%   ORIGINAL: h4/poly/POLY__ADD__CLAUSES_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/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/prim__rec/num__Axiom: !f e. ?fn. fn h4/num/0 = e /\ (!n. fn (h4/num/SUC n) = f n (fn n))
% Assm: h4/poly/poly__add__def_c1: !t l2 h. h4/poly/poly__add (h4/list/CONS h t) l2 = h4/bool/COND (l2 = h4/list/NIL) (h4/list/CONS h t) (h4/list/CONS (h4/realax/real__add h (h4/list/HD l2)) (h4/poly/poly__add t (h4/list/TL l2)))
% Assm: h4/poly/poly__add__def_c0: !l2. h4/poly/poly__add h4/list/NIL l2 = l2
% Assm: h4/poly/poly__mul__def_c1: !t l2 h. h4/poly/poly__mul (h4/list/CONS h t) l2 = h4/bool/COND (t = h4/list/NIL) (h4/poly/_23_23 h l2) (h4/poly/poly__add (h4/poly/_23_23 h l2) (h4/list/CONS (h4/real/real__of__num h4/num/0) (h4/poly/poly__mul t l2)))
% Assm: h4/poly/POLY__ADD__CLAUSES_c0: !p2. h4/poly/poly__add h4/list/NIL p2 = p2
% Assm: h4/poly/poly__diff__def: !l. h4/poly/diff l = h4/bool/COND (l = h4/list/NIL) h4/list/NIL (h4/poly/poly__diff__aux (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/TL l))
% Assm: h4/poly/poly__mul__def_c0: !l2. h4/poly/poly__mul h4/list/NIL l2 = h4/list/NIL
% Assm: h4/poly/poly__exp__def_c0: !p. h4/poly/poly__exp p h4/num/0 = h4/list/CONS (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h4/list/NIL
% Assm: h4/poly/poly__cmul__def_c1: !t h c. h4/poly/_23_23 c (h4/list/CONS h t) = h4/list/CONS (h4/realax/real__mul c h) (h4/poly/_23_23 c t)
% Assm: h4/poly/poly__exp__def_c1: !p n. h4/poly/poly__exp p (h4/num/SUC n) = h4/poly/poly__mul p (h4/poly/poly__exp p n)
% Assm: h4/poly/poly__diff__aux__def_c1: !t n h. h4/poly/poly__diff__aux n (h4/list/CONS h t) = h4/list/CONS (h4/realax/real__mul (h4/real/real__of__num n) h) (h4/poly/poly__diff__aux (h4/num/SUC n) t)
% Assm: h4/poly/poly__def_c1: !x t h. h4/poly/poly (h4/list/CONS h t) x = h4/realax/real__add h (h4/realax/real__mul x (h4/poly/poly t x))
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/list/NOT__CONS__NIL: !a1 a0. ~(h4/list/CONS a0 a1 = h4/list/NIL)
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/TL0: !t h. h4/list/TL (h4/list/CONS h t) = t
% Assm: h4/list/HD0: !t h. h4/list/HD (h4/list/CONS h t) = h
% Assm: h4/poly/poly__def_c0: !x. h4/poly/poly h4/list/NIL x = h4/real/real__of__num h4/num/0
% Assm: h4/poly/poly__diff__aux__def_c0: !n. h4/poly/poly__diff__aux n h4/list/NIL = h4/list/NIL
% Assm: h4/poly/poly__cmul__def_c0: !c. h4/poly/_23_23 c h4/list/NIL = h4/list/NIL
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/list/SET__TO__LIST__EMPTY: h4/list/SET__TO__LIST h4/pred__set/EMPTY = h4/list/NIL
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/list/EXISTS__SIMP: !l c. h4/list/EXISTS (\x. c) l <=> ~(l = h4/list/NIL) /\ c
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/list/FRONT__CONS_c0: !x. h4/list/FRONT (h4/list/CONS x h4/list/NIL) = h4/list/NIL
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/list/SET__TO__LIST__THM: !s. h4/pred__set/FINITE s ==> h4/list/SET__TO__LIST s = h4/bool/COND (s = h4/pred__set/EMPTY) h4/list/NIL (h4/list/CONS (h4/pred__set/CHOICE s) (h4/list/SET__TO__LIST (h4/pred__set/REST s)))
% Assm: h4/pred__set/FINITE__EMPTY: h4/pred__set/FINITE h4/pred__set/EMPTY
% Assm: h4/rich__list/EL__PRE__LENGTH: !l. ~(l = h4/list/NIL) ==> h4/list/EL (h4/prim__rec/PRE (h4/list/LENGTH l)) l = h4/list/LAST l
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/rich__list/COUNT__LIST__def_c0: h4/rich__list/COUNT__LIST h4/num/0 = h4/list/NIL
% Assm: h4/list/EXISTS__DEF_c1: !t h P. h4/list/EXISTS P (h4/list/CONS h t) <=> P h \/ h4/list/EXISTS P t
% Assm: h4/bool/ABS__SIMP: !t2 t1. (\x. t1) t2 = t1
% Assm: h4/list/EXISTS__DEF_c0: !P. h4/list/EXISTS P h4/list/NIL <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/list/SNOC__INDUCT: !P. P h4/list/NIL /\ (!l. P l ==> (!x. P (h4/list/SNOC x l))) ==> (!l. P l)
% Assm: h4/list/LENGTH__SNOC: !x l. h4/list/LENGTH (h4/list/SNOC x l) = h4/num/SUC (h4/list/LENGTH l)
% Assm: h4/list/FRONT__DEF: !t h. h4/list/FRONT (h4/list/CONS h t) = h4/bool/COND (t = h4/list/NIL) h4/list/NIL (h4/list/CONS h (h4/list/FRONT t))
% Assm: h4/list/REVERSE__EQ__SING: !l e. h4/list/REVERSE l = h4/list/CONS e h4/list/NIL <=> l = h4/list/CONS e h4/list/NIL
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/list/hidden____20__40ind____typelist1____def: h4/list/_20_40ind__typelist1 = (\a0 a1. h4/list/_20_40ind__typelist2 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/list/_20_40ind__typelist3 a1)))
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/list/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/list/list__nchotomy0: !ll. ll = h4/list/NIL \/ (?a l. ll = h4/list/CONS a l)
% Assm: h4/list/isPREFIX__THM_c0: !l. h4/list/isPREFIX h4/list/NIL l <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/prim__rec/PRE0_c1: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm: h4/list/EL__LENGTH__SNOC: !x l. h4/list/EL (h4/list/LENGTH l) (h4/list/SNOC x l) = x
% Assm: h4/list/LAST__SNOC: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/list/isPREFIX__THM_c1: !t h. h4/list/isPREFIX (h4/list/CONS h t) h4/list/NIL <=> F
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/rich__list/FILTER__FOLDR: !l P. h4/list/FILTER P l = h4/list/FOLDR (\x l_27. h4/bool/COND (P x) (h4/list/CONS x l_27) l_27) h4/list/NIL l
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/CONJ__COMM: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm: h4/list/REVERSE__EQ__NIL: !l. h4/list/REVERSE l = h4/list/NIL <=> l = h4/list/NIL
% Assm: h4/list/REVERSE__DEF_c1: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% Assm: h4/list/REVERSE__DEF_c0: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm: h4/list/APPEND__EQ__SING: !l2 l1 e. h4/list/APPEND l1 l2 = h4/list/CONS e h4/list/NIL <=> l1 = h4/list/CONS e h4/list/NIL /\ l2 = h4/list/NIL \/ l1 = h4/list/NIL /\ l2 = h4/list/CONS e h4/list/NIL
% Assm: h4/list/list__distinct: !a1 a0. ~(h4/list/NIL = h4/list/CONS a0 a1)
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/isPREFIX0_c1: !t l h. h4/list/isPREFIX (h4/list/CONS h t) l <=> h4/list/list__CASE l F (\h_27 t_27. h = h_27 /\ h4/list/isPREFIX t t_27)
% Assm: h4/list/SINGL__LIST__APPLY__R: !l. h4/list/LIST__BIND l (\x. h4/list/CONS x h4/list/NIL) = l
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/FOLDR0_c0: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm: h4/list/FOLDR0_c1: !x l f e. h4/list/FOLDR f e (h4/list/CONS x l) = f x (h4/list/FOLDR f e l)
% Assm: h4/list/FILTER0_c1: !t h P. h4/list/FILTER P (h4/list/CONS h t) = h4/bool/COND (P h) (h4/list/CONS h (h4/list/FILTER P t)) (h4/list/FILTER P t)
% Assm: h4/list/FILTER0_c0: !P. h4/list/FILTER P h4/list/NIL = h4/list/NIL
% Assm: h4/rich__list/BUTLASTN__LENGTH__NIL0: !l. h4/rich__list/BUTLASTN (h4/list/LENGTH l) l = h4/list/NIL
% Assm: h4/list/FRONT__CONS__EQ__NIL_c0: !xs x. h4/list/FRONT (h4/list/CONS x xs) = h4/list/NIL <=> xs = h4/list/NIL
% Assm: h4/rich__list/IS__PREFIX_c0: !l. h4/list/isPREFIX h4/list/NIL l <=> T
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/list/LIST__BIND__THM_c1: !t h f. h4/list/LIST__BIND (h4/list/CONS h t) f = h4/list/APPEND (f h) (h4/list/LIST__BIND t f)
% Assm: h4/list/LIST__BIND__THM_c0: !f. h4/list/LIST__BIND h4/list/NIL f = h4/list/NIL
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/rich__list/BUTLASTN0_c1: !x n l. h4/rich__list/BUTLASTN (h4/num/SUC n) (h4/list/SNOC x l) = h4/rich__list/BUTLASTN n l
% Assm: h4/rich__list/BUTLASTN0_c0: !l. h4/rich__list/BUTLASTN h4/num/0 l = l
% Assm: h4/list/LIST__TO__SET__DEF_c0: !x. h4/list/LIST__TO__SET h4/list/NIL x <=> F
% Assm: h4/list/LIST__REL__def_c2: !bs b R. h4/list/LIST__REL R h4/list/NIL (h4/list/CONS b bs) <=> F
% Assm: h4/bool/FORALL__AND__THM: !Q P. (!x. P x /\ Q x) <=> (!x. P x) /\ (!x. Q x)
% Assm: h4/list/NULL__DEF_c0: h4/list/NULL h4/list/NIL <=> T
% Assm: h4/list/NULL__DEF_c1: !t h. h4/list/NULL (h4/list/CONS h t) <=> F
% Assm: h4/list/NOT__NIL__CONS: !a1 a0. ~(h4/list/NIL = h4/list/CONS a0 a1)
% Assm: h4/list/FRONT__CONS_c1: !z y x. h4/list/FRONT (h4/list/CONS x (h4/list/CONS y z)) = h4/list/CONS x (h4/list/FRONT (h4/list/CONS y z))
% Assm: h4/list/MAP20_c0: !f. h4/list/MAP2 f h4/list/NIL h4/list/NIL = h4/list/NIL
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/list/LIST__REL__def0: h4/list/LIST__REL = (\R a0 a1. !LIST__REL_27. (!a00 a10. a00 = h4/list/NIL /\ a10 = h4/list/NIL \/ (?h1 h2 t1 t2. a00 = h4/list/CONS h1 t1 /\ a10 = h4/list/CONS h2 t2 /\ R h1 h2 /\ LIST__REL_27 t1 t2) ==> LIST__REL_27 a00 a10) ==> LIST__REL_27 a0 a1)
% Assm: h4/bool/BOUNDED__THM: !v. h4/bool/BOUNDED v <=> T
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/list/MAP2__tupled__primitive__def: h4/list/MAP2__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!h2 h1 t2 t1 f. R (h4/pair/_2C f (h4/pair/_2C t1 t2)) (h4/pair/_2C f (h4/pair/_2C (h4/list/CONS h1 t1) (h4/list/CONS h2 t2)))))) (\MAP2__tupled a. h4/pair/pair__CASE a (\f v1. h4/pair/pair__CASE v1 (\v2 v3. h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (\h1 t1. h4/list/list__CASE v3 (h4/combin/I h4/list/NIL) (\h2 t2. h4/combin/I (h4/list/CONS (f h1 h2) (MAP2__tupled (h4/pair/_2C f (h4/pair/_2C t1 t2)))))))))
% Assm: h4/list/MAP2__curried__def: !x2 x1 x. h4/list/MAP2 x x1 x2 = h4/list/MAP2__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/list/list__size__def_c1: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/list/list__size f a1))
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Goal: !p1. h4/poly/poly__add p1 h4/list/NIL = p1
%   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_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (happ (happ h4/list/CONS a0) a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% 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_polys_polyu_u_addu_u_defu_c1]: !t l2 h. ?v. (v <=> l2 = h4/list/NIL) /\ h4/poly/poly__add (happ (happ h4/list/CONS h) t) l2 = h4/bool/COND v (happ (happ h4/list/CONS h) t) (happ (happ h4/list/CONS (h4/realax/real__add h (h4/list/HD l2))) (h4/poly/poly__add t (h4/list/TL l2)))
% Assm [h4s_polys_polyu_u_addu_u_defu_c0]: !l2. h4/poly/poly__add h4/list/NIL l2 = l2
% Assm [h4s_polys_polyu_u_mulu_u_defu_c1]: !t l2 h. ?v. (v <=> t = h4/list/NIL) /\ h4/poly/poly__mul (happ (happ h4/list/CONS h) t) l2 = h4/bool/COND v (h4/poly/_23_23 h l2) (h4/poly/poly__add (h4/poly/_23_23 h l2) (happ (happ h4/list/CONS (h4/real/real__of__num h4/num/0)) (h4/poly/poly__mul t l2)))
% Assm [h4s_polys_POLYu_u_ADDu_u_CLAUSESu_c0]: !p2. h4/poly/poly__add h4/list/NIL p2 = p2
% Assm [h4s_polys_polyu_u_diffu_u_def]: !l. ?v. (v <=> l = h4/list/NIL) /\ h4/poly/diff l = h4/bool/COND v h4/list/NIL (h4/poly/poly__diff__aux (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/list/TL l))
% Assm [h4s_polys_polyu_u_mulu_u_defu_c0]: !l2. h4/poly/poly__mul h4/list/NIL l2 = h4/list/NIL
% Assm [h4s_polys_polyu_u_expu_u_defu_c0]: !p. h4/poly/poly__exp p h4/num/0 = happ (happ h4/list/CONS (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/list/NIL
% Assm [h4s_polys_polyu_u_cmulu_u_defu_c1]: !t h c. h4/poly/_23_23 c (happ (happ h4/list/CONS h) t) = happ (happ h4/list/CONS (h4/realax/real__mul c h)) (h4/poly/_23_23 c t)
% Assm [h4s_polys_polyu_u_expu_u_defu_c1]: !p n. h4/poly/poly__exp p (h4/num/SUC n) = h4/poly/poly__mul p (h4/poly/poly__exp p n)
% Assm [h4s_polys_polyu_u_diffu_u_auxu_u_defu_c1]: !t n h. h4/poly/poly__diff__aux n (happ (happ h4/list/CONS h) t) = happ (happ h4/list/CONS (h4/realax/real__mul (h4/real/real__of__num n) h)) (h4/poly/poly__diff__aux (h4/num/SUC n) t)
% Assm [h4s_polys_polyu_u_defu_c1]: !x t h. h4/poly/poly (happ (happ h4/list/CONS h) t) x = h4/realax/real__add h (h4/realax/real__mul x (h4/poly/poly t x))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_lists_NOTu_u_CONSu_u_NIL]: !a1 a0. ~(happ (happ h4/list/CONS a0) a1 = h4/list/NIL)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% Assm [h4s_lists_TL0]: !t h. h4/list/TL (happ (happ h4/list/CONS h) t) = t
% Assm [h4s_lists_HD0]: !t h. h4/list/HD (happ (happ h4/list/CONS h) t) = h
% Assm [h4s_polys_polyu_u_defu_c0]: !x. h4/poly/poly h4/list/NIL x = h4/real/real__of__num h4/num/0
% Assm [h4s_polys_polyu_u_diffu_u_auxu_u_defu_c0]: !n. h4/poly/poly__diff__aux n h4/list/NIL = h4/list/NIL
% Assm [h4s_polys_polyu_u_cmulu_u_defu_c0]: !c. h4/poly/_23_23 c h4/list/NIL = h4/list/NIL
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_lists_SETu_u_TOu_u_LISTu_u_EMPTY]: h4/list/SET__TO__LIST h4/pred__set/EMPTY = h4/list/NIL
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_lists_EXISTSu_u_SIMP]: !_0. (!c x. happ (happ _0 c) x <=> c) ==> (!l c. h4/list/EXISTS (happ _0 c) l <=> ~(l = h4/list/NIL) /\ c)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_lists_FRONTu_u_CONSu_c0]: !x. h4/list/FRONT (happ (happ h4/list/CONS x) h4/list/NIL) = h4/list/NIL
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_lists_SETu_u_TOu_u_LISTu_u_THM]: !s. h4/pred__set/FINITE s ==> (?v. (v <=> s = h4/pred__set/EMPTY) /\ h4/list/SET__TO__LIST s = h4/bool/COND v h4/list/NIL (happ (happ h4/list/CONS (h4/pred__set/CHOICE s)) (h4/list/SET__TO__LIST (h4/pred__set/REST s))))
% Assm [h4s_predu_u_sets_FINITEu_u_EMPTY]: h4/pred__set/FINITE h4/pred__set/EMPTY
% Assm [h4s_richu_u_lists_ELu_u_PREu_u_LENGTH]: !l. ~(l = h4/list/NIL) ==> h4/list/EL (h4/prim__rec/PRE (h4/list/LENGTH l)) l = h4/list/LAST l
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_richu_u_lists_COUNTu_u_LISTu_u_defu_c0]: h4/rich__list/COUNT__LIST h4/num/0 = h4/list/NIL
% Assm [h4s_lists_EXISTSu_u_DEFu_c1]: !t h P. h4/list/EXISTS P (happ (happ h4/list/CONS h) t) <=> happ P h \/ h4/list/EXISTS P t
% Assm [h4s_bools_ABSu_u_SIMP]: !t2 t1. t1 = t1
% Assm [h4s_lists_EXISTSu_u_DEFu_c0]: !P. h4/list/EXISTS P h4/list/NIL <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_lists_SNOCu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!l. happ P l ==> (!x. happ P (h4/list/SNOC x l))) ==> (!l. happ P l)
% Assm [h4s_lists_LENGTHu_u_SNOC]: !x l. h4/list/LENGTH (h4/list/SNOC x l) = h4/num/SUC (h4/list/LENGTH l)
% Assm [h4s_lists_FRONTu_u_DEF]: !t h. ?v. (v <=> t = h4/list/NIL) /\ h4/list/FRONT (happ (happ h4/list/CONS h) t) = h4/bool/COND v h4/list/NIL (happ (happ h4/list/CONS h) (h4/list/FRONT t))
% Assm [h4s_lists_REVERSEu_u_EQu_u_SING]: !l e. h4/list/REVERSE l = happ (happ h4/list/CONS e) h4/list/NIL <=> l = happ (happ h4/list/CONS e) h4/list/NIL
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/list/_20_40ind__typelist1 x) x = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/list/_20_40ind__typelist3 x) _0)))
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_lists_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_lists_listu_u_nchotomy0]: !ll. ll = h4/list/NIL \/ (?a l. ll = happ (happ h4/list/CONS a) l)
% Assm [h4s_lists_isPREFIXu_u_THMu_c0]: !l. h4/list/isPREFIX h4/list/NIL l <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_primu_u_recs_PRE0u_c1]: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm [h4s_lists_ELu_u_LENGTHu_u_SNOC]: !x l. h4/list/EL (h4/list/LENGTH l) (h4/list/SNOC x l) = x
% Assm [h4s_lists_LASTu_u_SNOC]: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_lists_isPREFIXu_u_THMu_c1]: !t h. h4/list/isPREFIX (happ (happ h4/list/CONS h) t) h4/list/NIL <=> F
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_richu_u_lists_FILTERu_u_FOLDR]: !_1. (!P x l_27. happ (happ (happ _1 P) x) l_27 = h4/bool/COND (happ P x) (happ (happ h4/list/CONS x) l_27) l_27) ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!l P. h4/list/FILTER P l = h4/list/FOLDR (happ _0 P) h4/list/NIL l))
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_CONJu_u_COMM]: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm [h4s_lists_REVERSEu_u_EQu_u_NIL]: !l. h4/list/REVERSE l = h4/list/NIL <=> l = h4/list/NIL
% Assm [h4s_lists_REVERSEu_u_DEFu_c1]: !t h. h4/list/REVERSE (happ (happ h4/list/CONS h) t) = h4/list/APPEND (h4/list/REVERSE t) (happ (happ h4/list/CONS h) h4/list/NIL)
% Assm [h4s_lists_REVERSEu_u_DEFu_c0]: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_APPENDu_u_EQu_u_SING]: !l2 l1 e. h4/list/APPEND l1 l2 = happ (happ h4/list/CONS e) h4/list/NIL <=> l1 = happ (happ h4/list/CONS e) h4/list/NIL /\ l2 = h4/list/NIL \/ l1 = h4/list/NIL /\ l2 = happ (happ h4/list/CONS e) h4/list/NIL
% Assm [h4s_lists_listu_u_distinct]: !a1 a0. ~(h4/list/NIL = happ (happ h4/list/CONS a0) a1)
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_isPREFIX0u_c1]: !_1. (!h h_27 t t_27. happ (happ (happ (happ _1 h) h_27) t) t_27 <=> h = h_27 /\ h4/list/isPREFIX t t_27) ==> (!_0. (!h t h_27. happ (happ (happ _0 h) t) h_27 = happ (happ (happ _1 h) h_27) t) ==> (!t l h. h4/list/isPREFIX (happ (happ h4/list/CONS h) t) l <=> h4/list/list__CASE l F (happ (happ _0 h) t)))
% Assm [h4s_lists_SINGLu_u_LISTu_u_APPLYu_u_R]: !_0. (!x. happ _0 x = happ (happ h4/list/CONS x) h4/list/NIL) ==> (!l. h4/list/LIST__BIND l _0 = l)
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% Assm [h4s_lists_FOLDR0u_c0]: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm [h4s_lists_FOLDR0u_c1]: !x l f e. h4/list/FOLDR f e (happ (happ h4/list/CONS x) l) = happ (happ f x) (h4/list/FOLDR f e l)
% Assm [h4s_lists_FILTER0u_c1]: !t h P. h4/list/FILTER P (happ (happ h4/list/CONS h) t) = h4/bool/COND (happ P h) (happ (happ h4/list/CONS h) (h4/list/FILTER P t)) (h4/list/FILTER P t)
% Assm [h4s_lists_FILTER0u_c0]: !P. h4/list/FILTER P h4/list/NIL = h4/list/NIL
% Assm [h4s_richu_u_lists_BUTLASTNu_u_LENGTHu_u_NIL0]: !l. h4/rich__list/BUTLASTN (h4/list/LENGTH l) l = h4/list/NIL
% Assm [h4s_lists_FRONTu_u_CONSu_u_EQu_u_NILu_c0]: !xs x. h4/list/FRONT (happ (happ h4/list/CONS x) xs) = h4/list/NIL <=> xs = h4/list/NIL
% Assm [h4s_richu_u_lists_ISu_u_PREFIXu_c0]: !l. h4/list/isPREFIX h4/list/NIL l <=> T
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (happ (happ h4/list/CONS h) l1) l2 = happ (happ h4/list/CONS h) (h4/list/APPEND l1 l2)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_lists_LISTu_u_BINDu_u_THMu_c1]: !t h f. h4/list/LIST__BIND (happ (happ h4/list/CONS h) t) f = h4/list/APPEND (happ f h) (h4/list/LIST__BIND t f)
% Assm [h4s_lists_LISTu_u_BINDu_u_THMu_c0]: !f. h4/list/LIST__BIND h4/list/NIL f = h4/list/NIL
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_richu_u_lists_BUTLASTN0u_c1]: !x n l. h4/rich__list/BUTLASTN (h4/num/SUC n) (h4/list/SNOC x l) = h4/rich__list/BUTLASTN n l
% Assm [h4s_richu_u_lists_BUTLASTN0u_c0]: !l. h4/rich__list/BUTLASTN h4/num/0 l = l
% Assm [h4s_lists_LISTu_u_TOu_u_SETu_u_DEFu_c0]: !x. h4/list/LIST__TO__SET h4/list/NIL x <=> F
% Assm [h4s_lists_LISTu_u_RELu_u_defu_c2]: !bs b R. h4/list/LIST__REL R h4/list/NIL (happ (happ h4/list/CONS b) bs) <=> F
% 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_lists_NULLu_u_DEFu_c0]: h4/list/NULL h4/list/NIL <=> T
% Assm [h4s_lists_NULLu_u_DEFu_c1]: !t h. h4/list/NULL (happ (happ h4/list/CONS h) t) <=> F
% Assm [h4s_lists_NOTu_u_NILu_u_CONS]: !a1 a0. ~(h4/list/NIL = happ (happ h4/list/CONS a0) a1)
% Assm [h4s_lists_FRONTu_u_CONSu_c1]: !z y x. h4/list/FRONT (happ (happ h4/list/CONS x) (happ (happ h4/list/CONS y) z)) = happ (happ h4/list/CONS x) (h4/list/FRONT (happ (happ h4/list/CONS y) z))
% Assm [h4s_lists_MAP20u_c0]: !f. h4/list/MAP2 f h4/list/NIL h4/list/NIL = h4/list/NIL
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_lists_LISTu_u_RELu_u_def0]: !x x x. h4/list/LIST__REL x x x <=> (!LIST__REL_27. (!a00 a10. a00 = h4/list/NIL /\ a10 = h4/list/NIL \/ (?h1 h2 t1 t2. a00 = happ (happ h4/list/CONS h1) t1 /\ a10 = happ (happ h4/list/CONS h2) t2 /\ happ (happ x h1) h2 /\ happ (happ LIST__REL_27 t1) t2) ==> happ (happ LIST__REL_27 a00) a10) ==> happ (happ LIST__REL_27 x) x)
% Assm [h4s_bools_BOUNDEDu_u_THM]: !v. h4/bool/BOUNDED v <=> T
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_lists_MAP2u_u_tupledu_u_primitiveu_u_def]: !_10. (!h1 h2 MAP2__tupled f t1 t2. happ (happ (happ (happ (happ (happ _10 h1) h2) MAP2__tupled) f) t1) t2 = h4/combin/I (happ (happ h4/list/CONS (happ (happ f h1) h2)) (happ MAP2__tupled (h4/pair/_2C f (h4/pair/_2C t1 t2))))) ==> (!_9. (!h1 MAP2__tupled f t1 h2. happ (happ (happ (happ (happ _9 h1) MAP2__tupled) f) t1) h2 = happ (happ (happ (happ (happ _10 h1) h2) MAP2__tupled) f) t1) ==> (!_8. (!v3 h1 MAP2__tupled f t1. happ (happ (happ (happ (happ _8 v3) h1) MAP2__tupled) f) t1 = h4/list/list__CASE v3 (h4/combin/I h4/list/NIL) (happ (happ (happ (happ _9 h1) MAP2__tupled) f) t1)) ==> (!_7. (!v3 MAP2__tupled f h1. happ (happ (happ (happ _7 v3) MAP2__tupled) f) h1 = happ (happ (happ (happ _8 v3) h1) MAP2__tupled) f) ==> (!_6. (!v2 MAP2__tupled f v3. happ (happ (happ (happ _6 v2) MAP2__tupled) f) v3 = h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (happ (happ (happ _7 v3) MAP2__tupled) f)) ==> (!_5. (!MAP2__tupled f v2. happ (happ (happ _5 MAP2__tupled) f) v2 = happ (happ (happ _6 v2) MAP2__tupled) f) ==> (!_4. (!MAP2__tupled f v1. happ (happ (happ _4 MAP2__tupled) f) v1 = h4/pair/pair__CASE v1 (happ (happ _5 MAP2__tupled) f)) ==> (!_3. (!MAP2__tupled f. happ (happ _3 MAP2__tupled) f = happ (happ _4 MAP2__tupled) f) ==> (!_2. (!MAP2__tupled a. happ (happ _2 MAP2__tupled) a = h4/pair/pair__CASE a (happ _3 MAP2__tupled)) ==> (!_1. (!MAP2__tupled. happ _1 MAP2__tupled = happ _2 MAP2__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!h2 h1 t2 t1 f. happ (happ R (h4/pair/_2C f (h4/pair/_2C t1 t2))) (h4/pair/_2C f (h4/pair/_2C (happ (happ h4/list/CONS h1) t1) (happ (happ h4/list/CONS h2) t2))))) ==> h4/list/MAP2__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% Assm [h4s_lists_MAP2u_u_curriedu_u_def]: !x2 x1 x. h4/list/MAP2 x x1 x2 = happ h4/list/MAP2__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (happ (happ h4/list/CONS a0) a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/list/list__size f a1))
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (happ (happ h4/list/CONS a0) a1) v f = happ (happ f a0) a1
% 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_ltu_c0]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Goal: !p1. h4/poly/poly__add p1 h4/list/NIL = p1
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_Q1305110,TV_Q1305106]: ![V_f, V_g]: (![V_x]: s(TV_Q1305106,happ(s(t_fun(TV_Q1305110,TV_Q1305106),V_f),s(TV_Q1305110,V_x))) = s(TV_Q1305106,happ(s(t_fun(TV_Q1305110,TV_Q1305106),V_g),s(TV_Q1305110,V_x))) => s(t_fun(TV_Q1305110,TV_Q1305106),V_f) = s(t_fun(TV_Q1305110,TV_Q1305106),V_g))).
fof(ah4s_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_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_polys_polyu_u_addu_u_defu_c1, axiom, ![V_t, V_l2, V_h]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)) & s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_add(s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))),s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_h),s(t_h4s_realaxs_real,h4s_lists_hd(s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))))))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_add(s(t_h4s_lists_list(t_h4s_realaxs_real),V_t),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))))))))))).
fof(ah4s_polys_polyu_u_addu_u_defu_c0, axiom, ![V_l2]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_add(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2)).
fof(ah4s_polys_polyu_u_mulu_u_defu_c1, axiom, ![V_t, V_l2, V_h]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_lists_list(t_h4s_realaxs_real),V_t) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)) & s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_h),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_add(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_h),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))),s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(s(t_h4s_lists_list(t_h4s_realaxs_real),V_t),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))))))))))).
fof(ah4s_polys_POLYu_u_ADDu_u_CLAUSESu_c0, axiom, ![V_p2]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_add(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_realaxs_real),V_p2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),V_p2)).
fof(ah4s_polys_polyu_u_diffu_u_def, axiom, ![V_l]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_lists_list(t_h4s_realaxs_real),V_l) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)) & s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_diff(s(t_h4s_lists_list(t_h4s_realaxs_real),V_l))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_diffu_u_aux(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_realaxs_real),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_realaxs_real),V_l))))))))).
fof(ah4s_polys_polyu_u_mulu_u_defu_c0, axiom, ![V_l2]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_realaxs_real),V_l2))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)).
fof(ah4s_polys_polyu_u_expu_u_defu_c0, axiom, ![V_p]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_exp(s(t_h4s_lists_list(t_h4s_realaxs_real),V_p),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real),h4s_lists_nil)))).
fof(ah4s_polys_polyu_u_cmulu_u_defu_c1, axiom, ![V_t, V_h, V_c]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_c),s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))))) = s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_c),s(t_h4s_realaxs_real,V_h))))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_c),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t)))))).
fof(ah4s_polys_polyu_u_expu_u_defu_c1, axiom, ![V_p, V_n]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_exp(s(t_h4s_lists_list(t_h4s_realaxs_real),V_p),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_mul(s(t_h4s_lists_list(t_h4s_realaxs_real),V_p),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_exp(s(t_h4s_lists_list(t_h4s_realaxs_real),V_p),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_polys_polyu_u_diffu_u_auxu_u_defu_c1, axiom, ![V_t, V_n, V_h]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_diffu_u_aux(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))))) = s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_h))))),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_diffu_u_aux(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t)))))).
fof(ah4s_polys_polyu_u_defu_c1, axiom, ![V_x, V_t, V_h]: s(t_h4s_realaxs_real,h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real)),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_lists_list(t_h4s_realaxs_real),t_h4s_lists_list(t_h4s_realaxs_real))),h4s_lists_cons),s(t_h4s_realaxs_real,V_h))),s(t_h4s_lists_list(t_h4s_realaxs_real),V_t))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_h),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),V_t),s(t_h4s_realaxs_real,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_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_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_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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_lists_NOTu_u_CONSu_u_NIL, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_nil))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_CONDu_u_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_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_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_TL0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lists_list(TV_u_27a),V_t)).
fof(ah4s_lists_HD0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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(TV_u_27a,V_h)).
fof(ah4s_polys_polyu_u_defu_c0, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_polys_poly(s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_polys_polyu_u_diffu_u_auxu_u_defu_c0, axiom, ![V_n]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_diffu_u_aux(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)).
fof(ah4s_polys_polyu_u_cmulu_u_defu_c0, axiom, ![V_c]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_u_23u_23(s(t_h4s_realaxs_real,V_c),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil)).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_lists_SETu_u_TOu_u_LISTu_u_EMPTY, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
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_lists_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_c, V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_bool,V_c))),s(TV_u_27a,V_x))) = s(t_bool,V_c) => ![V_l, V_c]: (p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_bool,V_c))),s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> (~ (s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)) & p(s(t_bool,V_c)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_FRONTu_u_CONSu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_front(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
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_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_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_lists_SETu_u_TOu_u_LISTu_u_THM, axiom, ![TV_u_27a]: ![V_s]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) => ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)) & s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s)))))))))))).
fof(ah4s_predu_u_sets_FINITEu_u_EMPTY, axiom, ![TV_u_27a]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))))).
fof(ah4s_richu_u_lists_ELu_u_PREu_u_LENGTH, axiom, ![TV_u_27a]: ![V_l]: (~ (s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)) => s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_richu_u_lists_COUNTu_u_LISTu_u_defu_c0, axiom, s(t_h4s_lists_list(t_h4s_nums_num),h4s_richu_u_lists_countu_u_list(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil)).
fof(ah4s_lists_EXISTSu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: (p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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)))))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h)))) | p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_bools_ABSu_u_SIMP, axiom, ![TV_u_27b,TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,V_t1) = s(TV_u_27a,V_t1)).
fof(ah4s_lists_EXISTSu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,f)).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_SNOCu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_l]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))) => ![V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),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_l)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_LENGTHu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_nums_num,h4s_lists_length(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_l))))) = 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_l)))))).
fof(ah4s_lists_FRONTu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_h]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_lists_list(TV_u_27a),V_t) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)) & s(t_h4s_lists_list(TV_u_27a),h4s_lists_front(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_front(s(t_h4s_lists_list(TV_u_27a),V_t))))))))).
fof(ah4s_lists_REVERSEu_u_EQu_u_SING, axiom, ![TV_u_27a]: ![V_l, V_e]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e))),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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, 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_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_x0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))).
fof(ah4s_lists_CONS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
fof(ah4s_lists_listu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_lists_list(TV_u_27a),V_a)).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_lists_listu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27listu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => 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,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_lists_listu_u_nchotomy0, axiom, ![TV_u_27a]: ![V_ll]: (s(t_h4s_lists_list(TV_u_27a),V_ll) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) | ?[V_a, V_l]: s(t_h4s_lists_list(TV_u_27a),V_ll) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ah4s_lists_isPREFIXu_u_THMu_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_bool,t)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_primu_u_recs_PRE0u_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_lists_ELu_u_LENGTHu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),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_l))))) = s(TV_u_27a,V_x)).
fof(ah4s_lists_LASTu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_lists_last(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_l))))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_isPREFIXu_u_THMu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,f)).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),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(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_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_richu_u_lists_FILTERu_u_FOLDR, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_P, V_x, V_lu_27]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lu_27))),s(t_h4s_lists_list(TV_u_27a),V_lu_27))) => ![V_uu_0]: (![V_P, V_x]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),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_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONJu_u_COMM, 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))))).
fof(ah4s_lists_REVERSEu_u_EQu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(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) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_lists_REVERSEu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_t))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_nil)))))).
fof(ah4s_lists_REVERSEu_u_DEFu_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_APPENDu_u_EQu_u_SING, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_e]: (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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) <=> ((s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) & s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)) | (s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))))).
fof(ah4s_lists_listu_u_distinct, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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))))).
fof(ah4s_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_isPREFIX0u_c1, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_h, V_hu_27, V_t, V_tu_27]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)))),V_uu_1),s(TV_u_27a,V_h))),s(TV_u_27a,V_hu_27))),s(t_h4s_lists_list(TV_u_27a),V_t))),s(t_h4s_lists_list(TV_u_27a),V_tu_27)))) <=> (s(TV_u_27a,V_h) = s(TV_u_27a,V_hu_27) & p(s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),V_t),s(t_h4s_lists_list(TV_u_27a),V_tu_27)))))) => ![V_uu_0]: (![V_h, V_t, V_hu_27]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_bool)))),V_uu_0),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))),s(TV_u_27a,V_hu_27))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)))),V_uu_1),s(TV_u_27a,V_h))),s(TV_u_27a,V_hu_27))),s(t_h4s_lists_list(TV_u_27a),V_t))) => ![V_t, V_l, V_h]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lists_list(TV_u_27a),V_l))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_bool,f),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_bool)))),V_uu_0),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))).
fof(ah4s_lists_SINGLu_u_LISTu_u_APPLYu_u_R, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_lists_list(TV_u_27a)),V_uu_0),s(TV_u_27a,V_x))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) => ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_bind(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_fun(TV_u_27a,t_h4s_lists_list(TV_u_27a)),V_uu_0))) = s(t_h4s_lists_list(TV_u_27a),V_l))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_FOLDR0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e)).
fof(ah4s_lists_FOLDR0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f, V_e]: s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_l))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_FILTER0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_FILTER0u_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_richu_u_lists_BUTLASTNu_u_LENGTHu_u_NIL0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_FRONTu_u_CONSu_u_EQu_u_NILu_c0, axiom, ![TV_u_27a]: ![V_xs, V_x]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_front(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_xs))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) <=> s(t_h4s_lists_list(TV_u_27a),V_xs) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_richu_u_lists_ISu_u_PREFIXu_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_bool,h4s_lists_isprefix(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_bool,t)).
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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_LISTu_u_BINDu_u_THMu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_bind(s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_h))),s(t_h4s_lists_list(TV_u_27b),V_t))),s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27a)),V_f))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27a)),V_f),s(TV_u_27b,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_bind(s(t_h4s_lists_list(TV_u_27b),V_t),s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27a)),V_f)))))).
fof(ah4s_lists_LISTu_u_BINDu_u_THMu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_f]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_bind(s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil),s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27a)),V_f))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
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_richu_u_lists_BUTLASTN0u_c1, axiom, ![TV_u_27a]: ![V_x, V_n, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(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,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_richu_u_lists_BUTLASTN0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_LISTu_u_TOu_u_SETu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27a,V_x))) = s(t_bool,f)).
fof(ah4s_lists_LISTu_u_RELu_u_defu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_bs, V_b, V_R]: s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))))) = s(t_bool,f)).
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_lists_NULLu_u_DEFu_c0, axiom, ![TV_u_27a]: s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_lists_NULLu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_bool,f)).
fof(ah4s_lists_NOTu_u_NILu_u_CONS, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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))))).
fof(ah4s_lists_FRONTu_u_CONSu_c1, axiom, ![TV_u_27a]: ![V_z, V_y, V_x]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_front(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_y))),s(t_h4s_lists_list(TV_u_27a),V_z))))))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_front(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_y))),s(t_h4s_lists_list(TV_u_27a),V_z)))))))).
fof(ah4s_lists_MAP20u_c0, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_f]: s(t_h4s_lists_list(TV_u_27c),h4s_lists_map2(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27c),h4s_lists_nil)).
fof(ah4s_bools_EXISTSu_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_RELu_u_def0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_x0, V_x1]: (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_x),s(t_h4s_lists_list(TV_u_27a),V_x0),s(t_h4s_lists_list(TV_u_27b),V_x1)))) <=> ![V_LISTu_u_RELu_27]: (![V_a00, V_a10]: (((s(t_h4s_lists_list(TV_u_27a),V_a00) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & s(t_h4s_lists_list(TV_u_27b),V_a10) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)) | ?[V_h1, V_h2, V_t1, V_t2]: (s(t_h4s_lists_list(TV_u_27a),V_a00) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h1))),s(t_h4s_lists_list(TV_u_27a),V_t1))) & (s(t_h4s_lists_list(TV_u_27b),V_a10) = s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_h2))),s(t_h4s_lists_list(TV_u_27b),V_t2))) & (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_x),s(TV_u_27a,V_h1))),s(TV_u_27b,V_h2)))) & p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_t1))),s(t_h4s_lists_list(TV_u_27b),V_t2)))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_a00))),s(t_h4s_lists_list(TV_u_27b),V_a10))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_h4s_lists_list(TV_u_27b),V_x1))))))).
fof(ah4s_bools_BOUNDEDu_u_THM, axiom, ![V_v]: s(t_bool,h4s_bools_bounded(s(t_bool,V_v))) = s(t_bool,t)).
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_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (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_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
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_lists_MAP2u_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_10]: (![V_h1, V_h2, V_MAP2u_u_tupled, V_f, V_t1, V_t2]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))))),V_uu_10),s(TV_u_27b,V_h1))),s(TV_u_27c,V_h2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27b),V_t1))),s(t_h4s_lists_list(TV_u_27c),V_t2))) = s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_h1))),s(TV_u_27c,V_h2))))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_t1),s(t_h4s_lists_list(TV_u_27c),V_t2))))))))))) => ![V_uu_9]: (![V_h1, V_MAP2u_u_tupled, V_f, V_t1, V_h2]: s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))))),V_uu_9),s(TV_u_27b,V_h1))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27b),V_t1))),s(TV_u_27c,V_h2))) = s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))))),V_uu_10),s(TV_u_27b,V_h1))),s(TV_u_27c,V_h2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27b),V_t1))) => ![V_uu_8]: (![V_v3, V_h1, V_MAP2u_u_tupled, V_f, V_t1]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))))),V_uu_8),s(t_h4s_lists_list(TV_u_27c),V_v3))),s(TV_u_27b,V_h1))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27b),V_t1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27c),V_v3),s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))),s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))))),V_uu_9),s(TV_u_27b,V_h1))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27b),V_t1))))) => ![V_uu_7]: (![V_v3, V_MAP2u_u_tupled, V_f, V_h1]: s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))))),V_uu_7),s(t_h4s_lists_list(TV_u_27c),V_v3))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27b,V_h1))) = s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27b,t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))))),V_uu_8),s(t_h4s_lists_list(TV_u_27c),V_v3))),s(TV_u_27b,V_h1))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) => ![V_uu_6]: (![V_v2, V_MAP2u_u_tupled, V_f, V_v3]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),V_uu_6),s(t_h4s_lists_list(TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27c),V_v3))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27b),V_v2),s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))),s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27a)))))),V_uu_7),s(t_h4s_lists_list(TV_u_27c),V_v3))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))))) => ![V_uu_5]: (![V_MAP2u_u_tupled, V_f, V_v2]: s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_lists_list(TV_u_27b),V_v2))) = s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),V_uu_6),s(t_h4s_lists_list(TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) => ![V_uu_4]: (![V_MAP2u_u_tupled, V_f, V_v1]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),V_v1))) = s(t_h4s_lists_list(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),V_v1),s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))))) => ![V_uu_3]: (![V_MAP2u_u_tupled, V_f]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) => ![V_uu_2]: (![V_MAP2u_u_tupled, V_a]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),V_a))) = s(t_h4s_lists_list(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),V_a),s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),t_h4s_lists_list(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))))) => ![V_uu_1]: (![V_MAP2u_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),V_MAP2u_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_bool)),V_R)))) & ![V_h2, V_h1, V_t2, V_t1, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_t1),s(t_h4s_lists_list(TV_u_27c),V_t2))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_h1))),s(t_h4s_lists_list(TV_u_27b),V_t1))),s(t_h4s_lists_list(TV_u_27c),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27c)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27c))),h4s_lists_cons),s(TV_u_27c,V_h2))),s(t_h4s_lists_list(TV_u_27c),V_t2)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),h4s_lists_map2u_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a))),V_uu_1))))))))))))))).
fof(ah4s_lists_MAP2u_u_curriedu_u_def, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_x2, V_x1, V_x]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_map2(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_x),s(t_h4s_lists_list(TV_u_27b),V_x1),s(t_h4s_lists_list(TV_u_27c),V_x2))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),t_h4s_lists_list(TV_u_27a)),h4s_lists_map2u_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),h4s_pairs_u_2c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_x),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_x1),s(t_h4s_lists_list(TV_u_27c),V_x2)))))))).
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_lists_listu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),V_a1)))))))).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
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_ltu_c0, 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_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ch4s_polys_POLYu_u_ADDu_u_CLAUSESu_c1, conjecture, ![V_p1]: s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_polys_polyu_u_add(s(t_h4s_lists_list(t_h4s_realaxs_real),V_p1),s(t_h4s_lists_list(t_h4s_realaxs_real),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_realaxs_real),V_p1)).
