%   ORIGINAL: h4/bitstring/bitify__ind
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bitstring/bitify__tupled__primitive__def: h4/bitstring/bitify__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!l a. R (h4/pair/_2C (h4/list/CONS h4/num/0 a) l) (h4/pair/_2C a (h4/list/CONS F l))) /\ (!l a. R (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l) (h4/pair/_2C a (h4/list/CONS T l))))) (\bitify__tupled a_27. h4/pair/pair__CASE a_27 (\a v1. h4/list/list__CASE v1 (h4/combin/I a) (\v2 l. h4/bool/COND v2 (h4/combin/I (bitify__tupled (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l))) (h4/combin/I (bitify__tupled (h4/pair/_2C (h4/list/CONS h4/num/0 a) l))))))
% Assm: h4/bool/TRUTH: T
% Assm: h4/numposrep/l2n20: h4/numposrep/l2n2 = h4/numposrep/l2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/numposrep/l2n__2__thms_c1: !t. h4/numposrep/l2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) t) = h4/arithmetic/NUMERAL (h4/numposrep/l2n2 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) t))
% Assm: h4/numposrep/l2n__2__thms_c4: !t. h4/numposrep/l2n2 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) t) = h4/arithmetic/BIT1 (h4/numposrep/l2n2 t)
% Assm: h4/numposrep/l2n__2__thms_c0: !t. h4/numposrep/l2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/list/CONS h4/num/0 t) = h4/arithmetic/NUMERAL (h4/numposrep/l2n2 (h4/list/CONS h4/num/0 t))
% Assm: h4/numposrep/l2n__2__thms_c3: !t. h4/numposrep/l2n2 (h4/list/CONS h4/num/0 t) = h4/numeral/iDUB (h4/numposrep/l2n2 t)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/list/list__Axiom: !f1 f0. ?fn. fn h4/list/NIL = f0 /\ (!a0 a1. fn (h4/list/CONS a0 a1) = f1 a0 a1 (fn a1))
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% 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/rich__list/AND__EL__DEF: h4/rich__list/AND__EL = h4/list/EVERY h4/combin/I
% Assm: h4/rich__list/OR__EL__DEF: h4/rich__list/OR__EL = h4/list/EXISTS h4/combin/I
% Assm: h4/bitstring/boolify__def_c1: !n l a. h4/bitstring/boolify a (h4/list/CONS n l) = h4/bitstring/boolify (h4/list/CONS (~(n = h4/num/0)) a) l
% Assm: h4/bitstring/bitify__curried__def: !x1 x. h4/bitstring/bitify x x1 = h4/bitstring/bitify__tupled (h4/pair/_2C x x1)
% Assm: h4/rich__list/AND__EL__FOLDR: !l. h4/rich__list/AND__EL l <=> h4/list/FOLDR $and T l
% Assm: h4/rich__list/AND__EL__FOLDL: !l. h4/rich__list/AND__EL l <=> h4/list/FOLDL $and T l
% Assm: h4/rich__list/OR__EL__FOLDR: !l. h4/rich__list/OR__EL l <=> h4/list/FOLDR $or F l
% Assm: h4/rich__list/OR__EL__FOLDL: !l. h4/rich__list/OR__EL l <=> h4/list/FOLDL $or F l
% Assm: h4/words/word__reduce__def: !w f. h4/words/word__reduce f w = h4/fcp/FCP (h4/combin/K (h4/bool/LET (\l. h4/list/FOLDL f (h4/list/HD l) (h4/list/TL l)) (h4/list/GENLIST (\i. h4/fcp/fcp__index w (h4/arithmetic/_2D (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i)) (h4/fcp/dimindex h4/bool/the__value))))
% Assm: h4/numposrep/BOOLIFY__def_c1: !n m a. h4/numposrep/BOOLIFY (h4/num/SUC n) m a = h4/numposrep/BOOLIFY n (h4/arithmetic/DIV2 m) (h4/list/CONS (h4/arithmetic/ODD m) a)
% Assm: h4/words/word__reduce__n2w: !n f. h4/words/word__reduce f (h4/words/n2w n) = h4/fcp/FCP (h4/combin/K (h4/bool/LET (\l. h4/list/FOLDL f (h4/list/HD l) (h4/list/TL l)) (h4/numposrep/BOOLIFY (h4/fcp/dimindex h4/bool/the__value) n h4/list/NIL)))
% Assm: h4/rich__list/EVERY__FOLDR: !l P. h4/list/EVERY P l <=> h4/list/FOLDR (\x l_27. P x /\ l_27) T l
% Assm: h4/rich__list/EVERY__FOLDL: !l P. h4/list/EVERY P l <=> h4/list/FOLDL (\l_27 x. l_27 /\ P x) T l
% Assm: h4/rich__list/EXISTS__FOLDR: !l P. h4/list/EXISTS P l <=> h4/list/FOLDR (\x l_27. P x \/ l_27) F l
% Assm: h4/rich__list/EXISTS__FOLDL: !l P. h4/list/EXISTS P l <=> h4/list/FOLDL (\l_27 x. l_27 \/ P x) F l
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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/NOT__NOT: !t. ~ ~t <=> t
% 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/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/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/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/arithmetic/EXP__1_c1: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/numposrep/l2n__pow2__compute_c1: !t p h. h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p) (h4/list/CONS h t) = h4/arithmetic/_2B (h4/bit/MOD__2EXP p h) (h4/bit/TIMES__2EXP p (h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p) t))
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% 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/MULT__COMM: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/numeral/iDUB0: !x. h4/numeral/iDUB x = h4/arithmetic/_2B x x
% 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/arithmetic/ZERO__MOD: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__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__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = 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/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c22: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm: h4/arithmetic/LESS__MOD: !n k. h4/prim__rec/_3C k n ==> h4/arithmetic/MOD k n = k
% 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/bit/BIT__OF__BITS__THM: !n l h a. h4/arithmetic/_3C_3D (h4/arithmetic/_2B l n) h ==> (h4/bit/BIT n (h4/bit/BITS h l a) <=> h4/bit/BIT (h4/arithmetic/_2B l n) a)
% Assm: h4/bit/BIT0__ODD: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/numposrep/BOOLIFY__def_c0: !m a. h4/numposrep/BOOLIFY h4/num/0 m a = a
% Assm: h4/rich__list/APPEND__SNOC1: !x l2 l1. h4/list/APPEND (h4/list/SNOC x l1) l2 = h4/list/APPEND l1 (h4/list/CONS x l2)
% Assm: h4/list/GENLIST0_c1: !n f. h4/list/GENLIST f (h4/num/SUC n) = h4/list/SNOC (f n) (h4/list/GENLIST f n)
% Assm: h4/list/GENLIST__FUN__EQ: !n g f. h4/list/GENLIST f n = h4/list/GENLIST g n <=> (!x. h4/prim__rec/_3C x n ==> f x = g x)
% Assm: h4/list/GENLIST0_c0: !f. h4/list/GENLIST f h4/num/0 = h4/list/NIL
% Assm: h4/list/APPEND__11_c1: !l3 l2 l1. h4/list/APPEND l2 l1 = h4/list/APPEND l3 l1 <=> l2 = l3
% Assm: h4/list/APPEND__11__LENGTH_c1: !l2_27 l2 l1_27 l1. h4/list/LENGTH l2 = h4/list/LENGTH l2_27 ==> (h4/list/APPEND l1 l2 = h4/list/APPEND l1_27 l2_27 <=> l1 = l1_27 /\ l2 = l2_27)
% Assm: h4/list/APPEND__ASSOC: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c6: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm: h4/numeral/numeral__add_c4: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/list/APPEND__NIL: !l. h4/list/APPEND l h4/list/NIL = l
% Assm: h4/numeral/numeral__add_c3: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/arithmetic/DIV2__def: !n. h4/arithmetic/DIV2 n = h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/SUB__RIGHT__EQ: !p n m. h4/arithmetic/_2D m n = p <=> m = h4/arithmetic/_2B n p \/ h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D p h4/num/0
% Assm: h4/arithmetic/SUB__RIGHT__SUB: !p n m. h4/arithmetic/_2D (h4/arithmetic/_2D m n) p = h4/arithmetic/_2D m (h4/arithmetic/_2B n p)
% Assm: h4/arithmetic/SUB__LEFT__ADD: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2D n p) = h4/bool/COND (h4/arithmetic/_3C_3D n p) m (h4/arithmetic/_2D (h4/arithmetic/_2B m n) p)
% Assm: h4/arithmetic/SUB__LEFT__SUC: !n m. h4/num/SUC (h4/arithmetic/_2D m n) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/num/SUC h4/num/0) (h4/arithmetic/_2D (h4/num/SUC m) n)
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/SUB__RIGHT__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D m n) p <=> h4/arithmetic/_3C_3D m (h4/arithmetic/_2B n p)
% Assm: h4/arithmetic/SUB__EQUAL__0: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/SUC__SUB1: !m. h4/arithmetic/_2D (h4/num/SUC m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/arithmetic/SUB__RIGHT__LESS: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__CLAUSES_c1: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bit/BIT__DIV2: !n i. h4/bit/BIT n (h4/arithmetic/DIV i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> h4/bit/BIT (h4/num/SUC n) i
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Goal: !P. (!a. P a h4/list/NIL) /\ (!a l. P (h4/list/CONS h4/num/0 a) l ==> P a (h4/list/CONS F l)) /\ (!a l. P (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l ==> P a (h4/list/CONS T l)) ==> (!v v1. P v v1)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bitstrings_bitifyu_u_tupledu_u_primitiveu_u_def]: !_6. (!v2 bitify__tupled a l. happ (happ (happ (happ _6 v2) bitify__tupled) a) l = h4/bool/COND v2 (happ h4/combin/I (happ bitify__tupled (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l))) (happ h4/combin/I (happ bitify__tupled (h4/pair/_2C (h4/list/CONS h4/num/0 a) l)))) ==> (!_5. (!bitify__tupled a v2. happ (happ (happ _5 bitify__tupled) a) v2 = happ (happ (happ _6 v2) bitify__tupled) a) ==> (!_4. (!bitify__tupled a v1. happ (happ (happ _4 bitify__tupled) a) v1 = h4/list/list__CASE v1 (happ h4/combin/I a) (happ (happ _5 bitify__tupled) a)) ==> (!_3. (!bitify__tupled a. happ (happ _3 bitify__tupled) a = happ (happ _4 bitify__tupled) a) ==> (!_2. (!bitify__tupled a_27. happ (happ _2 bitify__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 bitify__tupled)) ==> (!_1. (!bitify__tupled. happ _1 bitify__tupled = happ _2 bitify__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!l a. happ (happ R (h4/pair/_2C (h4/list/CONS h4/num/0 a) l)) (h4/pair/_2C a (h4/list/CONS F l))) /\ (!l a. happ (happ R (h4/pair/_2C (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) l)) (h4/pair/_2C a (h4/list/CONS T l)))) ==> h4/bitstring/bitify__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_numposreps_l2n20]: h4/numposrep/l2n2 = h4/numposrep/l2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_numposreps_l2nu_u_2u_u_thmsu_c1]: !t. happ (h4/numposrep/l2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) t) = h4/arithmetic/NUMERAL (happ h4/numposrep/l2n2 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) t))
% Assm [h4s_numposreps_l2nu_u_2u_u_thmsu_c4]: !t. happ h4/numposrep/l2n2 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) t) = h4/arithmetic/BIT1 (happ h4/numposrep/l2n2 t)
% Assm [h4s_numposreps_l2nu_u_2u_u_thmsu_c0]: !t. happ (h4/numposrep/l2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/list/CONS h4/num/0 t) = h4/arithmetic/NUMERAL (happ h4/numposrep/l2n2 (h4/list/CONS h4/num/0 t))
% Assm [h4s_numposreps_l2nu_u_2u_u_thmsu_c3]: !t. happ h4/numposrep/l2n2 (h4/list/CONS h4/num/0 t) = h4/numeral/iDUB (happ h4/numposrep/l2n2 t)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (h4/list/CONS a0 a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_combins_Iu_u_THM]: !x. happ h4/combin/I x = x
% 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_richu_u_lists_ANDu_u_ELu_u_DEF]: h4/rich__list/AND__EL = h4/list/EVERY h4/combin/I
% Assm [h4s_richu_u_lists_ORu_u_ELu_u_DEF]: h4/rich__list/OR__EL = h4/list/EXISTS h4/combin/I
% Assm [h4s_bitstrings_boolifyu_u_defu_c1]: !n l a. ?v. (v <=> ~(n = h4/num/0)) /\ h4/bitstring/boolify a (h4/list/CONS n l) = h4/bitstring/boolify (h4/list/CONS v a) l
% Assm [h4s_bitstrings_bitifyu_u_curriedu_u_def]: !x1 x. h4/bitstring/bitify x x1 = happ h4/bitstring/bitify__tupled (h4/pair/_2C x x1)
% Assm [h4s_richu_u_lists_ANDu_u_ELu_u_FOLDR]: !l. happ h4/rich__list/AND__EL l <=> h4/list/FOLDR $and T l
% Assm [h4s_richu_u_lists_ANDu_u_ELu_u_FOLDL]: !l. happ h4/rich__list/AND__EL l <=> h4/list/FOLDL $and T l
% Assm [h4s_richu_u_lists_ORu_u_ELu_u_FOLDR]: !l. happ h4/rich__list/OR__EL l <=> h4/list/FOLDR $or F l
% Assm [h4s_richu_u_lists_ORu_u_ELu_u_FOLDL]: !l. happ h4/rich__list/OR__EL l <=> h4/list/FOLDL $or F l
% Assm [h4s_wordss_wordu_u_reduceu_u_def]: !_1. (!w i. happ (happ _1 w) i <=> h4/fcp/fcp__index w (h4/arithmetic/_2D (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i)) ==> (!_0. (!f l. happ (happ _0 f) l <=> h4/list/FOLDL f (h4/list/HD l) (h4/list/TL l)) ==> (!w f. h4/words/word__reduce f w = h4/fcp/FCP (h4/combin/K (h4/bool/LET (happ _0 f) (h4/list/GENLIST (happ _1 w) (h4/fcp/dimindex h4/bool/the__value))))))
% Assm [h4s_numposreps_BOOLIFYu_u_defu_c1]: !n m a. h4/numposrep/BOOLIFY (h4/num/SUC n) m a = h4/numposrep/BOOLIFY n (h4/arithmetic/DIV2 m) (h4/list/CONS (happ h4/arithmetic/ODD m) a)
% Assm [h4s_wordss_wordu_u_reduceu_u_n2w]: !_0. (!f l. happ (happ _0 f) l <=> h4/list/FOLDL f (h4/list/HD l) (h4/list/TL l)) ==> (!n f. h4/words/word__reduce f (h4/words/n2w n) = h4/fcp/FCP (h4/combin/K (h4/bool/LET (happ _0 f) (h4/numposrep/BOOLIFY (h4/fcp/dimindex h4/bool/the__value) n h4/list/NIL))))
% Assm [h4s_richu_u_lists_EVERYu_u_FOLDR]: !_1. (!P x l_27. happ (happ (happ _1 P) x) l_27 <=> happ P x /\ l_27) ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!l P. happ (h4/list/EVERY P) l <=> h4/list/FOLDR (happ _0 P) T l))
% Assm [h4s_richu_u_lists_EVERYu_u_FOLDL]: !_1. (!l_27 P x. happ (happ (happ _1 l_27) P) x <=> l_27 /\ happ P x) ==> (!_0. (!P l_27. happ (happ _0 P) l_27 = happ (happ _1 l_27) P) ==> (!l P. happ (h4/list/EVERY P) l <=> h4/list/FOLDL (happ _0 P) T l))
% Assm [h4s_richu_u_lists_EXISTSu_u_FOLDR]: !_1. (!P x l_27. happ (happ (happ _1 P) x) l_27 <=> happ P x \/ l_27) ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!l P. happ (h4/list/EXISTS P) l <=> h4/list/FOLDR (happ _0 P) F l))
% Assm [h4s_richu_u_lists_EXISTSu_u_FOLDL]: !_1. (!l_27 P x. happ (happ (happ _1 l_27) P) x <=> l_27 \/ happ P x) ==> (!_0. (!P l_27. happ (happ _0 P) l_27 = happ (happ _1 l_27) P) ==> (!l P. happ (h4/list/EXISTS P) l <=> h4/list/FOLDL (happ _0 P) F l))
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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_NOTu_u_NOT]: !t. ~ ~t <=> t
% 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_bits_TIMESu_u_2EXPu_u_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 [h4s_bits_MODu_u_2EXPu_u_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 [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_arithmetics_EXPu_u_1u_c1]: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_numposreps_l2nu_u_pow2u_u_computeu_c1]: !t p h. happ (h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p)) (h4/list/CONS h t) = h4/arithmetic/_2B (h4/bit/MOD__2EXP p h) (h4/bit/TIMES__2EXP p (happ (h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p)) t))
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_arithmetics_TIMES2]: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm [h4s_arithmetics_MULTu_u_COMM]: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% 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_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_numerals_iDUB0]: !x. h4/numeral/iDUB x = h4/arithmetic/_2B x x
% 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_arithmetics_ZEROu_u_MOD]: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_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_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = 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_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm [h4s_arithmetics_LESSu_u_MOD]: !n k. h4/prim__rec/_3C k n ==> h4/arithmetic/MOD k n = k
% 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_bits_BITu_u_OFu_u_BITSu_u_THM]: !n l h a. h4/arithmetic/_3C_3D (h4/arithmetic/_2B l n) h ==> (happ (h4/bit/BIT n) (h4/bit/BITS h l a) <=> happ (h4/bit/BIT (h4/arithmetic/_2B l n)) a)
% Assm [h4s_bits_BIT0u_u_ODD]: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_numposreps_BOOLIFYu_u_defu_c0]: !m a. h4/numposrep/BOOLIFY h4/num/0 m a = a
% Assm [h4s_richu_u_lists_APPENDu_u_SNOC1]: !x l2 l1. h4/list/APPEND (h4/list/SNOC x l1) l2 = h4/list/APPEND l1 (h4/list/CONS x l2)
% Assm [h4s_lists_GENLIST0u_c1]: !n f. h4/list/GENLIST f (h4/num/SUC n) = h4/list/SNOC (happ f n) (h4/list/GENLIST f n)
% Assm [h4s_lists_GENLISTu_u_FUNu_u_EQ]: !n g f. h4/list/GENLIST f n = h4/list/GENLIST g n <=> (!x. h4/prim__rec/_3C x n ==> happ f x = happ g x)
% Assm [h4s_lists_GENLIST0u_c0]: !f. h4/list/GENLIST f h4/num/0 = h4/list/NIL
% Assm [h4s_lists_APPENDu_u_11u_c1]: !l3 l2 l1. h4/list/APPEND l2 l1 = h4/list/APPEND l3 l1 <=> l2 = l3
% Assm [h4s_lists_APPENDu_u_11u_u_LENGTHu_c1]: !l2_27 l2 l1_27 l1. h4/list/LENGTH l2 = h4/list/LENGTH l2_27 ==> (h4/list/APPEND l1 l2 = h4/list/APPEND l1_27 l2_27 <=> l1 = l1_27 /\ l2 = l2_27)
% Assm [h4s_lists_APPENDu_u_ASSOC]: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c6]: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm [h4s_numerals_numeralu_u_addu_c4]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_lists_APPENDu_u_NIL]: !l. h4/list/APPEND l h4/list/NIL = l
% Assm [h4s_numerals_numeralu_u_addu_c3]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_arithmetics_DIV2u_u_def]: !n. h4/arithmetic/DIV2 n = h4/arithmetic/DIV n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_EQ]: !p n m. h4/arithmetic/_2D m n = p <=> m = h4/arithmetic/_2B n p \/ h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D p h4/num/0
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_SUB]: !p n m. h4/arithmetic/_2D (h4/arithmetic/_2D m n) p = h4/arithmetic/_2D m (h4/arithmetic/_2B n p)
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_ADD]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2D n p) = h4/bool/COND (h4/arithmetic/_3C_3D n p) m (h4/arithmetic/_2D (h4/arithmetic/_2B m n) p)
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_SUC]: !n m. h4/num/SUC (h4/arithmetic/_2D m n) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/num/SUC h4/num/0) (h4/arithmetic/_2D (h4/num/SUC m) n)
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D m n) p <=> h4/arithmetic/_3C_3D m (h4/arithmetic/_2B n p)
% Assm [h4s_arithmetics_SUBu_u_EQUALu_u_0]: !c. h4/arithmetic/_2D c c = h4/num/0
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_SUCu_u_SUB1]: !m. h4/arithmetic/_2D (h4/num/SUC m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESS]: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bits_BITu_u_DIV2]: !n i. happ (h4/bit/BIT n) (h4/arithmetic/DIV i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) <=> happ (h4/bit/BIT (h4/num/SUC n)) i
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Goal: !P. (!a. happ (happ P a) h4/list/NIL) /\ (!a l. happ (happ P (h4/list/CONS h4/num/0 a)) l ==> happ (happ P a) (h4/list/CONS F l)) /\ (!a l. happ (happ P (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a)) l ==> happ (happ P a) (h4/list/CONS T l)) ==> (!v v1. happ (happ P v) v1)
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_Q1164988,TV_Q1164984]: ![V_f, V_g]: (![V_x]: s(TV_Q1164984,happ(s(t_fun(TV_Q1164988,TV_Q1164984),V_f),s(TV_Q1164988,V_x))) = s(TV_Q1164984,happ(s(t_fun(TV_Q1164988,TV_Q1164984),V_g),s(TV_Q1164988,V_x))) => s(t_fun(TV_Q1164988,TV_Q1164984),V_f) = s(t_fun(TV_Q1164988,TV_Q1164984),V_g))).
fof(ah4s_bitstrings_bitifyu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_6]: (![V_v2, V_bitifyu_u_tupled, V_a, V_l]: s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_6),s(t_bool,V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_v2),s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_h4s_nums_num)),h4s_combins_i),s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))))),s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_h4s_nums_num)),h4s_combins_i),s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))))))) => ![V_uu_5]: (![V_bitifyu_u_tupled, V_a, V_v2]: s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_bool,V_v2))) = s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_6),s(t_bool,V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))) => ![V_uu_4]: (![V_bitifyu_u_tupled, V_a, V_v1]: s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_v1))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_bool),V_v1),s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_h4s_nums_num)),h4s_combins_i),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_bool,t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))))) => ![V_uu_3]: (![V_bitifyu_u_tupled, V_a]: s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))) = s(t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))) => ![V_uu_2]: (![V_bitifyu_u_tupled, V_au_27]: s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),V_au_27))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),V_au_27),s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_h4s_lists_list(t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))))) => ![V_uu_1]: (![V_bitifyu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),V_bitifyu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R)))) & (![V_l, V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,f),s(t_h4s_lists_list(t_bool),V_l)))))))) & ![V_l, V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),V_l))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),V_a),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,t),s(t_h4s_lists_list(t_bool),V_l))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),h4s_bitstrings_bitifyu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num))),V_uu_1))))))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_numposreps_l2n20, axiom, s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n2) = s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(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_numposreps_l2nu_u_2u_u_thmsu_c1, axiom, ![V_t]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_lists_list(t_h4s_nums_num),V_t))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n2),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_lists_list(t_h4s_nums_num),V_t)))))))).
fof(ah4s_numposreps_l2nu_u_2u_u_thmsu_c4, axiom, ![V_t]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n2),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_lists_list(t_h4s_nums_num),V_t))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n2),s(t_h4s_lists_list(t_h4s_nums_num),V_t)))))).
fof(ah4s_numposreps_l2nu_u_2u_u_thmsu_c0, axiom, ![V_t]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_t))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n2),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_t)))))))).
fof(ah4s_numposreps_l2nu_u_2u_u_thmsu_c3, axiom, ![V_t]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n2),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_t))))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n2),s(t_h4s_lists_list(t_h4s_nums_num),V_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_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_a1))))))).
fof(ah4s_bools_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_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_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_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_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
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_richu_u_lists_ANDu_u_ELu_u_DEF, axiom, s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_richu_u_lists_andu_u_el) = s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_lists_every(s(t_fun(t_bool,t_bool),h4s_combins_i)))).
fof(ah4s_richu_u_lists_ORu_u_ELu_u_DEF, axiom, s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_richu_u_lists_oru_u_el) = s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_lists_exists(s(t_fun(t_bool,t_bool),h4s_combins_i)))).
fof(ah4s_bitstrings_boolifyu_u_defu_c1, axiom, ![V_n, V_l, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0))) & s(t_h4s_lists_list(t_bool),h4s_bitstrings_boolify(s(t_h4s_lists_list(t_bool),V_a),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_h4s_nums_num),V_l))))) = s(t_h4s_lists_list(t_bool),h4s_bitstrings_boolify(s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,V_v),s(t_h4s_lists_list(t_bool),V_a))),s(t_h4s_lists_list(t_h4s_nums_num),V_l))))).
fof(ah4s_bitstrings_bitifyu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_x),s(t_h4s_lists_list(t_bool),V_x1))) = s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),t_h4s_lists_list(t_h4s_nums_num)),h4s_bitstrings_bitifyu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_nums_num),t_h4s_lists_list(t_bool)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_nums_num),V_x),s(t_h4s_lists_list(t_bool),V_x1)))))).
fof(ah4s_richu_u_lists_ANDu_u_ELu_u_FOLDR, axiom, ![V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_richu_u_lists_andu_u_el),s(t_h4s_lists_list(t_bool),V_l))) = s(t_bool,h4s_lists_foldr(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_and),s(t_bool,t),s(t_h4s_lists_list(t_bool),V_l)))).
fof(ah4s_richu_u_lists_ANDu_u_ELu_u_FOLDL, axiom, ![V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_richu_u_lists_andu_u_el),s(t_h4s_lists_list(t_bool),V_l))) = s(t_bool,h4s_lists_foldl(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_and),s(t_bool,t),s(t_h4s_lists_list(t_bool),V_l)))).
fof(ah4s_richu_u_lists_ORu_u_ELu_u_FOLDR, axiom, ![V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_richu_u_lists_oru_u_el),s(t_h4s_lists_list(t_bool),V_l))) = s(t_bool,h4s_lists_foldr(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_or),s(t_bool,f),s(t_h4s_lists_list(t_bool),V_l)))).
fof(ah4s_richu_u_lists_ORu_u_ELu_u_FOLDL, axiom, ![V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),h4s_richu_u_lists_oru_u_el),s(t_h4s_lists_list(t_bool),V_l))) = s(t_bool,h4s_lists_foldl(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_or),s(t_bool,f),s(t_h4s_lists_list(t_bool),V_l)))).
fof(ah4s_wordss_wordu_u_reduceu_u_def, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_w, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_i))))) => ![V_uu_0]: (![V_f, V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_bool),V_l))) = s(t_bool,h4s_lists_foldl(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_bool,h4s_lists_hd(s(t_h4s_lists_list(t_bool),V_l))),s(t_h4s_lists_list(t_bool),h4s_lists_tl(s(t_h4s_lists_list(t_bool),V_l))))) => ![V_w, V_f]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_reduce(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),h4s_combins_k(s(t_bool,h4s_bools_let(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_bool),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))))))))).
fof(ah4s_numposreps_BOOLIFYu_u_defu_c1, axiom, ![V_n, V_m, V_a]: s(t_h4s_lists_list(t_bool),h4s_numposreps_boolify(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(t_bool),V_a))) = s(t_h4s_lists_list(t_bool),h4s_numposreps_boolify(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,V_m))),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd),s(t_h4s_nums_num,V_m))),s(t_h4s_lists_list(t_bool),V_a)))))).
fof(ah4s_wordss_wordu_u_reduceu_u_n2w, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_f, V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_bool),V_l))) = s(t_bool,h4s_lists_foldl(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_bool,h4s_lists_hd(s(t_h4s_lists_list(t_bool),V_l))),s(t_h4s_lists_list(t_bool),h4s_lists_tl(s(t_h4s_lists_list(t_bool),V_l))))) => ![V_n, V_f]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_reduce(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),h4s_combins_k(s(t_bool,h4s_bools_let(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_uu_0),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_lists_list(t_bool),h4s_numposreps_boolify(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),h4s_lists_nil))))))))))).
fof(ah4s_richu_u_lists_EVERYu_u_FOLDR, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_P, V_x, V_lu_27]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))),s(t_bool,V_lu_27)))) <=> (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,V_lu_27)))) => ![V_uu_0]: (![V_P, V_x]: s(t_fun(t_bool,t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) => ![V_l, V_P]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_bool,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_bool,t),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_richu_u_lists_EVERYu_u_FOLDL, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_lu_27, V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_bool,V_lu_27))),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x)))) <=> (p(s(t_bool,V_lu_27)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))))) => ![V_uu_0]: (![V_P, V_lu_27]: s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_bool,t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_bool,V_lu_27))) = s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_bool,V_lu_27))),s(t_fun(TV_u_27a,t_bool),V_P))) => ![V_l, V_P]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_bool,h4s_lists_foldl(s(t_fun(t_bool,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_bool,t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_bool,t),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_richu_u_lists_EXISTSu_u_FOLDR, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_P, V_x, V_lu_27]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))),s(t_bool,V_lu_27)))) <=> (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,V_lu_27)))) => ![V_uu_0]: (![V_P, V_x]: s(t_fun(t_bool,t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) => ![V_l, V_P]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_bool,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_bool,f),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_richu_u_lists_EXISTSu_u_FOLDL, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_lu_27, V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_bool,V_lu_27))),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x)))) <=> (p(s(t_bool,V_lu_27)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))))) => ![V_uu_0]: (![V_P, V_lu_27]: s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_bool,t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_bool,V_lu_27))) = s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_bool,V_lu_27))),s(t_fun(TV_u_27a,t_bool),V_P))) => ![V_l, V_P]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_bool,h4s_lists_foldl(s(t_fun(t_bool,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_bool,t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_bool,f),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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,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_bits_MODu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(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_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_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
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_arithmetics_EXPu_u_1u_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_numposreps_l2nu_u_pow2u_u_computeu_c1, axiom, ![V_t, V_p, V_h]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(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_p))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,V_h),s(t_h4s_lists_list(t_h4s_nums_num),V_t))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_h))),s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(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_p))))),s(t_h4s_lists_list(t_h4s_nums_num),V_t)))))))).
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_arithmetics_TIMES2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_MULTu_u_COMM, axiom, ![V_n, V_m]: s(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,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
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_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_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_numerals_iDUB0, axiom, ![V_x]: s(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_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_arithmetics_ZEROu_u_MOD, axiom, ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_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_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_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_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_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_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m)))))) <=> ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_LESSu_u_MOD, axiom, ![V_n, V_k]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_k))).
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_bits_BITu_u_OFu_u_BITSu_u_THM, axiom, ![V_n, V_l, V_h, V_a]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_h)))) => s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_a))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_a))))).
fof(ah4s_bits_BIT0u_u_ODD, axiom, s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_0))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd)).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_numposreps_BOOLIFYu_u_defu_c0, axiom, ![V_m, V_a]: s(t_h4s_lists_list(t_bool),h4s_numposreps_boolify(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(t_bool),V_a))) = s(t_h4s_lists_list(t_bool),V_a)).
fof(ah4s_richu_u_lists_APPENDu_u_SNOC1, axiom, ![TV_u_27a]: ![V_x, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_GENLIST0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_lists_GENLISTu_u_FUNu_u_EQ, axiom, ![TV_u_27a]: ![V_n, V_g, V_f]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,V_n))) <=> ![V_x]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n)))) => s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_x))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,V_x)))))).
fof(ah4s_lists_GENLIST0u_c0, axiom, ![TV_u_27a]: ![V_f]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_APPENDu_u_11u_c1, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l3),s(t_h4s_lists_list(TV_u_27a),V_l1))) <=> s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),V_l3))).
fof(ah4s_lists_APPENDu_u_11u_u_LENGTHu_c1, axiom, ![TV_u_27a]: ![V_l2u_27, V_l2, V_l1u_27, V_l1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2u_27))) => (s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1u_27),s(t_h4s_lists_list(TV_u_27a),V_l2u_27))) <=> (s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),V_l1u_27) & s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),V_l2u_27))))).
fof(ah4s_lists_APPENDu_u_ASSOC, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l3))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),V_l3)))).
fof(ah4s_lists_LENGTH0u_c0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_LENGTH0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0u_27),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_addu_c6, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_addu_c4, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_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_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_lists_APPENDu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_numerals_numeralu_u_addu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_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_arithmetics_SUBu_u_RIGHTu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_p) <=> (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))) | (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_SUB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_SUBu_u_LEFTu_u_ADD, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_SUBu_u_LEFTu_u_SUC, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),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,V_n)))))).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_SUBu_u_EQUALu_u_0, axiom, ![V_c]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_c),s(t_h4s_nums_num,V_c))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_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(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_LESS, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_p))))))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_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_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bits_BITu_u_DIV2, axiom, ![V_n, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_i),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_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_i)))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_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_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_dcu_u_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_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(ch4s_bitstrings_bitifyu_u_ind, conjecture, ![V_P]: ((![V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_P),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),h4s_lists_nil)))) & (![V_a, V_l]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_P),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_a))))),s(t_h4s_lists_list(t_bool),V_l)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_P),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,f),s(t_h4s_lists_list(t_bool),V_l))))))) & ![V_a, V_l]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_P),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_lists_list(t_h4s_nums_num),V_a))))),s(t_h4s_lists_list(t_bool),V_l)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_P),s(t_h4s_lists_list(t_h4s_nums_num),V_a))),s(t_h4s_lists_list(t_bool),h4s_lists_cons(s(t_bool,t),s(t_h4s_lists_list(t_bool),V_l))))))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_bool),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_fun(t_h4s_lists_list(t_bool),t_bool)),V_P),s(t_h4s_lists_list(t_h4s_nums_num),V_v))),s(t_h4s_lists_list(t_bool),V_v1)))))).
