h4/words/word__and a b) = h4/words/word__or (h4/words/word__1comp a) (h4/words/word__1comp b)
% Assm: h4/words/WORD__AND__ABSORD: !b a. h4/words/word__or a (h4/words/word__and a b) = a
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% 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/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/bool/OR__CLAUSES_c4: !t. t \/ t <=> t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/words/word__0: !i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> ~h4/fcp/fcp__index (h4/words/n2w h4/num/0) i
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/words/word__T0: !i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index h4/words/word__T i
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/words/word__1comp__def: !w. h4/words/word__1comp w = h4/fcp/FCP (\i. ~h4/fcp/fcp__index w i)
% Assm: h4/words/WORD__AND__IDEM: !a. h4/words/word__and a a = a
% Assm: h4/words/WORD__AND__CLAUSES_c2: !a. h4/words/word__and (h4/words/n2w h4/num/0) a = h4/words/n2w h4/num/0
% Assm: h4/words/WORD__AND__ASSOC: !c b a. h4/words/word__and (h4/words/word__and a b) c = h4/words/word__and a (h4/words/word__and b c)
% Assm: h4/words/WORD__AND__CLAUSES_c4: !a. h4/words/word__and a a = a
% Assm: h4/words/WORD__AND__COMM: !b a. h4/words/word__and a b = h4/words/word__and b a
% Assm: h4/words/WORD__AND__CLAUSES_c0: !a. h4/words/word__and h4/words/word__T a = a
% Assm: h4/words/WORD__AND__CLAUSES_c3: !a. h4/words/word__and a (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Assm: h4/words/WORD__AND__CLAUSES_c1: !a. h4/words/word__and a h4/words/word__T = a
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/words/word__and__n2w: !n m. h4/words/word__and (h4/words/n2w n) (h4/words/n2w m) = h4/words/n2w (h4/bit/BITWISE (h4/fcp/dimindex h4/bool/the__value) $and n m)
% Assm: h4/words/WORD__OR__CLAUSES_c1: !a. h4/words/word__or a h4/words/word__T = h4/words/word__T
% Assm: h4/words/word__join__def: !w v. h4/words/word__join v w = h4/bool/LET (h4/bool/LET (\cv cw. h4/words/word__or (h4/words/word__lsl cv (h4/fcp/dimindex h4/bool/the__value)) cw) (h4/words/w2w v)) (h4/words/w2w w)
% Assm: h4/words/WORD__OR__CLAUSES_c3: !a. h4/words/word__or a (h4/words/n2w h4/num/0) = a
% Assm: h4/words/WORD__OR__CLAUSES_c0: !a. h4/words/word__or h4/words/word__T a = h4/words/word__T
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/words/WORD__OR__CLAUSES_c2: !a. h4/words/word__or (h4/words/n2w h4/num/0) a = a
% Assm: h4/words/word__or__n2w: !n m. h4/words/word__or (h4/words/n2w n) (h4/words/n2w m) = h4/words/n2w (h4/bit/BITWISE (h4/fcp/dimindex h4/bool/the__value) $or n m)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/words/concat__word__list__def_c1: !t h. h4/words/concat__word__list (h4/list/CONS h t) = h4/words/word__or (h4/words/w2w h) (h4/words/word__lsl (h4/words/concat__word__list t) (h4/fcp/dimindex h4/bool/the__value))
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/words/n2w__def: !n. h4/words/n2w n = h4/fcp/FCP (\i. h4/bit/BIT i n)
% Assm: h4/bit/BITWISE__THM: !x op n b a. h4/prim__rec/_3C x n ==> (h4/bit/BIT x (h4/bit/BITWISE n op a b) <=> op (h4/bit/BIT x a) (h4/bit/BIT x b))
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/words/word__xor__def: !w v. h4/words/word__xor v w = h4/fcp/FCP (\i. ~(h4/fcp/fcp__index v i <=> h4/fcp/fcp__index w i))
% Assm: h4/words/word__reverse__def: !w. h4/words/word__reverse w = h4/fcp/FCP (\i. h4/fcp/fcp__index w (h4/arithmetic/_2D (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i))
% Assm: h4/words/word__div__def: !w v. h4/words/word__div v w = h4/words/n2w (h4/arithmetic/DIV (h4/words/w2n v) (h4/words/w2n w))
% 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/words/word__slice__def: !l h. h4/words/word__slice h l = (\w. h4/fcp/FCP (\i. h4/arithmetic/_3C_3D l i /\ h4/arithmetic/_3C_3D i (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ h4/fcp/fcp__index w i))
% Assm: h4/words/word__lt__def: !b a. h4/words/word__lt a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. ~(n <=> v))))) (h4/words/nzcv a b)
% Assm: h4/words/add__with__carry__def: !y x carry__in. h4/words/add__with__carry (h4/pair/_2C x (h4/pair/_2C y carry__in)) = h4/bool/LET (\unsigned__sum. h4/bool/LET (\result. h4/bool/LET (h4/bool/LET (\carry__out overflow. h4/pair/_2C result (h4/pair/_2C carry__out overflow)) (~(h4/words/w2n result = unsigned__sum))) ((h4/words/word__msb x <=> h4/words/word__msb y) /\ ~(h4/words/word__msb x <=> h4/words/word__msb result))) (h4/words/n2w unsigned__sum)) (h4/arithmetic/_2B (h4/arithmetic/_2B (h4/words/w2n x) (h4/words/w2n y)) (h4/bool/COND carry__in (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/num/0))
% Assm: h4/words/word__eq__0: !w. w = h4/words/n2w h4/num/0 <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> ~h4/fcp/fcp__index w i)
% Assm: h4/words/word__compare__def: !b a. h4/words/word__compare a b = h4/bool/COND (a = b) (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/words/n2w h4/num/0)
% Assm: h4/words/word__log2__def: !w. h4/words/word__log2 w = h4/words/n2w (h4/bit/LOG2 (h4/words/w2n w))
% Assm: h4/words/word__hi__def: !b a. h4/words/word__hi a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. c /\ ~z)))) (h4/words/nzcv a b)
% Assm: h4/words/l2w__w2l: !w b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b ==> h4/words/l2w b (h4/words/w2l b w) = w
% Assm: h4/words/saturate__sub__def: !b a. h4/words/saturate__sub a b = h4/words/n2w (h4/arithmetic/_2D (h4/words/w2n a) (h4/words/w2n b))
% Assm: h4/words/word__lsr__def: !w n. h4/words/word__lsr w n = h4/fcp/FCP (\i. h4/prim__rec/_3C (h4/arithmetic/_2B i n) (h4/fcp/dimindex h4/bool/the__value) /\ h4/fcp/fcp__index w (h4/arithmetic/_2B i n))
% Assm: h4/words/word__xnor__def: !w v. h4/words/word__xnor v w = h4/fcp/FCP (\i. h4/fcp/fcp__index v i <=> h4/fcp/fcp__index w i)
% Assm: h4/words/word__lsl__bv__def: !w n. h4/words/word__lsl__bv w n = h4/words/word__lsl w (h4/words/w2n n)
% Assm: h4/words/word__2comp__def: !w. h4/words/word__2comp w = h4/words/n2w (h4/arithmetic/_2D (h4/words/dimword h4/bool/the__value) (h4/words/w2n w))
% Assm: h4/words/word__lsr__bv__def: !w n. h4/words/word__lsr__bv w n = h4/words/word__lsr w (h4/words/w2n n)
% Assm: h4/words/WORD__NOT__XOR_c0: !b a. h4/words/word__xor (h4/words/word__1comp a) (h4/words/word__1comp b) = h4/words/word__xor a b
% Assm: h4/words/WORD__NOT__XOR_c2: !b a. h4/words/word__xor (h4/words/word__1comp a) b = h4/words/word__1comp (h4/words/word__xor a b)
% Assm: h4/words/word__srem__def: !b a. h4/words/word__srem a b = h4/bool/COND (h4/words/word__msb a) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__2comp (h4/words/word__mod (h4/words/word__2comp a) (h4/words/word__2comp b))) (h4/words/word__2comp (h4/words/word__mod (h4/words/word__2comp a) b))) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__mod a (h4/words/word__2comp b)) (h4/words/word__mod a b))
% Assm: h4/words/word__smin__def: !b a. h4/words/word__smin a b = h4/bool/COND (h4/words/word__lt a b) a b
% Assm: h4/words/saturate__add__def: !b a. h4/words/saturate__add a b = h4/words/saturate__n2w (h4/arithmetic/_2B (h4/words/w2n a) (h4/words/w2n b))
% Assm: h4/words/nzcv__def: !b a. h4/words/nzcv a b = h4/bool/LET (\q. h4/bool/LET (\r. h4/pair/_2C (h4/words/word__msb r) (h4/pair/_2C (r = h4/words/n2w h4/num/0) (h4/pair/_2C (h4/bit/BIT (h4/fcp/dimindex h4/bool/the__value) q \/ b = h4/words/n2w h4/num/0) (~(h4/words/word__msb a <=> h4/words/word__msb b) /\ ~(h4/words/word__msb r <=> h4/words/word__msb a))))) (h4/words/n2w q)) (h4/arithmetic/_2B (h4/words/w2n a) (h4/words/w2n (h4/words/word__2comp b)))
% Assm: h4/words/word__bits__def: !l h. h4/words/word__bits h l = (\w. h4/fcp/FCP (\i. h4/arithmetic/_3C_3D (h4/arithmetic/_2B i l) (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ h4/fcp/fcp__index w (h4/arithmetic/_2B i l)))
% Assm: h4/words/n2w__w2n: !w. h4/words/n2w (h4/words/w2n w) = w
% Assm: h4/words/word__min__def: !b a. h4/words/word__min a b = h4/bool/COND (h4/words/word__lo a b) a b
% Assm: h4/words/word__smax__def: !b a. h4/words/word__smax a b = h4/bool/COND (h4/words/word__lt a b) b a
% Assm: h4/words/word__add__def: !w v. h4/words/word__add v w = h4/words/n2w (h4/arithmetic/_2B (h4/words/w2n v) (h4/words/w2n w))
% Assm: h4/words/word__asr__def: !w n. h4/words/word__asr w n = h4/fcp/FCP (\i. h4/bool/COND (h4/arithmetic/_3C_3D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/_2B i n)) (h4/words/word__msb w) (h4/fcp/fcp__index w (h4/arithmetic/_2B i n)))
% Assm: h4/words/WORD__XOR__ASSOC: !c b a. h4/words/word__xor (h4/words/word__xor a b) c = h4/words/word__xor a (h4/words/word__xor b c)
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/words/l2w__def: !l b. h4/words/l2w b l = h4/words/n2w (h4/numposrep/l2n b l)
% Assm: h4/words/w2l__def: !w b. h4/words/w2l b w = h4/numposrep/n2l b (h4/words/w2n w)
% Assm: h4/numposrep/l2n__n2l: !n b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b ==> h4/numposrep/l2n b (h4/numposrep/n2l b n) = n
% Assm: h4/words/word__ls__def: !b a. h4/words/word__ls a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. ~c \/ z)))) (h4/words/nzcv a b)
% Assm: h4/words/word__mod__def: !w v. h4/words/word__mod v w = h4/words/n2w (h4/arithmetic/MOD (h4/words/w2n v) (h4/words/w2n w))
% Assm: h4/words/bit__count__upto__def: !w n. h4/words/bit__count__upto n w = h4/sum__num/SUM n (\i. h4/bool/COND (h4/fcp/fcp__index w i) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/num/0)
% Assm: h4/words/WORD__NOT__XOR_c1: !b a. h4/words/word__xor a (h4/words/word__1comp b) = h4/words/word__1comp (h4/words/word__xor a b)
% Assm: h4/words/w2n__def: !w. h4/words/w2n w = h4/sum__num/SUM (h4/fcp/dimindex h4/bool/the__value) (\i. h4/bit/SBIT (h4/fcp/fcp__index w i) i)
% Assm: h4/words/saturate__mul__def: !b a. h4/words/saturate__mul a b = h4/words/saturate__n2w (h4/arithmetic/_2A (h4/words/w2n a) (h4/words/w2n b))
% Assm: h4/words/WORD__XOR__CLAUSES_c3: !a. h4/words/word__xor a (h4/words/n2w h4/num/0) = a
% Assm: h4/words/bit__count__def: !w. h4/words/bit__count w = h4/words/bit__count__upto (h4/fcp/dimindex h4/bool/the__value) w
% Assm: h4/words/word__mul__def: !w v. h4/words/word__mul v w = h4/words/n2w (h4/arithmetic/_2A (h4/words/w2n v) (h4/words/w2n w))
% Assm: h4/words/word__asr__bv__def: !w n. h4/words/word__asr__bv w n = h4/words/word__asr w (h4/words/w2n n)
% Assm: h4/words/word__abs__def: !w. h4/words/word__abs w = h4/bool/COND (h4/words/word__lt w (h4/words/n2w h4/num/0)) (h4/words/word__2comp w) w
% Assm: h4/words/word__lsl__def: !w n. h4/words/word__lsl w n = h4/fcp/FCP (\i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ h4/arithmetic/_3C_3D n i /\ h4/fcp/fcp__index w (h4/arithmetic/_2D i n))
% Assm: h4/words/word__sub__def: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% Assm: h4/words/WORD__XOR__CLAUSES_c4: !a. h4/words/word__xor a a = h4/words/n2w h4/num/0
% Assm: h4/words/word__ror__def: !w n. h4/words/word__ror w n = h4/fcp/FCP (\i. h4/fcp/fcp__index w (h4/arithmetic/MOD (h4/arithmetic/_2B i n) (h4/fcp/dimindex h4/bool/the__value)))
% Assm: h4/words/s2w__w2s: !w n2c c2n b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ (!x. h4/prim__rec/_3C x b ==> c2n (n2c x) = x) ==> h4/words/s2w b c2n (h4/words/w2s b n2c w) = w
% Assm: h4/words/WORD__MSB__1COMP: !w. h4/words/word__msb (h4/words/word__1comp w) <=> ~h4/words/word__msb w
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/words/s2w__def: !s f b. h4/words/s2w b f s = h4/words/n2w (h4/ASCIInumbers/s2n b f s)
% Assm: h4/words/w2s__def: !w f b. h4/words/w2s b f w = h4/ASCIInumbers/n2s b f (h4/words/w2n w)
% Assm: h4/ASCIInumbers/s2n__n2s: !n2c n c2n b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ (!x. h4/prim__rec/_3C x b ==> c2n (n2c x) = x) ==> h4/ASCIInumbers/s2n b c2n (h4/ASCIInumbers/n2s b n2c n) = n
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/words/DIMINDEX__GT__0: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Goal: !b a. h4/words/word__and a (h4/words/word__or a b) = a
%   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_wordss_wordu_u_oru_u_def]: !_0. (!v w i. happ (happ (happ _0 v) w) i <=> h4/fcp/fcp__index v i \/ h4/fcp/fcp__index w i) ==> (!w v. h4/words/word__or v w = h4/fcp/FCP (happ (happ _0 v) w))
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_TRUTH]: T
% 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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_fcps_CARTu_u_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 [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_fcps_FCPu_u_BETA]: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = happ g i
% Assm [h4s_wordss_WORDu_u_DEu_u_MORGANu_u_THMu_c1]: !b a. h4/words/word__1comp (h4/words/word__or a b) = h4/words/word__and (h4/words/word__1comp a) (h4/words/word__1comp b)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_wordss_wordu_u_andu_u_def]: !_0. (!v w i. happ (happ (happ _0 v) w) i <=> h4/fcp/fcp__index v i /\ h4/fcp/fcp__index w i) ==> (!w v. h4/words/word__and v w = h4/fcp/FCP (happ (happ _0 v) w))
% Assm [h4s_wordss_WORDu_u_ORu_u_ASSOC]: !c b a. h4/words/word__or (h4/words/word__or a b) c = h4/words/word__or a (h4/words/word__or b c)
% Assm [h4s_wordss_WORDu_u_ORu_u_IDEM]: !a. h4/words/word__or a a = a
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c4]: !a. h4/words/word__or a a = a
% Assm [h4s_wordss_WORDu_u_ORu_u_COMM]: !b a. h4/words/word__or a b = h4/words/word__or b a
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_fcps_FCPu_u_ETA]: !_0. (!g i. happ (happ _0 g) i = h4/fcp/fcp__index g i) ==> (!g. h4/fcp/FCP (happ _0 g) = g)
% Assm [h4s_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (h4/list/CONS a0 a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% Assm [h4s_wordss_WORDu_u_DEu_u_MORGANu_u_THMu_c0]: !b a. h4/words/word__1comp (h4/words/word__and a b) = h4/words/word__or (h4/words/word__1comp a) (h4/words/word__1comp b)
% Assm [h4s_wordss_WORDu_u_ANDu_u_ABSORD]: !b a. h4/words/word__or a (h4/words/word__and a b) = a
% 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_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% 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_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_bools_ORu_u_CLAUSESu_c4]: !t. t \/ t <=> t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_wordss_wordu_u_0]: !i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> ~h4/fcp/fcp__index (h4/words/n2w h4/num/0) i
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_wordss_wordu_u_T0]: !i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index h4/words/word__T i
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_wordss_wordu_u_1compu_u_def]: !_0. (!w i. happ (happ _0 w) i <=> ~h4/fcp/fcp__index w i) ==> (!w. h4/words/word__1comp w = h4/fcp/FCP (happ _0 w))
% Assm [h4s_wordss_WORDu_u_ANDu_u_IDEM]: !a. h4/words/word__and a a = a
% Assm [h4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c2]: !a. h4/words/word__and (h4/words/n2w h4/num/0) a = h4/words/n2w h4/num/0
% Assm [h4s_wordss_WORDu_u_ANDu_u_ASSOC]: !c b a. h4/words/word__and (h4/words/word__and a b) c = h4/words/word__and a (h4/words/word__and b c)
% Assm [h4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c4]: !a. h4/words/word__and a a = a
% Assm [h4s_wordss_WORDu_u_ANDu_u_COMM]: !b a. h4/words/word__and a b = h4/words/word__and b a
% Assm [h4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c0]: !a. h4/words/word__and h4/words/word__T a = a
% Assm [h4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c3]: !a. h4/words/word__and a (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Assm [h4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c1]: !a. h4/words/word__and a h4/words/word__T = a
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_wordss_wordu_u_andu_u_n2w]: !n m. h4/words/word__and (h4/words/n2w n) (h4/words/n2w m) = h4/words/n2w (h4/bit/BITWISE (h4/fcp/dimindex h4/bool/the__value) $and n m)
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c1]: !a. h4/words/word__or a h4/words/word__T = h4/words/word__T
% Assm [h4s_wordss_wordu_u_joinu_u_def]: !_1. (!cv cw. happ (happ _1 cv) cw = h4/words/word__or (h4/words/word__lsl cv (h4/fcp/dimindex h4/bool/the__value)) cw) ==> (!_0. (!cv. happ _0 cv = happ _1 cv) ==> (!w v. h4/words/word__join v w = h4/bool/LET (h4/bool/LET _0 (h4/words/w2w v)) (h4/words/w2w w)))
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c3]: !a. h4/words/word__or a (h4/words/n2w h4/num/0) = a
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c0]: !a. h4/words/word__or h4/words/word__T a = h4/words/word__T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c2]: !a. h4/words/word__or (h4/words/n2w h4/num/0) a = a
% Assm [h4s_wordss_wordu_u_oru_u_n2w]: !n m. h4/words/word__or (h4/words/n2w n) (h4/words/n2w m) = h4/words/n2w (h4/bit/BITWISE (h4/fcp/dimindex h4/bool/the__value) $or n m)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_wordss_concatu_u_wordu_u_listu_u_defu_c1]: !t h. h4/words/concat__word__list (h4/list/CONS h t) = h4/words/word__or (h4/words/w2w h) (h4/words/word__lsl (h4/words/concat__word__list t) (h4/fcp/dimindex h4/bool/the__value))
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_wordss_n2wu_u_def]: !_0. (!n i. happ (happ _0 n) i <=> h4/bit/BIT i n) ==> (!n. h4/words/n2w n = h4/fcp/FCP (happ _0 n))
% Assm [h4s_bits_BITWISEu_u_THM]: !x op n b a. h4/prim__rec/_3C x n ==> (h4/bit/BIT x (h4/bit/BITWISE n op a b) <=> happ (happ op (h4/bit/BIT x a)) (h4/bit/BIT x b))
% 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_wordss_wordu_u_xoru_u_def]: !_0. (!v w i. happ (happ (happ _0 v) w) i <=> ~(h4/fcp/fcp__index v i <=> h4/fcp/fcp__index w i)) ==> (!w v. h4/words/word__xor v w = h4/fcp/FCP (happ (happ _0 v) w))
% Assm [h4s_wordss_wordu_u_reverseu_u_def]: !_0. (!w i. happ (happ _0 w) i <=> h4/fcp/fcp__index w (h4/arithmetic/_2D (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i)) ==> (!w. h4/words/word__reverse w = h4/fcp/FCP (happ _0 w))
% Assm [h4s_wordss_wordu_u_divu_u_def]: !w v. h4/words/word__div v w = h4/words/n2w (h4/arithmetic/DIV (h4/words/w2n v) (h4/words/w2n w))
% 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))) /\ h4/fcp/fcp__index w b
% Assm [h4s_wordss_wordu_u_sliceu_u_def]: !_0. (!l h x i. happ (happ (happ (happ _0 l) h) x) i <=> h4/arithmetic/_3C_3D l i /\ h4/arithmetic/_3C_3D i (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ h4/fcp/fcp__index x i) ==> (!l h x. h4/words/word__slice h l x = h4/fcp/FCP (happ (happ (happ _0 l) h) x))
% Assm [h4s_wordss_wordu_u_ltu_u_def]: !_3. (!n v. happ (happ _3 n) v <=> ~(n <=> v)) ==> (!_2. (!n c. happ (happ _2 n) c = happ _3 n) ==> (!_1. (!n z. happ (happ _1 n) z = h4/pair/UNCURRY (happ _2 n)) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY (happ _1 n)) ==> (!b a. h4/words/word__lt a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_wordss_addu_u_withu_u_carryu_u_def]: !_3. (!result carry__out overflow. happ (happ (happ _3 result) carry__out) overflow = h4/pair/_2C result (h4/pair/_2C carry__out overflow)) ==> (!_2. (!result carry__out. happ (happ _2 result) carry__out = happ (happ _3 result) carry__out) ==> (!_1. (!unsigned__sum y x result. ?v. (v <=> (h4/words/word__msb x <=> h4/words/word__msb y) /\ ~(h4/words/word__msb x <=> h4/words/word__msb result)) /\ (?v'. (v' <=> ~(h4/words/w2n result = unsigned__sum)) /\ happ (happ (happ (happ _1 unsigned__sum) y) x) result = h4/bool/LET (h4/bool/LET (happ _2 result) v') v)) ==> (!_0. (!y x unsigned__sum. happ (happ (happ _0 y) x) unsigned__sum = h4/bool/LET (happ (happ (happ _1 unsigned__sum) y) x) (h4/words/n2w unsigned__sum)) ==> (!y x carry__in. h4/words/add__with__carry (h4/pair/_2C x (h4/pair/_2C y carry__in)) = h4/bool/LET (happ (happ _0 y) x) (h4/arithmetic/_2B (h4/arithmetic/_2B (h4/words/w2n x) (h4/words/w2n y)) (h4/bool/COND carry__in (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/num/0))))))
% Assm [h4s_wordss_wordu_u_equ_u_0]: !w. w = h4/words/n2w h4/num/0 <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> ~h4/fcp/fcp__index w i)
% Assm [h4s_wordss_wordu_u_compareu_u_def]: !b a. ?v. (v <=> a = b) /\ h4/words/word__compare a b = h4/bool/COND v (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/words/n2w h4/num/0)
% Assm [h4s_wordss_wordu_u_log2u_u_def]: !w. h4/words/word__log2 w = h4/words/n2w (h4/bit/LOG2 (h4/words/w2n w))
% Assm [h4s_wordss_wordu_u_hiu_u_def]: !_3. (!c z v. happ (happ (happ _3 c) z) v <=> c /\ ~z) ==> (!_2. (!z c. happ (happ _2 z) c = happ (happ _3 c) z) ==> (!_1. (!z. happ _1 z = h4/pair/UNCURRY (happ _2 z)) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY _1) ==> (!b a. h4/words/word__hi a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_wordss_l2wu_u_w2l]: !w b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b ==> h4/words/l2w b (h4/words/w2l b w) = w
% Assm [h4s_wordss_saturateu_u_subu_u_def]: !b a. h4/words/saturate__sub a b = h4/words/n2w (h4/arithmetic/_2D (h4/words/w2n a) (h4/words/w2n b))
% Assm [h4s_wordss_wordu_u_lsru_u_def]: !_0. (!w n i. happ (happ (happ _0 w) n) i <=> h4/prim__rec/_3C (h4/arithmetic/_2B i n) (h4/fcp/dimindex h4/bool/the__value) /\ h4/fcp/fcp__index w (h4/arithmetic/_2B i n)) ==> (!w n. h4/words/word__lsr w n = h4/fcp/FCP (happ (happ _0 w) n))
% Assm [h4s_wordss_wordu_u_xnoru_u_def]: !_0. (!v w i. happ (happ (happ _0 v) w) i <=> h4/fcp/fcp__index v i <=> h4/fcp/fcp__index w i) ==> (!w v. h4/words/word__xnor v w = h4/fcp/FCP (happ (happ _0 v) w))
% Assm [h4s_wordss_wordu_u_lslu_u_bvu_u_def]: !w n. h4/words/word__lsl__bv w n = h4/words/word__lsl w (h4/words/w2n n)
% Assm [h4s_wordss_wordu_u_2compu_u_def]: !w. h4/words/word__2comp w = h4/words/n2w (h4/arithmetic/_2D (h4/words/dimword h4/bool/the__value) (h4/words/w2n w))
% Assm [h4s_wordss_wordu_u_lsru_u_bvu_u_def]: !w n. h4/words/word__lsr__bv w n = h4/words/word__lsr w (h4/words/w2n n)
% Assm [h4s_wordss_WORDu_u_NOTu_u_XORu_c0]: !b a. h4/words/word__xor (h4/words/word__1comp a) (h4/words/word__1comp b) = h4/words/word__xor a b
% Assm [h4s_wordss_WORDu_u_NOTu_u_XORu_c2]: !b a. h4/words/word__xor (h4/words/word__1comp a) b = h4/words/word__1comp (h4/words/word__xor a b)
% Assm [h4s_wordss_wordu_u_sremu_u_def]: !b a. h4/words/word__srem a b = h4/bool/COND (h4/words/word__msb a) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__2comp (h4/words/word__mod (h4/words/word__2comp a) (h4/words/word__2comp b))) (h4/words/word__2comp (h4/words/word__mod (h4/words/word__2comp a) b))) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__mod a (h4/words/word__2comp b)) (h4/words/word__mod a b))
% Assm [h4s_wordss_wordu_u_sminu_u_def]: !b a. h4/words/word__smin a b = h4/bool/COND (h4/words/word__lt a b) a b
% Assm [h4s_wordss_saturateu_u_addu_u_def]: !b a. h4/words/saturate__add a b = h4/words/saturate__n2w (h4/arithmetic/_2B (h4/words/w2n a) (h4/words/w2n b))
% Assm [h4s_wordss_nzcvu_u_def]: !_1. (!q b a r. ?v. (v <=> ~(h4/words/word__msb a <=> h4/words/word__msb b) /\ ~(h4/words/word__msb r <=> h4/words/word__msb a)) /\ (?v'. (v' <=> h4/bit/BIT (h4/fcp/dimindex h4/bool/the__value) q \/ b = h4/words/n2w h4/num/0) /\ (?v''. (v'' <=> r = h4/words/n2w h4/num/0) /\ happ (happ (happ (happ _1 q) b) a) r = h4/pair/_2C (h4/words/word__msb r) (h4/pair/_2C v'' (h4/pair/_2C v' v))))) ==> (!_0. (!b a q. happ (happ (happ _0 b) a) q = h4/bool/LET (happ (happ (happ _1 q) b) a) (h4/words/n2w q)) ==> (!b a. h4/words/nzcv a b = h4/bool/LET (happ (happ _0 b) a) (h4/arithmetic/_2B (h4/words/w2n a) (h4/words/w2n (h4/words/word__2comp b)))))
% Assm [h4s_wordss_wordu_u_bitsu_u_def]: !_0. (!h x l i. happ (happ (happ (happ _0 h) x) l) i <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2B i l) (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) /\ h4/fcp/fcp__index x (h4/arithmetic/_2B i l)) ==> (!l h x. h4/words/word__bits h l x = h4/fcp/FCP (happ (happ (happ _0 h) x) l))
% Assm [h4s_wordss_n2wu_u_w2n]: !w. h4/words/n2w (h4/words/w2n w) = w
% Assm [h4s_wordss_wordu_u_minu_u_def]: !b a. h4/words/word__min a b = h4/bool/COND (h4/words/word__lo a b) a b
% Assm [h4s_wordss_wordu_u_smaxu_u_def]: !b a. h4/words/word__smax a b = h4/bool/COND (h4/words/word__lt a b) b a
% Assm [h4s_wordss_wordu_u_addu_u_def]: !w v. h4/words/word__add v w = h4/words/n2w (h4/arithmetic/_2B (h4/words/w2n v) (h4/words/w2n w))
% Assm [h4s_wordss_wordu_u_asru_u_def]: !_0. (!w n i. happ (happ (happ _0 w) n) i <=> h4/bool/COND (h4/arithmetic/_3C_3D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/_2B i n)) (h4/words/word__msb w) (h4/fcp/fcp__index w (h4/arithmetic/_2B i n))) ==> (!w n. h4/words/word__asr w n = h4/fcp/FCP (happ (happ _0 w) n))
% Assm [h4s_wordss_WORDu_u_XORu_u_ASSOC]: !c b a. h4/words/word__xor (h4/words/word__xor a b) c = h4/words/word__xor a (h4/words/word__xor b c)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_wordss_l2wu_u_def]: !l b. h4/words/l2w b l = h4/words/n2w (h4/numposrep/l2n b l)
% Assm [h4s_wordss_w2lu_u_def]: !w b. h4/words/w2l b w = h4/numposrep/n2l b (h4/words/w2n w)
% Assm [h4s_numposreps_l2nu_u_n2l]: !n b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b ==> h4/numposrep/l2n b (h4/numposrep/n2l b n) = n
% Assm [h4s_wordss_wordu_u_lsu_u_def]: !_3. (!c z v. happ (happ (happ _3 c) z) v <=> ~c \/ z) ==> (!_2. (!z c. happ (happ _2 z) c = happ (happ _3 c) z) ==> (!_1. (!z. happ _1 z = h4/pair/UNCURRY (happ _2 z)) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY _1) ==> (!b a. h4/words/word__ls a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_wordss_wordu_u_modu_u_def]: !w v. h4/words/word__mod v w = h4/words/n2w (h4/arithmetic/MOD (h4/words/w2n v) (h4/words/w2n w))
% Assm [h4s_wordss_bitu_u_countu_u_uptou_u_def]: !_0. (!w i. happ (happ _0 w) i = h4/bool/COND (h4/fcp/fcp__index w i) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/num/0) ==> (!w n. h4/words/bit__count__upto n w = h4/sum__num/SUM n (happ _0 w))
% Assm [h4s_wordss_WORDu_u_NOTu_u_XORu_c1]: !b a. h4/words/word__xor a (h4/words/word__1comp b) = h4/words/word__1comp (h4/words/word__xor a b)
% Assm [h4s_wordss_w2nu_u_def]: !_0. (!w i. happ (happ _0 w) i = h4/bit/SBIT (h4/fcp/fcp__index w i) i) ==> (!w. h4/words/w2n w = h4/sum__num/SUM (h4/fcp/dimindex h4/bool/the__value) (happ _0 w))
% Assm [h4s_wordss_saturateu_u_mulu_u_def]: !b a. h4/words/saturate__mul a b = h4/words/saturate__n2w (h4/arithmetic/_2A (h4/words/w2n a) (h4/words/w2n b))
% Assm [h4s_wordss_WORDu_u_XORu_u_CLAUSESu_c3]: !a. h4/words/word__xor a (h4/words/n2w h4/num/0) = a
% Assm [h4s_wordss_bitu_u_countu_u_def]: !w. h4/words/bit__count w = h4/words/bit__count__upto (h4/fcp/dimindex h4/bool/the__value) w
% Assm [h4s_wordss_wordu_u_mulu_u_def]: !w v. h4/words/word__mul v w = h4/words/n2w (h4/arithmetic/_2A (h4/words/w2n v) (h4/words/w2n w))
% Assm [h4s_wordss_wordu_u_asru_u_bvu_u_def]: !w n. h4/words/word__asr__bv w n = h4/words/word__asr w (h4/words/w2n n)
% Assm [h4s_wordss_wordu_u_absu_u_def]: !w. h4/words/word__abs w = h4/bool/COND (h4/words/word__lt w (h4/words/n2w h4/num/0)) (h4/words/word__2comp w) w
% Assm [h4s_wordss_wordu_u_lslu_u_def]: !_0. (!w n i. happ (happ (happ _0 w) n) i <=> h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) /\ h4/arithmetic/_3C_3D n i /\ h4/fcp/fcp__index w (h4/arithmetic/_2D i n)) ==> (!w n. h4/words/word__lsl w n = h4/fcp/FCP (happ (happ _0 w) n))
% Assm [h4s_wordss_wordu_u_subu_u_def]: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% Assm [h4s_wordss_WORDu_u_XORu_u_CLAUSESu_c4]: !a. h4/words/word__xor a a = h4/words/n2w h4/num/0
% Assm [h4s_wordss_wordu_u_roru_u_def]: !_0. (!w n i. happ (happ (happ _0 w) n) i <=> h4/fcp/fcp__index w (h4/arithmetic/MOD (h4/arithmetic/_2B i n) (h4/fcp/dimindex h4/bool/the__value))) ==> (!w n. h4/words/word__ror w n = h4/fcp/FCP (happ (happ _0 w) n))
% Assm [h4s_wordss_s2wu_u_w2s]: !w n2c c2n b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ (!x. h4/prim__rec/_3C x b ==> happ c2n (happ n2c x) = x) ==> h4/words/s2w b c2n (h4/words/w2s b n2c w) = w
% Assm [h4s_wordss_WORDu_u_MSBu_u_1COMP]: !w. h4/words/word__msb (h4/words/word__1comp w) <=> ~h4/words/word__msb w
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_wordss_s2wu_u_def]: !s f b. h4/words/s2w b f s = h4/words/n2w (h4/ASCIInumbers/s2n b f s)
% Assm [h4s_wordss_w2su_u_def]: !w f b. h4/words/w2s b f w = h4/ASCIInumbers/n2s b f (h4/words/w2n w)
% Assm [h4s_ASCIInumberss_s2nu_u_n2s]: !n2c n c2n b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ (!x. h4/prim__rec/_3C x b ==> happ c2n (happ n2c x) = x) ==> h4/ASCIInumbers/s2n b c2n (h4/ASCIInumbers/n2s b n2c n) = n
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_wordss_DIMINDEXu_u_GTu_u_0]: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Goal: !b a. h4/words/word__and a (h4/words/word__or a b) = a
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_Q1203111,TV_Q1203107]: ![V_f, V_g]: (![V_x]: s(TV_Q1203107,happ(s(t_fun(TV_Q1203111,TV_Q1203107),V_f),s(TV_Q1203111,V_x))) = s(TV_Q1203107,happ(s(t_fun(TV_Q1203111,TV_Q1203107),V_g),s(TV_Q1203111,V_x))) => s(t_fun(TV_Q1203111,TV_Q1203107),V_f) = s(t_fun(TV_Q1203111,TV_Q1203107),V_g))).
fof(ah4s_wordss_wordu_u_oru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_v, V_w, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_nums_num,V_i)))) | p(s(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)))))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
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_TRUTH, axiom, p(s(t_bool,t))).
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_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_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,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,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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
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,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_wordss_WORDu_u_DEu_u_MORGANu_u_THMu_c1, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_wordss_wordu_u_andu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_v, V_w, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_nums_num,V_i)))) & p(s(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)))))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_WORDu_u_ORu_u_ASSOC, axiom, ![TV_u_27a]: ![V_c, V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c)))))).
fof(ah4s_wordss_WORDu_u_ORu_u_IDEM, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c4, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ORu_u_COMM, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
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_fcps_FCPu_u_ETA, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_g, 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)),V_uu_0),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g),s(t_h4s_nums_num,V_i))) => ![V_g]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(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)),V_uu_0),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g))))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g))).
fof(ah4s_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),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,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_a1))))))).
fof(ah4s_wordss_WORDu_u_DEu_u_MORGANu_u_THMu_c0, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ah4s_wordss_WORDu_u_ANDu_u_ABSORD, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
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_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_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_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_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_bools_ORu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_wordss_wordu_u_0, axiom, ![TV_u_27a]: ![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,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_i))))))).
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_wordss_wordu_u_T0, axiom, ![TV_u_27a]: ![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,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t),s(t_h4s_nums_num,V_i)))))).
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_wordss_wordu_u_1compu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_i]: (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)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> ~ (p(s(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)))))) => ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = 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_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_WORDu_u_ANDu_u_IDEM, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c2, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_wordss_WORDu_u_ANDu_u_ASSOC, axiom, ![TV_u_27a]: ![V_c, V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c)))))).
fof(ah4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c4, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ANDu_u_COMM, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
fof(ah4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c3, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
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_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_wordss_wordu_u_andu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_m]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_bits_bitwise(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_and),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_wordss_wordu_u_joinu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_cv, V_cw]: s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv))),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cw))) = s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv),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,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cw))) => ![V_uu_0]: (![V_cv]: s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_0),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv))) = s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),V_cv))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_join(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w))) = s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b))),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)))),V_uu_0),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))))),s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w)))))))).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c3, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c2, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_wordu_u_oru_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_m]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_bits_bitwise(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_or),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_wordss_concatu_u_wordu_u_listu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_concatu_u_wordu_u_list(s(t_h4s_lists_list(t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_lists_cons(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_h),s(t_h4s_lists_list(t_h4s_fcps_cart(t_bool,TV_u_27a)),V_t))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_h))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_concatu_u_wordu_u_list(s(t_h4s_lists_list(t_h4s_fcps_cart(t_bool,TV_u_27a)),V_t))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_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_wordss_n2wu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n, V_i]: 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)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))) => ![V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(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)),V_uu_0),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_bits_BITWISEu_u_THM, axiom, ![V_x, V_op, V_n, V_b, V_a]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n)))) => s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_bits_bitwise(s(t_h4s_nums_num,V_n),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_op),s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b))))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_op),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_a))))),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_b))))))).
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_wordss_wordu_u_xoru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_v, V_w, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> ~ (s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_nums_num,V_i))) = s(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))))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_wordu_u_reverseu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, 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)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_nums_num,V_i))))) => ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_reverse(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = 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_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_wordu_u_divu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_div(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))))).
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,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_wordss_wordu_u_sliceu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_l, V_h, V_x, V_i]: (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)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)))),V_uu_0),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,V_h))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_i)))) & (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_h),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,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x),s(t_h4s_nums_num,V_i))))))) => ![V_l, V_h, V_x]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))) = 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_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)))),V_uu_0),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,V_h))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))))))).
fof(ah4s_wordss_wordu_u_ltu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_n, V_v]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_3),s(t_bool,V_n))),s(t_bool,V_v)))) <=> ~ (s(t_bool,V_n) = s(t_bool,V_v))) => ![V_uu_2]: (![V_n, V_c]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_n))),s(t_bool,V_c))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_3),s(t_bool,V_n))) => ![V_uu_1]: (![V_n, V_z]: s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool))),V_uu_1),s(t_bool,V_n))),s(t_bool,V_z))) = 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)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_n))))) => ![V_uu_0]: (![V_n]: s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0),s(t_bool,V_n))) = s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool))),V_uu_1),s(t_bool,V_n))))) => ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_wordss_nzcv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))))).
fof(ah4s_wordss_addu_u_withu_u_carryu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_result, V_carryu_u_out, V_overflow]: s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),happ(s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_3),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_carryu_u_out))),s(t_bool,V_overflow))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result),s(t_h4s_pairs_prod(t_bool,t_bool),h4s_pairs_u_2c(s(t_bool,V_carryu_u_out),s(t_bool,V_overflow))))) => ![V_uu_2]: (![V_result, V_carryu_u_out]: s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_2),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_carryu_u_out))) = s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_3),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_carryu_u_out))) => ![V_uu_1]: (![V_unsignedu_u_sum, V_y, V_x, V_result]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))) & ~ (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result)))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> ~ (s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))) = s(t_h4s_nums_num,V_unsignedu_u_sum))) & s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_1),s(t_h4s_nums_num,V_unsignedu_u_sum))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_bools_let(s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),h4s_bools_let(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_2),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_vi_))),s(t_bool,V_v))))) => ![V_uu_0]: (![V_y, V_x, V_unsignedu_u_sum]: s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,V_unsignedu_u_sum))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_1),s(t_h4s_nums_num,V_unsignedu_u_sum))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_unsignedu_u_sum))))) => ![V_y, V_x, V_carryu_u_in]: s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_wordss_addu_u_withu_u_carry(s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_bool)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_bool),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y),s(t_bool,V_carryu_u_in))))))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_carryu_u_in),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)))))))))))).
fof(ah4s_wordss_wordu_u_equ_u_0, axiom, ![TV_u_27a]: ![V_w]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))) <=> ![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,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_wordss_wordu_u_compareu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)) & s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_compare(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))))).
fof(ah4s_wordss_wordu_u_log2u_u_def, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_log2(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_bits_log2(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))))).
fof(ah4s_wordss_wordu_u_hiu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_c, V_z, V_v]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_c))),s(t_bool,V_z))),s(t_bool,V_v)))) <=> (p(s(t_bool,V_c)) & ~ (p(s(t_bool,V_z))))) => ![V_uu_2]: (![V_z, V_c]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_z))),s(t_bool,V_c))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_c))),s(t_bool,V_z))) => ![V_uu_1]: (![V_z]: s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1),s(t_bool,V_z))) = 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)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_z))))) => ![V_uu_0]: (![V_n]: s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0),s(t_bool,V_n))) = s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1))) => ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_hi(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_wordss_nzcv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))))).
fof(ah4s_wordss_l2wu_u_w2l, axiom, ![TV_u_27a]: ![V_w, V_b]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_b)))) => s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_l2w(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),h4s_wordss_w2l(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))).
fof(ah4s_wordss_saturateu_u_subu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_saturateu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))).
fof(ah4s_wordss_wordu_u_lsru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_n, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i)))) <=> (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_i),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_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n)))))))) => ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsr(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_n))) = 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_nums_num,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_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_wordu_u_xnoru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_v, V_w, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_nums_num,V_i))) = s(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)))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xnor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_wordu_u_lslu_u_bvu_u_def, axiom, ![TV_u_27a]: ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lslu_u_bv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),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),V_w),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_n)))))).
fof(ah4s_wordss_wordu_u_2compu_u_def, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))))).
fof(ah4s_wordss_wordu_u_lsru_u_bvu_u_def, axiom, ![TV_u_27a]: ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsru_u_bv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsr(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_n)))))).
fof(ah4s_wordss_WORDu_u_NOTu_u_XORu_c0, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))).
fof(ah4s_wordss_WORDu_u_NOTu_u_XORu_c2, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ah4s_wordss_wordu_u_sremu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_srem(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mod(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mod(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mod(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mod(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))).
fof(ah4s_wordss_wordu_u_sminu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_smin(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))).
fof(ah4s_wordss_saturateu_u_addu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_saturateu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_saturateu_u_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))).
fof(ah4s_wordss_nzcvu_u_def, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_q, V_b, V_a, V_r]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (~ (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & ~ (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> (p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,V_q)))) | s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) & ?[V_vi_i_]: ((p(s(t_bool,V_vi_i_)) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) & s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))))),V_uu_1),s(t_h4s_nums_num,V_q))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r))) = s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_pairs_u_2c(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),h4s_pairs_u_2c(s(t_bool,V_vi_i_),s(t_h4s_pairs_prod(t_bool,t_bool),h4s_pairs_u_2c(s(t_bool,V_vi_),s(t_bool,V_v)))))))))) => ![V_uu_0]: (![V_b, V_a, V_q]: s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,V_q))) = s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))))),V_uu_1),s(t_h4s_nums_num,V_q))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_q))))) => ![V_b, V_a]: s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_wordss_nzcv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))))))).
fof(ah4s_wordss_wordu_u_bitsu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_h, V_x, V_l, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)))),V_uu_0),s(t_h4s_nums_num,V_h))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_h),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,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_l)))))))) => ![V_l, V_h, V_x]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))) = 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_nums_num,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_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)))),V_uu_0),s(t_h4s_nums_num,V_h))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,V_l))))))).
fof(ah4s_wordss_n2wu_u_w2n, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)).
fof(ah4s_wordss_wordu_u_minu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_min(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))).
fof(ah4s_wordss_wordu_u_smaxu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_smax(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
fof(ah4s_wordss_wordu_u_addu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))))).
fof(ah4s_wordss_wordu_u_asru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_n, V_i]: 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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(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_u_2b(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))),s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))))) => ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_asr(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_n))) = 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_nums_num,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_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_WORDu_u_XORu_u_ASSOC, axiom, ![TV_u_27a]: ![V_c, V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c)))))).
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_l2wu_u_def, axiom, ![TV_u_27a]: ![V_l, V_b]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_l2w(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))).
fof(ah4s_wordss_w2lu_u_def, axiom, ![TV_u_27a]: ![V_w, V_b]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_wordss_w2l(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_numposreps_n2l(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_numposreps_l2nu_u_n2l, axiom, ![V_n, V_b]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_b)))) => s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),h4s_numposreps_n2l(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n))).
fof(ah4s_wordss_wordu_u_lsu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_c, V_z, V_v]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_c))),s(t_bool,V_z))),s(t_bool,V_v)))) <=> (~ (p(s(t_bool,V_c))) | p(s(t_bool,V_z)))) => ![V_uu_2]: (![V_z, V_c]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_z))),s(t_bool,V_c))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_c))),s(t_bool,V_z))) => ![V_uu_1]: (![V_z]: s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1),s(t_bool,V_z))) = 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)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_z))))) => ![V_uu_0]: (![V_n]: s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0),s(t_bool,V_n))) = s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1))) => ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_wordss_nzcv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))))).
fof(ah4s_wordss_wordu_u_modu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mod(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))))).
fof(ah4s_wordss_bitu_u_countu_u_uptou_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_i]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = s(t_h4s_nums_num,h4s_bools_cond(s(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_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_w, V_n]: s(t_h4s_nums_num,h4s_wordss_bitu_u_countu_u_upto(s(t_h4s_nums_num,V_n),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_nums_num,h4s_sumu_u_nums_sum(s(t_h4s_nums_num,V_n),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_WORDu_u_NOTu_u_XORu_c1, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ah4s_wordss_w2nu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_i]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = s(t_h4s_nums_num,h4s_bits_sbit(s(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_h4s_nums_num,V_i))) => ![V_w]: s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_nums_num,h4s_sumu_u_nums_sum(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_saturateu_u_mulu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_saturateu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_saturateu_u_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))).
fof(ah4s_wordss_WORDu_u_XORu_u_CLAUSESu_c3, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_bitu_u_countu_u_def, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_nums_num,h4s_wordss_bitu_u_count(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_nums_num,h4s_wordss_bitu_u_countu_u_upto(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))).
fof(ah4s_wordss_wordu_u_mulu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))))).
fof(ah4s_wordss_wordu_u_asru_u_bvu_u_def, axiom, ![TV_u_27a]: ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_asru_u_bv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_asr(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_n)))))).
fof(ah4s_wordss_wordu_u_absu_u_def, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_abs(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))).
fof(ah4s_wordss_wordu_u_lslu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_n, V_i]: (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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))),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,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_i)))) & p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))))))) => ![V_w, 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),V_w),s(t_h4s_nums_num,V_n))) = 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_nums_num,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_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_wordu_u_subu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_XORu_u_CLAUSESu_c4, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_wordss_wordu_u_roru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_n, V_i]: 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)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),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))))))) => ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_ror(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_n))) = 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_nums_num,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_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_s2wu_u_w2s, axiom, ![TV_u_27a]: ![V_w, V_n2c, V_c2n, V_b]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_b)))) & ![V_x]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_b)))) => s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_c2n),s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_n2c),s(t_h4s_nums_num,V_x))))) = s(t_h4s_nums_num,V_x))) => s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_s2w(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_c2n),s(t_h4s_lists_list(t_h4s_strings_char),h4s_wordss_w2s(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_n2c),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))).
fof(ah4s_wordss_WORDu_u_MSBu_u_1COMP, axiom, ![TV_u_27a]: ![V_w]: (p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))) <=> ~ (p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_wordss_s2wu_u_def, axiom, ![TV_u_27a]: ![V_s, V_f, V_b]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_s2w(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_f),s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_asciinumberss_s2n(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_f),s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))).
fof(ah4s_wordss_w2su_u_def, axiom, ![TV_u_27a]: ![V_w, V_f, V_b]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_wordss_w2s(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_f),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_asciinumberss_n2s(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_f),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_ASCIInumberss_s2nu_u_n2s, axiom, ![V_n2c, V_n, V_c2n, V_b]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_b)))) & ![V_x]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_b)))) => s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_c2n),s(t_h4s_strings_char,happ(s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_n2c),s(t_h4s_nums_num,V_x))))) = s(t_h4s_nums_num,V_x))) => s(t_h4s_nums_num,h4s_asciinumberss_s2n(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_c2n),s(t_h4s_lists_list(t_h4s_strings_char),h4s_asciinumberss_n2s(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_nums_num,t_h4s_strings_char),V_n2c),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n))).
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_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(ch4s_wordss_WORDu_u_ORu_u_ABSORB, conjecture, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
