%   ORIGINAL: h4/numeral__bit/NUMERAL__TIMES__2EXP_c1
% 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/prim__rec/num__Axiom: !f e. ?fn. fn h4/num/0 = e /\ (!n. fn (h4/num/SUC n) = f n (fn n))
% Assm: h4/bit/TIMES__2EXP__def: !x n. h4/bit/TIMES__2EXP x n = h4/arithmetic/_2A n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm: h4/numeral__bit/NUMERAL__TIMES__2EXP_c0: !n. h4/bit/TIMES__2EXP n h4/num/0 = h4/num/0
% Assm: h4/numeral__bit/SFUNPOW__def_c0: !x f. h4/numeral__bit/SFUNPOW f h4/num/0 x = x
% Assm: h4/numeral__bit/SFUNPOW__def_c1: !x n f. h4/numeral__bit/SFUNPOW f (h4/num/SUC n) x = h4/bool/COND (x = h4/num/0) h4/num/0 (h4/numeral__bit/SFUNPOW f n (f x))
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/arithmetic/MULT__CLAUSES_c0: !m. h4/arithmetic/_2A h4/num/0 m = h4/num/0
% Assm: h4/numeral/bit__initiality: !zf b2f b1f. ?f. f h4/arithmetic/ZERO = zf /\ (!n. f (h4/arithmetic/BIT1 n) = b1f n (f n)) /\ (!n. f (h4/arithmetic/BIT2 n) = b2f n (f n))
% Assm: h4/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/numeral__bit/NUMERAL__BIT__MODF_c4: !y x n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) f (h4/arithmetic/NUMERAL x) b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/numeral/iDUB e)) (h4/bool/COND (f b (h4/arithmetic/ODD x)) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm: h4/numeral__bit/NUMERAL__BIT__MODF_c1: !y n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f h4/num/0 b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) f h4/num/0 (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/numeral/iDUB e)) (h4/bool/COND (f b F) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm: h4/numeral__bit/NUMERAL__BIT__REV_c4: !y x n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) (h4/arithmetic/NUMERAL x) y = h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/bool/COND (h4/arithmetic/ODD x) (h4/arithmetic/BIT1 y) (h4/numeral/iDUB y))
% Assm: h4/numeral__bit/NUMERAL__BIT__REV_c3: !y x n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL x) y = h4/numeral__bit/BIT__REV (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/bool/COND (h4/arithmetic/ODD x) (h4/arithmetic/BIT1 y) (h4/numeral/iDUB y))
% Assm: h4/numeral__bit/NUMERAL__BIT__MODF_c3: !y x n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f (h4/arithmetic/NUMERAL x) b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) f (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/numeral/iDUB e)) (h4/bool/COND (f b (h4/arithmetic/ODD x)) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm: h4/numeral__bit/NUMERAL__BIT__MODF_c2: !y n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) f h4/num/0 b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f h4/num/0 (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/numeral/iDUB e)) (h4/bool/COND (f b F) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm: h4/numeral__bit/iDUB__NUMERAL: !i. h4/numeral/iDUB (h4/arithmetic/NUMERAL i) = h4/arithmetic/NUMERAL (h4/numeral/iDUB i)
% Assm: h4/numeral/iSUB__DEF_c2: !x n b. h4/numeral/iSUB b (h4/arithmetic/BIT2 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT2 n) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m))) (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m)) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)))
% Assm: h4/numeral__bit/numeral__imod__2exp_c5: !x n. h4/numeral__bit/iMOD__2EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 x)) (h4/arithmetic/BIT2 n) = h4/numeral/iDUB (h4/numeral__bit/iMOD__2EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) (h4/num/SUC n))
% Assm: h4/numeral__bit/NUMERAL__BIT__REV_c2: !y n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) h4/num/0 y = h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) h4/num/0 (h4/numeral/iDUB y)
% Assm: h4/numeral__bit/iBITWISE0_c1: !x opr b a. h4/numeral__bit/iBITWISE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) opr a b = h4/bool/LET (\w. h4/bool/COND (opr (h4/arithmetic/ODD a) (h4/arithmetic/ODD b)) (h4/arithmetic/BIT1 w) (h4/numeral/iDUB w)) (h4/numeral__bit/iBITWISE (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) opr (h4/arithmetic/DIV2 a) (h4/arithmetic/DIV2 b))
% Assm: h4/numeral__bit/NUMERAL__BIT__REV_c1: !y n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) h4/num/0 y = h4/numeral__bit/BIT__REV (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h4/num/0 (h4/numeral/iDUB y)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/numeral/iDUB0: !x. h4/numeral/iDUB x = h4/arithmetic/_2B x x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/numeral__bit/numeral__imod__2exp_c4: !x n. h4/numeral__bit/iMOD__2EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) (h4/arithmetic/BIT2 n) = h4/numeral/iDUB (h4/numeral__bit/iMOD__2EXP (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/num/SUC n))
% Assm: h4/arithmetic/ALT__ZERO: h4/arithmetic/ZERO = h4/num/0
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/numeral__bit/iBITWISE0_c2: !x opr b a. h4/numeral__bit/iBITWISE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 x)) opr a b = h4/bool/LET (\w. h4/bool/COND (opr (h4/arithmetic/ODD a) (h4/arithmetic/ODD b)) (h4/arithmetic/BIT1 w) (h4/numeral/iDUB w)) (h4/numeral__bit/iBITWISE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) opr (h4/arithmetic/DIV2 a) (h4/arithmetic/DIV2 b))
% Assm: h4/numeral/iSUB__THM_c2: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = h4/numeral/iDUB n
% Assm: h4/arithmetic/BIT20: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm: h4/numeral/internal__mult__characterisation_c2: !n m. h4/numeral/internal__mult (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/numeral/internal__mult n m)) m)
% Assm: h4/arithmetic/SUC__ELIM__NUMERALS: !g f. (!n. g (h4/num/SUC n) = f n (h4/num/SUC n)) <=> (!n. g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = f (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) /\ (!n. g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))
% Assm: h4/numeral/numeral__distrib_c13: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% 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__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% 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/RIGHT__ADD__DISTRIB: !p n m. h4/arithmetic/_2A (h4/arithmetic/_2B m n) p = h4/arithmetic/_2B (h4/arithmetic/_2A m p) (h4/arithmetic/_2A n p)
% Assm: h4/arithmetic/MULT__LEFT__1: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/DIV2__def: !n. h4/arithmetic/DIV2 n = h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/arithmetic/BIT10: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm: h4/arithmetic/ADD_c0: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/numeral/numeral__suc_c1: !n. h4/num/SUC (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 n
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/numeral/numeral__distrib_c34: ~h4/arithmetic/ODD h4/num/0
% Assm: h4/numeral/numeral__distrib_c14: !n. h4/num/SUC (h4/arithmetic/NUMERAL n) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Assm: h4/arithmetic/DIV__UNIQUE: !q n k. (?r. k = h4/arithmetic/_2B (h4/arithmetic/_2A q n) r /\ h4/prim__rec/_3C r n) ==> h4/arithmetic/DIV k n = q
% Assm: h4/arithmetic/MULT__COMM: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c3: !n. h4/arithmetic/_2A h4/num/0 n = h4/num/0
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/bit/SBIT__def: !n b. h4/bit/SBIT b n = h4/bool/COND b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n) h4/num/0
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/numeral/internal__mult__def: h4/numeral/internal__mult = h4/arithmetic/_2A
% Assm: h4/numeral/numeral__mult_c3: !n m. h4/arithmetic/_2A (h4/arithmetic/BIT2 n) m = h4/numeral/iDUB (h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/_2A n m) m))
% Assm: h4/numeral/numeral__mult_c2: !n m. h4/arithmetic/_2A (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/arithmetic/_2A n m)) m)
% Assm: h4/numeral/numeral__mult_c0: !n. h4/arithmetic/_2A h4/arithmetic/ZERO n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__mult_c1: !n. h4/arithmetic/_2A n h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/numeral__bit/BIT__MODF__def_c1: !y x n f e b. h4/numeral__bit/BIT__MODF (h4/num/SUC n) f x b e y = h4/numeral__bit/BIT__MODF n f (h4/arithmetic/DIV x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) e) (h4/bool/COND (f b (h4/arithmetic/ODD x)) (h4/arithmetic/_2B e y) y)
% Assm: h4/numeral__bit/BIT__MODF__def_c0: !y x f e b. h4/numeral__bit/BIT__MODF h4/num/0 f x b e y = y
% Assm: h4/numeral__bit/BIT__REV__def_c1: !y x n. h4/numeral__bit/BIT__REV (h4/num/SUC n) x y = h4/numeral__bit/BIT__REV n (h4/arithmetic/DIV x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) y) (h4/bit/SBIT (h4/arithmetic/ODD x) h4/num/0))
% Assm: h4/numeral__bit/BIT__REV__def_c0: !y x. h4/numeral__bit/BIT__REV h4/num/0 x y = y
% Assm: h4/numeral/TWO__EXP__THM_c0: h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/numeral__bit/iBITWISE__def: h4/numeral__bit/iBITWISE = h4/bit/BITWISE
% Assm: h4/bit/BITWISE__EVAL: !op n b a. h4/bit/BITWISE (h4/num/SUC n) op a b = h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/bit/BITWISE n op (h4/arithmetic/DIV a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/DIV b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bit/SBIT (op (h4/arithmetic/ODD a) (h4/arithmetic/ODD b)) h4/num/0)
% Assm: h4/bit/BITWISE__def_c0: !y x op. h4/bit/BITWISE h4/num/0 op x y = h4/num/0
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/EXP0_c0: !m. h4/arithmetic/EXP m h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/numeral__bit/iMOD__2EXP0: h4/numeral__bit/iMOD__2EXP = h4/bit/MOD__2EXP
% 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/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bit/MOD__2EXP__def: !x n. h4/bit/MOD__2EXP x n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/FORALL__AND__THM: !Q P. (!x. P x /\ Q x) <=> (!x. P x) /\ (!x. Q x)
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/arithmetic/MOD__COMMON__FACTOR: !q p n. h4/prim__rec/_3C h4/num/0 n /\ h4/prim__rec/_3C h4/num/0 q ==> h4/arithmetic/_2A n (h4/arithmetic/MOD p q) = h4/arithmetic/MOD (h4/arithmetic/_2A n p) (h4/arithmetic/_2A n q)
% Assm: h4/arithmetic/ZERO__LESS__EXP: !n m. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/num/SUC n) m)
% Assm: h4/arithmetic/TIMES2: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm: h4/arithmetic/ADD1: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/arithmetic/TWO: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/EXP0_c1: !n m. h4/arithmetic/EXP m (h4/num/SUC n) = h4/arithmetic/_2A m (h4/arithmetic/EXP m n)
% Assm: h4/arithmetic/ADD_c1: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/prim__rec/LESS__0: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% 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/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% 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/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/numeral/iSUB__DEF_c1: !x n b. h4/numeral/iSUB b (h4/arithmetic/BIT1 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m)) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m))) (h4/numeral/iBIT__cases x (h4/numeral/iDUB n) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) (\m. h4/numeral/iDUB (h4/numeral/iSUB F n m)))
% Assm: h4/numeral/iSUB__DEF_c0: !x b. h4/numeral/iSUB b h4/arithmetic/ZERO x = h4/arithmetic/ZERO
% Assm: h4/numeral/iBIT__cases0_c2: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT2 n) zf bf1 bf2 = bf2 n
% Assm: h4/numeral/iBIT__cases0_c1: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT1 n) zf bf1 bf2 = bf1 n
% Assm: h4/numeral/iBIT__cases0_c0: !zf bf2 bf1. h4/numeral/iBIT__cases h4/arithmetic/ZERO zf bf1 bf2 = zf
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/arithmetic/ADD__CLAUSES_c3: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/ADD__CLAUSES_c2: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/ADD__CLAUSES_c1: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/arithmetic/SUC__SUB1: !m. h4/arithmetic/_2D (h4/num/SUC m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Goal: !x n. h4/bit/TIMES__2EXP n (h4/arithmetic/NUMERAL x) = h4/arithmetic/NUMERAL (h4/numeral__bit/SFUNPOW h4/numeral/iDUB n x)
%   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_primu_u_recs_numu_u_Axiom]: !f e. ?fn. happ fn h4/num/0 = e /\ (!n. happ fn (h4/num/SUC n) = happ (happ f n) (happ fn n))
% Assm [h4s_bits_TIMESu_u_2EXPu_u_def]: !x n. h4/bit/TIMES__2EXP x n = happ (happ h4/arithmetic/_2A n) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm [h4s_numeralu_u_bits_NUMERALu_u_TIMESu_u_2EXPu_c0]: !n. h4/bit/TIMES__2EXP n h4/num/0 = h4/num/0
% Assm [h4s_numeralu_u_bits_SFUNPOWu_u_defu_c0]: !x f. h4/numeral__bit/SFUNPOW f h4/num/0 x = x
% Assm [h4s_numeralu_u_bits_SFUNPOWu_u_defu_c1]: !x n f. ?v. (v <=> x = h4/num/0) /\ h4/numeral__bit/SFUNPOW f (h4/num/SUC n) x = h4/bool/COND v h4/num/0 (h4/numeral__bit/SFUNPOW f n (happ f x))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c0]: !m. happ (happ h4/arithmetic/_2A h4/num/0) m = h4/num/0
% Assm [h4s_numerals_bitu_u_initiality]: !zf b2f b1f. ?f. happ f h4/arithmetic/ZERO = zf /\ (!n. happ f (h4/arithmetic/BIT1 n) = happ (happ b1f n) (happ f n)) /\ (!n. happ f (h4/arithmetic/BIT2 n) = happ (happ b2f n) (happ f n))
% Assm [h4s_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c4]: !y x n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) f (h4/arithmetic/NUMERAL x) b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (happ h4/numeral/iDUB e)) (h4/bool/COND (happ (happ f b) (h4/arithmetic/ODD x)) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c1]: !y n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f h4/num/0 b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) f h4/num/0 (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (happ h4/numeral/iDUB e)) (h4/bool/COND (happ (happ f b) F) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c4]: !y x n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) (h4/arithmetic/NUMERAL x) y = h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/bool/COND (h4/arithmetic/ODD x) (h4/arithmetic/BIT1 y) (happ h4/numeral/iDUB y))
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c3]: !y x n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL x) y = h4/numeral__bit/BIT__REV (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/bool/COND (h4/arithmetic/ODD x) (h4/arithmetic/BIT1 y) (happ h4/numeral/iDUB y))
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c3]: !y x n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f (h4/arithmetic/NUMERAL x) b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) f (h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL x)) (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (happ h4/numeral/iDUB e)) (h4/bool/COND (happ (happ f b) (h4/arithmetic/ODD x)) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c2]: !y n f e b. h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) f h4/num/0 b (h4/arithmetic/NUMERAL e) y = h4/numeral__bit/BIT__MODF (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) f h4/num/0 (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (happ h4/numeral/iDUB e)) (h4/bool/COND (happ (happ f b) F) (h4/arithmetic/_2B (h4/arithmetic/NUMERAL e) y) y)
% Assm [h4s_numeralu_u_bits_iDUBu_u_NUMERAL]: !i. happ h4/numeral/iDUB (h4/arithmetic/NUMERAL i) = h4/arithmetic/NUMERAL (happ h4/numeral/iDUB i)
% Assm [h4s_numerals_iSUBu_u_DEFu_c2]: !_2. (!n m. happ (happ _2 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) ==> (!_1. (!n m. happ (happ _1 n) m = happ h4/numeral/iDUB (h4/numeral/iSUB T n m)) ==> (!_0. (!n m. happ (happ _0 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)) ==> (!x n b. h4/numeral/iSUB b (h4/arithmetic/BIT2 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT2 n) (happ _0 n) (happ _1 n)) (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (happ _1 n) (happ _2 n)))))
% Assm [h4s_numeralu_u_bits_numeralu_u_imodu_u_2expu_c5]: !x n. happ (happ h4/numeral__bit/iMOD__2EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 x))) (h4/arithmetic/BIT2 n) = happ h4/numeral/iDUB (happ (happ h4/numeral__bit/iMOD__2EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x))) (h4/num/SUC n))
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c2]: !y n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) h4/num/0 y = h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) h4/num/0 (happ h4/numeral/iDUB y)
% Assm [h4s_numeralu_u_bits_iBITWISE0u_c1]: !_0. (!opr a b w. happ (happ (happ (happ _0 opr) a) b) w = h4/bool/COND (happ (happ opr (h4/arithmetic/ODD a)) (h4/arithmetic/ODD b)) (h4/arithmetic/BIT1 w) (happ h4/numeral/iDUB w)) ==> (!x opr b a. happ (happ (happ (happ h4/numeral__bit/iBITWISE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x))) opr) a) b = h4/bool/LET (happ (happ (happ _0 opr) a) b) (happ (happ (happ (happ h4/numeral__bit/iBITWISE (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) opr) (h4/arithmetic/DIV2 a)) (h4/arithmetic/DIV2 b)))
% Assm [h4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c1]: !y n. h4/numeral__bit/BIT__REV (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) h4/num/0 y = h4/numeral__bit/BIT__REV (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h4/num/0 (happ h4/numeral/iDUB y)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_numerals_iDUB0]: !x. happ h4/numeral/iDUB x = h4/arithmetic/_2B x x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_numeralu_u_bits_numeralu_u_imodu_u_2expu_c4]: !x n. happ (happ h4/numeral__bit/iMOD__2EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x))) (h4/arithmetic/BIT2 n) = happ h4/numeral/iDUB (happ (happ h4/numeral__bit/iMOD__2EXP (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/num/SUC n))
% Assm [h4s_arithmetics_ALTu_u_ZERO]: h4/arithmetic/ZERO = h4/num/0
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_numeralu_u_bits_iBITWISE0u_c2]: !_0. (!opr a b w. happ (happ (happ (happ _0 opr) a) b) w = h4/bool/COND (happ (happ opr (h4/arithmetic/ODD a)) (h4/arithmetic/ODD b)) (h4/arithmetic/BIT1 w) (happ h4/numeral/iDUB w)) ==> (!x opr b a. happ (happ (happ (happ h4/numeral__bit/iBITWISE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 x))) opr) a) b = h4/bool/LET (happ (happ (happ _0 opr) a) b) (happ (happ (happ (happ h4/numeral__bit/iBITWISE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 x))) opr) (h4/arithmetic/DIV2 a)) (h4/arithmetic/DIV2 b)))
% Assm [h4s_numerals_iSUBu_u_THMu_c2]: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = happ h4/numeral/iDUB n
% Assm [h4s_arithmetics_BIT20]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm [h4s_numerals_internalu_u_multu_u_characterisationu_c2]: !n m. happ (happ h4/numeral/internal__mult (h4/arithmetic/BIT1 n)) m = h4/numeral/iZ (h4/arithmetic/_2B (happ h4/numeral/iDUB (happ (happ h4/numeral/internal__mult n) m)) m)
% Assm [h4s_arithmetics_SUCu_u_ELIMu_u_NUMERALS]: !g f. (!n. happ g (h4/num/SUC n) = happ (happ f n) (h4/num/SUC n)) <=> (!n. happ g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = happ (happ f (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) /\ (!n. happ g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = happ (happ f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))
% Assm [h4s_numerals_numeralu_u_distribu_c13]: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% 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_addu_c1]: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% 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_RIGHTu_u_ADDu_u_DISTRIB]: !p n m. happ (happ h4/arithmetic/_2A (h4/arithmetic/_2B m n)) p = h4/arithmetic/_2B (happ (happ h4/arithmetic/_2A m) p) (happ (happ h4/arithmetic/_2A n) p)
% Assm [h4s_arithmetics_MULTu_u_LEFTu_u_1]: !m. happ (happ h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) m = m
% Assm [h4s_arithmetics_DIV2u_u_def]: !n. h4/arithmetic/DIV2 n = h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_arithmetics_BIT10]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm [h4s_arithmetics_ADDu_c0]: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_numerals_numeralu_u_sucu_c1]: !n. h4/num/SUC (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 n
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm [h4s_numerals_numeralu_u_distribu_c34]: ~h4/arithmetic/ODD h4/num/0
% Assm [h4s_numerals_numeralu_u_distribu_c14]: !n. h4/num/SUC (h4/arithmetic/NUMERAL n) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Assm [h4s_arithmetics_DIVu_u_UNIQUE]: !q n k. (?r. k = h4/arithmetic/_2B (happ (happ h4/arithmetic/_2A q) n) r /\ h4/prim__rec/_3C r n) ==> h4/arithmetic/DIV k n = q
% Assm [h4s_arithmetics_MULTu_u_COMM]: !n m. happ (happ h4/arithmetic/_2A m) n = happ (happ h4/arithmetic/_2A n) m
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c3]: !n. happ (happ h4/arithmetic/_2A h4/num/0) n = h4/num/0
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_bits_SBITu_u_def]: !n b. h4/bit/SBIT b n = h4/bool/COND b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n) h4/num/0
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_numerals_internalu_u_multu_u_def]: h4/numeral/internal__mult = h4/arithmetic/_2A
% Assm [h4s_numerals_numeralu_u_multu_c3]: !n m. happ (happ h4/arithmetic/_2A (h4/arithmetic/BIT2 n)) m = happ h4/numeral/iDUB (h4/numeral/iZ (h4/arithmetic/_2B (happ (happ h4/arithmetic/_2A n) m) m))
% Assm [h4s_numerals_numeralu_u_multu_c2]: !n m. happ (happ h4/arithmetic/_2A (h4/arithmetic/BIT1 n)) m = h4/numeral/iZ (h4/arithmetic/_2B (happ h4/numeral/iDUB (happ (happ h4/arithmetic/_2A n) m)) m)
% Assm [h4s_numerals_numeralu_u_multu_c0]: !n. happ (happ h4/arithmetic/_2A h4/arithmetic/ZERO) n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_multu_c1]: !n. happ (happ h4/arithmetic/_2A n) h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_numeralu_u_bits_BITu_u_MODFu_u_defu_c1]: !y x n f e b. h4/numeral__bit/BIT__MODF (h4/num/SUC n) f x b e y = h4/numeral__bit/BIT__MODF n f (h4/arithmetic/DIV x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (happ (happ h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) e) (h4/bool/COND (happ (happ f b) (h4/arithmetic/ODD x)) (h4/arithmetic/_2B e y) y)
% Assm [h4s_numeralu_u_bits_BITu_u_MODFu_u_defu_c0]: !y x f e b. h4/numeral__bit/BIT__MODF h4/num/0 f x b e y = y
% Assm [h4s_numeralu_u_bits_BITu_u_REVu_u_defu_c1]: !y x n. h4/numeral__bit/BIT__REV (h4/num/SUC n) x y = h4/numeral__bit/BIT__REV n (h4/arithmetic/DIV x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B (happ (happ h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) y) (h4/bit/SBIT (h4/arithmetic/ODD x) h4/num/0))
% Assm [h4s_numeralu_u_bits_BITu_u_REVu_u_defu_c0]: !y x. h4/numeral__bit/BIT__REV h4/num/0 x y = y
% Assm [h4s_numerals_TWOu_u_EXPu_u_THMu_c0]: h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_numeralu_u_bits_iBITWISEu_u_def]: h4/numeral__bit/iBITWISE = h4/bit/BITWISE
% Assm [h4s_bits_BITWISEu_u_EVAL]: !op n b a. happ (happ (happ (happ h4/bit/BITWISE (h4/num/SUC n)) op) a) b = h4/arithmetic/_2B (happ (happ h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (happ (happ (happ (happ h4/bit/BITWISE n) op) (h4/arithmetic/DIV a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/arithmetic/DIV b (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/bit/SBIT (happ (happ op (h4/arithmetic/ODD a)) (h4/arithmetic/ODD b)) h4/num/0)
% Assm [h4s_bits_BITWISEu_u_defu_c0]: !y x op. happ (happ (happ (happ h4/bit/BITWISE h4/num/0) op) x) y = h4/num/0
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_EXP0u_c0]: !m. h4/arithmetic/EXP m h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_numeralu_u_bits_iMODu_u_2EXP0]: h4/numeral__bit/iMOD__2EXP = h4/bit/MOD__2EXP
% 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_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bits_MODu_u_2EXPu_u_def]: !x n. happ (happ h4/bit/MOD__2EXP x) n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_FORALLu_u_ANDu_u_THM]: !Q P. (!x. happ P x /\ happ Q x) <=> (!x. happ P x) /\ (!x. happ Q x)
% Assm [h4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_arithmetics_MODu_u_COMMONu_u_FACTOR]: !q p n. h4/prim__rec/_3C h4/num/0 n /\ h4/prim__rec/_3C h4/num/0 q ==> happ (happ h4/arithmetic/_2A n) (h4/arithmetic/MOD p q) = h4/arithmetic/MOD (happ (happ h4/arithmetic/_2A n) p) (happ (happ h4/arithmetic/_2A n) q)
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EXP]: !n m. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/num/SUC n) m)
% Assm [h4s_arithmetics_TIMES2]: !n. happ (happ h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) n = h4/arithmetic/_2B n n
% Assm [h4s_arithmetics_ADD1]: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_arithmetics_TWO]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_EXP0u_c1]: !n m. h4/arithmetic/EXP m (h4/num/SUC n) = happ (happ h4/arithmetic/_2A m) (h4/arithmetic/EXP m n)
% Assm [h4s_arithmetics_ADDu_c1]: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_primu_u_recs_LESSu_u_0]: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_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_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% 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_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_numerals_iSUBu_u_DEFu_c1]: !_2. (!n m. happ (happ _2 n) m = happ h4/numeral/iDUB (h4/numeral/iSUB F n m)) ==> (!_1. (!n m. happ (happ _1 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) ==> (!_0. (!n m. happ (happ _0 n) m = happ h4/numeral/iDUB (h4/numeral/iSUB T n m)) ==> (!x n b. h4/numeral/iSUB b (h4/arithmetic/BIT1 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (happ _0 n) (happ _1 n)) (h4/numeral/iBIT__cases x (happ h4/numeral/iDUB n) (happ _1 n) (happ _2 n)))))
% Assm [h4s_numerals_iSUBu_u_DEFu_c0]: !x b. h4/numeral/iSUB b h4/arithmetic/ZERO x = h4/arithmetic/ZERO
% Assm [h4s_numerals_iBITu_u_cases0u_c2]: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT2 n) zf bf1 bf2 = happ bf2 n
% Assm [h4s_numerals_iBITu_u_cases0u_c1]: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT1 n) zf bf1 bf2 = happ bf1 n
% Assm [h4s_numerals_iBITu_u_cases0u_c0]: !zf bf2 bf1. h4/numeral/iBIT__cases h4/arithmetic/ZERO zf bf1 bf2 = zf
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c3]: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c2]: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_arithmetics_SUCu_u_SUB1]: !m. h4/arithmetic/_2D (h4/num/SUC m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Goal: !x n. h4/bit/TIMES__2EXP n (h4/arithmetic/NUMERAL x) = h4/arithmetic/NUMERAL (h4/numeral__bit/SFUNPOW h4/numeral/iDUB n x)
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_Q1091155,TV_Q1091151]: ![V_f, V_g]: (![V_x]: s(TV_Q1091151,happ(s(t_fun(TV_Q1091155,TV_Q1091151),V_f),s(TV_Q1091155,V_x))) = s(TV_Q1091151,happ(s(t_fun(TV_Q1091155,TV_Q1091151),V_g),s(TV_Q1091155,V_x))) => s(t_fun(TV_Q1091155,TV_Q1091151),V_f) = s(t_fun(TV_Q1091155,TV_Q1091151),V_g))).
fof(ah4s_primu_u_recs_numu_u_Axiom, axiom, ![TV_u_27a]: ![V_f, V_e]: ?[V_fn]: (s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_fn),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_e) & ![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_fn),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_h4s_nums_num,V_n))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_fn),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_bits_TIMESu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),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,V_x)))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_TIMESu_u_2EXPu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_numeralu_u_bits_SFUNPOWu_u_defu_c0, axiom, ![V_x, V_f]: s(t_h4s_nums_num,h4s_numeralu_u_bits_sfunpow(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_numeralu_u_bits_SFUNPOWu_u_defu_c1, axiom, ![V_x, V_n, V_f]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_x) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_nums_num,h4s_numeralu_u_bits_sfunpow(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_numeralu_u_bits_sfunpow(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f),s(t_h4s_nums_num,V_x))))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_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_arithmetics_MULTu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_numerals_bitu_u_initiality, axiom, ![TV_u_27a]: ![V_zf, V_b2f, V_b1f]: ?[V_f]: (s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(TV_u_27a,V_zf) & (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_b1f),s(t_h4s_nums_num,V_n))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n))))) & ![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_b2f),s(t_h4s_nums_num,V_n))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c4, axiom, ![V_y, V_x, V_n, V_f, V_e, V_b]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_e))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_b))),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c1, axiom, ![V_y, V_n, V_f, V_e, V_b]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_e))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_b))),s(t_bool,f))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c4, axiom, ![V_y, V_x, V_n]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_y)))))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c3, axiom, ![V_y, V_x, V_n]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_y)))))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c3, axiom, ![V_y, V_x, V_n, V_f, V_e, V_b]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_e))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_b))),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c2, axiom, ![V_y, V_n, V_f, V_e, V_b]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_e))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_b))),s(t_bool,f))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numeralu_u_bits_iDUBu_u_NUMERAL, axiom, ![V_i]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_i))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_i)))))).
fof(ah4s_numerals_iSUBu_u_DEFu_c2, axiom, ![V_uu_2]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_1]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_0]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_x, V_n, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))))))))))).
fof(ah4s_numeralu_u_bits_numeralu_u_imodu_u_2expu_c5, axiom, ![V_x, V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numeralu_u_bits_imodu_u_2exp),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_x))))))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numeralu_u_bits_imodu_u_2exp),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c2, axiom, ![V_y, V_n]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numeralu_u_bits_iBITWISE0u_c1, axiom, ![V_uu_0]: (![V_opr, V_a, V_b, V_w]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,V_w))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_a))))),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_b))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_w))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_w))))) => ![V_x, V_opr, V_b, V_a]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_numeralu_u_bits_ibitwise),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))) = s(t_h4s_nums_num,h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_numeralu_u_bits_ibitwise),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_a))))),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_b))))))))).
fof(ah4s_numeralu_u_bits_NUMERALu_u_BITu_u_REVu_c1, axiom, ![V_y, V_n]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_y)))))).
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_numerals_iDUB0, axiom, ![V_x]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_x)))).
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_numeralu_u_bits_numeralu_u_imodu_u_2expu_c4, axiom, ![V_x, V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numeralu_u_bits_imodu_u_2exp),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numeralu_u_bits_imodu_u_2exp),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_arithmetics_ALTu_u_ZERO, axiom, s(t_h4s_nums_num,h4s_arithmetics_zero) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_numeralu_u_bits_iBITWISE0u_c2, axiom, ![V_uu_0]: (![V_opr, V_a, V_b, V_w]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,V_w))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_a))))),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_b))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_w))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_w))))) => ![V_x, V_opr, V_b, V_a]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_numeralu_u_bits_ibitwise),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_x))))))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))) = s(t_h4s_nums_num,h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_numeralu_u_bits_ibitwise),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_opr))),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_a))))),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_b))))))))).
fof(ah4s_numerals_iSUBu_u_THMu_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),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_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_BIT20, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))))).
fof(ah4s_numerals_internalu_u_multu_u_characterisationu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numerals_internalu_u_mult),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numerals_internalu_u_mult),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_SUCu_u_ELIMu_u_NUMERALS, axiom, ![TV_u_27a]: ![V_g, V_f]: (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) <=> (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) & ![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_numerals_numeralu_u_distribu_c13, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
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_addu_c1, 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,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,V_n)).
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_RIGHTu_u_ADDu_u_DISTRIB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_MULTu_u_LEFTu_u_1, axiom, ![V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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_DIV2u_u_def, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_BIT10, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ah4s_arithmetics_ADDu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_numerals_numeralu_u_sucu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(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_n)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c34, axiom, ~ (p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_numerals_numeralu_u_distribu_c14, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(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,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_DIVu_u_UNIQUE, axiom, ![V_q, V_n, V_k]: (?[V_r]: (s(t_h4s_nums_num,V_k) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_q))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_r))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_r),s(t_h4s_nums_num,V_n))))) => s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_q))).
fof(ah4s_arithmetics_MULTu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),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_c3, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_bits_SBITu_u_def, axiom, ![V_n, V_b]: s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,V_b),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_b),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,V_n))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_numerals_internalu_u_multu_u_def, axiom, s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numerals_internalu_u_mult) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a)).
fof(ah4s_numerals_numeralu_u_multu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_multu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_numeralu_u_multu_c0, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_numeralu_u_multu_c1, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_numeralu_u_bits_BITu_u_MODFu_u_defu_c1, axiom, ![V_y, V_x, V_n, V_f, V_e, V_b]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_e),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,V_n),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_x),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_arithmetics_u_2b(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_e))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_b))),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_e),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,V_y)))))).
fof(ah4s_numeralu_u_bits_BITu_u_MODFu_u_defu_c0, axiom, ![V_y, V_x, V_f, V_e, V_b]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_nums_0),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_e),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,V_y)).
fof(ah4s_numeralu_u_bits_BITu_u_REVu_u_defu_c1, axiom, ![V_y, V_x, V_n]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_x),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_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ah4s_numeralu_u_bits_BITu_u_REVu_u_defu_c0, axiom, ![V_y, V_x]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,V_y)).
fof(ah4s_numerals_TWOu_u_EXPu_u_THMu_c0, axiom, 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_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_numeralu_u_bits_iBITWISEu_u_def, axiom, s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_numeralu_u_bits_ibitwise) = s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_bits_bitwise)).
fof(ah4s_bits_BITWISEu_u_EVAL, axiom, ![V_op, V_n, V_b, V_a]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_bits_bitwise),s(t_h4s_nums_num,h4s_nums_suc(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_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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,h4s_arithmetics_div(s(t_h4s_nums_num,V_a),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_arithmetics_div(s(t_h4s_nums_num,V_b),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_bits_sbit(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_arithmetics_odd(s(t_h4s_nums_num,V_a))))),s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_b))))),s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_bits_BITWISEu_u_defu_c0, axiom, ![V_y, V_x, V_op]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_bits_bitwise),s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_op))),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_EXP0u_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_numeralu_u_bits_iMODu_u_2EXP0, axiom, s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_numeralu_u_bits_imodu_u_2exp) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_bits_modu_u_2exp)).
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_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_bits_MODu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_bits_modu_u_2exp),s(t_h4s_nums_num,V_x))),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_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,V_x)))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_FORALLu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ![V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_arithmetics_MODu_u_COMMONu_u_FACTOR, axiom, ![V_q, V_p, 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)))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_q))))) => s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_q))))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_q))))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EXP, axiom, ![V_n, V_m]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_TIMES2, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ADD1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_ONE, axiom, 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_suc(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_TWO, axiom, 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_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_EXP0u_c1, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_c1, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_primu_u_recs_LESSu_u_0, 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,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_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_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => 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_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_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_numerals_iSUBu_u_DEFu_c1, axiom, ![V_uu_2]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_1]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_0]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_x, V_n, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))))))))))).
fof(ah4s_numerals_iSUBu_u_DEFu_c0, axiom, ![V_x, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_iBITu_u_cases0u_c2, axiom, ![TV_u_27a]: ![V_zf, V_n, V_bf2, V_bf1]: s(TV_u_27a,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_zf),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_iBITu_u_cases0u_c1, axiom, ![TV_u_27a]: ![V_zf, V_n, V_bf2, V_bf1]: s(TV_u_27a,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_zf),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_iBITu_u_cases0u_c0, axiom, ![TV_u_27a]: ![V_zf, V_bf2, V_bf1]: s(TV_u_27a,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,h4s_arithmetics_zero),s(TV_u_27a,V_zf),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2))) = s(TV_u_27a,V_zf)).
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_arithmetics_ADDu_u_CLAUSESu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_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_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_SUCu_u_SUB1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,V_m)).
fof(ch4s_numeralu_u_bits_NUMERALu_u_TIMESu_u_2EXPu_c1, conjecture, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numeralu_u_bits_sfunpow(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numerals_idub),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_x)))))).
