%   ORIGINAL: h4/words/WORD__OR__IDEM
% 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/words/WORD__OR__COMM: !b a. h4/words/word__or a b = h4/words/word__or b a
% 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/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__CLAUSES_c4: !a. h4/words/word__or a a = a
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/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/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/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/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/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/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__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% 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__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__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/words/WORD__OR__CLAUSES_c2: !a. h4/words/word__or (h4/words/n2w h4/num/0) a = a
% 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/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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/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/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/fcp/FCP__ETA: !g. h4/fcp/FCP (\i. h4/fcp/fcp__index g i) = g
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> 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_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/OR__CLAUSES_c4: !t. t \/ t <=> t
% 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__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/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/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/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__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/words/WORD__XOR__CLAUSES_c0: !a. h4/words/word__xor h4/words/word__T a = h4/words/word__1comp a
% 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/dimindex__1__cases: !a. h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) ==> a = h4/words/n2w h4/num/0 \/ a = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/words/w2n__11: !w v. h4/words/w2n v = h4/words/w2n w <=> v = w
% Assm: h4/words/WORD__XOR__COMM: !b a. h4/words/word__xor a b = h4/words/word__xor b a
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% 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/w2s__def: !w f b. h4/words/w2s b f w = h4/ASCIInumbers/n2s b f (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/w2n__n2w: !n. h4/words/w2n (h4/words/n2w n) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm: h4/words/n2w__11: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm: h4/words/word__lo__def: !b a. h4/words/word__lo a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. ~c)))) (h4/words/nzcv a b)
% Assm: h4/words/word__signed__bits__def: !l h. h4/words/word__signed__bits h l = (\w. h4/fcp/FCP (\i. h4/arithmetic/_3C_3D 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/MIN (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)))))))
% Assm: h4/words/WORD__XOR__CLAUSES_c2: !a. h4/words/word__xor (h4/words/n2w h4/num/0) a = a
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% 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/w2n__eq__0: !w. h4/words/w2n w = h4/num/0 <=> w = h4/words/n2w h4/num/0
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/words/ranged__word__nchotomy: !w. ?n. w = h4/words/n2w n /\ h4/prim__rec/_3C n (h4/words/dimword h4/bool/the__value)
% Assm: h4/words/word__len__def: !w. h4/words/word__len w = h4/fcp/dimindex h4/bool/the__value
% 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__gt__def: !b a. h4/words/word__gt a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. ~z /\ (n <=> v))))) (h4/words/nzcv a b)
% Assm: h4/words/word__sdiv__def: !b a. h4/words/word__sdiv a b = h4/bool/COND (h4/words/word__msb a) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__div (h4/words/word__2comp a) (h4/words/word__2comp b)) (h4/words/word__2comp (h4/words/word__div (h4/words/word__2comp a) b))) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__2comp (h4/words/word__div a (h4/words/word__2comp b))) (h4/words/word__div a b))
% Assm: h4/words/WORD__AND__CLAUSES_c1: !a. h4/words/word__and a h4/words/word__T = 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__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/bool/NOT__CLAUSES_c1: ~T <=> F
% 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__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__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__smin__def: !b a. h4/words/word__smin a b = h4/bool/COND (h4/words/word__lt a b) a b
% Assm: h4/words/WORD__XOR__CLAUSES_c1: !a. h4/words/word__xor a h4/words/word__T = h4/words/word__1comp a
% Assm: h4/words/word__le__def: !b a. h4/words/word__le a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. z \/ ~(n <=> v))))) (h4/words/nzcv a b)
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/words/dimword__def: h4/words/dimword h4/bool/the__value = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c3: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__add_c6: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/arithmetic/EXP__1_c1: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/words/word__ror__bv__def: !w n. h4/words/word__ror__bv w n = h4/words/word__ror w (h4/words/w2n n)
% 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__nchotomy: !w. ?n. w = h4/words/n2w n
% Assm: h4/words/ZERO__LT__dimword: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm: h4/arithmetic/ZERO__MOD: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm: h4/words/WORD__AND__CLAUSES_c0: !a. h4/words/word__and h4/words/word__T a = a
% 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/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/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/words/n2w__w2n: !w. h4/words/n2w (h4/words/w2n w) = w
% 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/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/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
% Goal: !a. h4/words/word__or a a = 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_wordss_WORDu_u_ORu_u_COMM]: !b a. h4/words/word__or a b = h4/words/word__or b a
% 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_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_CLAUSESu_c4]: !a. h4/words/word__or a a = a
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_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_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_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_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_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_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_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% 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_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_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_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_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_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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_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_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_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_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> 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_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c4]: !t. t \/ t <=> t
% 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_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_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_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_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_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_wordss_WORDu_u_XORu_u_CLAUSESu_c0]: !a. h4/words/word__xor h4/words/word__T a = h4/words/word__1comp a
% 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_dimindexu_u_1u_u_cases]: !a. h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) ==> a = h4/words/n2w h4/num/0 \/ a = h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_wordss_w2nu_u_11]: !w v. h4/words/w2n v = h4/words/w2n w <=> v = w
% Assm [h4s_wordss_WORDu_u_XORu_u_COMM]: !b a. h4/words/word__xor a b = h4/words/word__xor b a
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% 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_w2su_u_def]: !w f b. h4/words/w2s b f w = h4/ASCIInumbers/n2s b f (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_w2nu_u_n2w]: !n. h4/words/w2n (h4/words/n2w n) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_wordss_n2wu_u_11]: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_wordss_wordu_u_lou_u_def]: !_3. (!c v. happ (happ _3 c) v <=> ~c) ==> (!_2. (!c. happ _2 c = happ _3 c) ==> (!_1. (!z. happ _1 z = h4/pair/UNCURRY _2) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY _1) ==> (!b a. h4/words/word__lo a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_wordss_wordu_u_signedu_u_bitsu_u_def]: !_0. (!x l h i. happ (happ (happ (happ _0 x) l) h) i <=> h4/arithmetic/_3C_3D 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/MIN (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)))))) ==> (!l h x. h4/words/word__signed__bits h l x = h4/fcp/FCP (happ (happ (happ _0 x) l) h))
% Assm [h4s_wordss_WORDu_u_XORu_u_CLAUSESu_c2]: !a. h4/words/word__xor (h4/words/n2w h4/num/0) a = a
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% 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_w2nu_u_equ_u_0]: !w. h4/words/w2n w = h4/num/0 <=> w = h4/words/n2w h4/num/0
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_wordss_rangedu_u_wordu_u_nchotomy]: !w. ?n. w = h4/words/n2w n /\ h4/prim__rec/_3C n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_wordss_wordu_u_lenu_u_def]: !w. h4/words/word__len w = h4/fcp/dimindex h4/bool/the__value
% 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_gtu_u_def]: !_3. (!z n v. happ (happ (happ _3 z) n) v <=> ~z /\ (n <=> v)) ==> (!_2. (!z n c. happ (happ (happ _2 z) n) c = happ (happ _3 z) n) ==> (!_1. (!n z. happ (happ _1 n) z = h4/pair/UNCURRY (happ (happ _2 z) n)) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY (happ _1 n)) ==> (!b a. h4/words/word__gt a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_wordss_wordu_u_sdivu_u_def]: !b a. h4/words/word__sdiv a b = h4/bool/COND (h4/words/word__msb a) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__div (h4/words/word__2comp a) (h4/words/word__2comp b)) (h4/words/word__2comp (h4/words/word__div (h4/words/word__2comp a) b))) (h4/bool/COND (h4/words/word__msb b) (h4/words/word__2comp (h4/words/word__div a (h4/words/word__2comp b))) (h4/words/word__div a b))
% Assm [h4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c1]: !a. h4/words/word__and a h4/words/word__T = 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_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_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% 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_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_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_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_WORDu_u_XORu_u_CLAUSESu_c1]: !a. h4/words/word__xor a h4/words/word__T = h4/words/word__1comp a
% Assm [h4s_wordss_wordu_u_leu_u_def]: !_3. (!z n v. happ (happ (happ _3 z) n) v <=> z \/ ~(n <=> v)) ==> (!_2. (!z n c. happ (happ (happ _2 z) n) c = happ (happ _3 z) n) ==> (!_1. (!n z. happ (happ _1 n) z = h4/pair/UNCURRY (happ (happ _2 z) n)) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY (happ _1 n)) ==> (!b a. h4/words/word__le a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_wordss_dimwordu_u_def]: h4/words/dimword h4/bool/the__value = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c3]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_addu_c6]: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_arithmetics_EXPu_u_1u_c1]: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_wordss_wordu_u_roru_u_bvu_u_def]: !w n. h4/words/word__ror__bv w n = h4/words/word__ror w (h4/words/w2n 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_nchotomy]: !w. ?n. w = h4/words/n2w n
% Assm [h4s_wordss_ZEROu_u_LTu_u_dimword]: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm [h4s_arithmetics_ZEROu_u_MOD]: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm [h4s_wordss_WORDu_u_ANDu_u_CLAUSESu_c0]: !a. h4/words/word__and h4/words/word__T a = a
% 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_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_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_wordss_n2wu_u_w2n]: !w. h4/words/n2w (h4/words/w2n w) = w
% 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_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_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
% Goal: !a. h4/words/word__or a a = 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_Q1203058,TV_Q1203054]: ![V_f, V_g]: (![V_x]: s(TV_Q1203054,happ(s(t_fun(TV_Q1203058,TV_Q1203054),V_f),s(TV_Q1203058,V_x))) = s(TV_Q1203054,happ(s(t_fun(TV_Q1203058,TV_Q1203054),V_g),s(TV_Q1203058,V_x))) => s(t_fun(TV_Q1203058,TV_Q1203054),V_f) = s(t_fun(TV_Q1203058,TV_Q1203054),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_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_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_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_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_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_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_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_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_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_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_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_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_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_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_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_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_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_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_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_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_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_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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_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_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_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_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_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_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_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
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_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_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_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_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_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_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_wordss_WORDu_u_XORu_u_CLAUSESu_c0, 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),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_1comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
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_dimindexu_u_1u_u_cases, axiom, ![TV_u_27a]: ![V_a]: (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_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) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_wordss_w2nu_u_11, axiom, ![TV_u_27a]: ![V_w, V_v]: (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))) <=> 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_XORu_u_COMM, 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),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_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
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_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_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_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_w2nu_u_n2w, axiom, ![TV_u_27a]: ![V_n]: s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))).
fof(ah4s_wordss_n2wu_u_11, axiom, ![TV_u_27a]: ![V_n, V_m]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_wordss_wordu_u_lou_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_c, 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_c))),s(t_bool,V_v)))) <=> ~ (p(s(t_bool,V_c)))) => ![V_uu_2]: (![V_c]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_2),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_c))) => ![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)),V_uu_2))) => ![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_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_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_signedu_u_bitsu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_l, V_h, 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_nums_num,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_fun(t_h4s_nums_num,t_bool)))),V_uu_0),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_h))),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,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_min(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)))))))))))))))) => ![V_l, V_h, V_x]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_signedu_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_nums_num,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_fun(t_h4s_nums_num,t_bool)))),V_uu_0),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_h))))))).
fof(ah4s_wordss_WORDu_u_XORu_u_CLAUSESu_c2, 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),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_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_w2nu_u_equ_u_0, axiom, ![TV_u_27a]: ![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_nums_0) <=> 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))))).
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_rangedu_u_wordu_u_nchotomy, axiom, ![TV_u_27a]: ![V_w]: ?[V_n]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))).
fof(ah4s_wordss_wordu_u_lenu_u_def, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_nums_num,h4s_wordss_wordu_u_len(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))).
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_gtu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_z, 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)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_z))),s(t_bool,V_n))),s(t_bool,V_v)))) <=> (~ (p(s(t_bool,V_z))) & s(t_bool,V_n) = s(t_bool,V_v))) => ![V_uu_2]: (![V_z, 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))),happ(s(t_fun(t_bool,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_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)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_z))),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))),happ(s(t_fun(t_bool,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_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_gt(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_sdivu_u_def, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sdiv(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_div(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_div(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_2comp(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_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_div(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_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_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_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_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
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_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_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_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_WORDu_u_XORu_u_CLAUSESu_c1, 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_wordu_u_t))) = 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)))).
fof(ah4s_wordss_wordu_u_leu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_z, 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)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_z))),s(t_bool,V_n))),s(t_bool,V_v)))) <=> (p(s(t_bool,V_z)) | ~ (s(t_bool,V_n) = s(t_bool,V_v)))) => ![V_uu_2]: (![V_z, 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))),happ(s(t_fun(t_bool,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_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)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_z))),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))),happ(s(t_fun(t_bool,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_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_le(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_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_wordss_dimwordu_u_def, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_addu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_addu_c6, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_sucu_c0, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_EXPu_u_1u_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_arithmetics_EQu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_wordss_wordu_u_roru_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_roru_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_ror(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_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_nchotomy, axiom, ![TV_u_27a]: ![V_w]: ?[V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n)))).
fof(ah4s_wordss_ZEROu_u_LTu_u_dimword, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_arithmetics_ZEROu_u_MOD, axiom, ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_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_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_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_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_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_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_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_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(ch4s_wordss_WORDu_u_ORu_u_IDEM, conjecture, ![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)).
